UNITS(1) General Commands Manual UNITS(1)
NAME
units — unit conversion and calculation program
SYNOPSIS
[options] [from-unit [to-unit]]
DESCRIPTION
The units program converts quantities expressed in various systems of
measurement to their equivalents in other systems of measurement. Like
many similar programs, it can handle multiplicative scale changes. It
can also handle nonlinear conversions such as Fahrenheit to Celsius;
see Temperature Conversions. The program can also perform conversions
from and to sums of units, such as converting between meters and feet
plus inches.
But Fahrenheit to Celsius is linear, you insist. Not so. A transfor-
mation T is linear if T(x + y) = T(x) + T(y) and this fails for
T(x) = ax + b. This transformation is affine, but not linear—see
https://en.wikipedia.org/wiki/Linear_map.
Basic operation is simple: you enter the units that you want to convert
from and the units that you want to convert to. You can use the pro-
gram interactively with prompts, or you can use it from the command
line.
Beyond simple unit conversions, units can be used as a general-purpose
scientific calculator that keeps track of units in its calculations.
You can form arbitrary complex mathematical expressions of dimensions
including sums, products, quotients, powers, and even roots of dimen-
sions. Thus you can ensure accuracy and dimensional consistency when
working with long expressions that involve many different units that
may combine in complex ways; for an illustration, see Complicated Unit
Expressions.
The units are defined in an external data file. You can use the exten-
sive data file that comes with this program, or you can provide your
own data file to suit your needs. You can also use your own data file
to supplement the standard data file.
You can change the default behavior of units with various options given
on the command line. See Invoking Units for a description of the avail-
able options.
INTERACTING WITH UNITS
To invoke units for interactive use, type units at your shell prompt.
The program will print something like this:
Currency exchange rates from www.timegenie.com on 2014-03-05
2860 units, 109 prefixes, 85 nonlinear units
You have:
At the ‘You have:’ prompt, type the quantity and units that you are
converting from. For example, if you want to convert ten meters to
feet, type 10 meters. Next, units will print ‘You want:’. You should
type the units you want to convert to. To convert to feet, you would
type feet. If the readline library was compiled in, then tab will com-
plete unit names. See Readline Support for more information about
readline. To quit the program type quit or exit at either prompt.
The result will be displayed in two ways. The first line of output,
which is marked with a ‘*’ to indicate multiplication, gives the result
of the conversion you have asked for. The second line of output, which
is marked with a ‘/’ to indicate division, gives the inverse of the
conversion factor. If you convert 10 meters to feet, units will print
* 32.808399
/ 0.03048
which tells you that 10 meters equals about 32.8 feet. The second num-
ber gives the conversion in the opposite direction. In this case, it
tells you that 1 foot is equal to about 0.03 dekameters since the
dekameter is 10 meters. It also tells you that 1/32.8 is about 0.03.
The units program prints the inverse because sometimes it is a more
convenient number. In the example above, for example, the inverse
value is an exact conversion: a foot is exactly 0.03048 dekameters.
But the number given the other direction is inexact.
If you convert grains to pounds, you will see the following:
You have: grains
You want: pounds
* 0.00014285714
/ 7000
From the second line of the output you can immediately see that a
grain is equal to a seven thousandth of a pound. This is not so obvi-
ous from the first line of the output. If you find the output format
confusing, try using the ‘--verbose’ option:
You have: grain
You want: aeginamina
grain = 0.00010416667 aeginamina
grain = (1 / 9600) aeginamina
If you request a conversion between units that measure reciprocal di-
mensions, then units will display the conversion results with an extra
note indicating that reciprocal conversion has been done:
You have: 6 ohms
You want: siemens
reciprocal conversion
* 0.16666667
/ 6
Reciprocal conversion can be suppressed by using the ‘--strict’ option.
As usual, use the ‘--verbose’ option to get more comprehensible output:
You have: tex
You want: typp
reciprocal conversion
1 / tex = 496.05465 typp
1 / tex = (1 / 0.0020159069) typp
You have: 20 mph
You want: sec/mile
reciprocal conversion
1 / 20 mph = 180 sec/mile
1 / 20 mph = (1 / 0.0055555556) sec/mile
If you enter incompatible unit types, the units program will print a
message indicating that the units are not conformable and it will dis-
play the reduced form for each unit:
You have: ergs/hour
You want: fathoms kg^2 / day
conformability error
2.7777778e-11 kg m^2 / sec^3
2.1166667e-05 kg^2 m / sec
If you only want to find the reduced form or definition of a unit, sim-
ply press Enter at the ‘You want:’ prompt. Here is an example:
You have: jansky
You want:
Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2
The output from units indicates that the jansky is defined to be equal
to a fluxunit which in turn is defined to be a certain combination of
watts, meters, and hertz. The fully reduced (and in this case somewhat
more cryptic) form appears on the far right.
Some named units are treated as dimensionless in some situations.
These units include the radian and steradian. These units will be
treated as equal to 1 in units conversions. Power is equal to torque
times angular velocity. This conversion can only be performed if the
radian is dimensionless.
You have: (14 ft lbf) (12 radians/sec)
You want: watts
* 227.77742
/ 0.0043902509
It is also possible to compute roots and other non-integer powers of
dimensionless units; this allows computations such as the altitude of
geosynchronous orbit:
You have: cuberoot(G earthmass / (circle/siderealday)^2) - earthradius
You want: miles
* 22243.267
/ 4.4957425e-05
Named dimensionless units are not treated as dimensionless in other
contexts. They cannot be used as exponents so for example,
‘meter^radian’ is forbidden.
If you want a list of options you can type ? at the ‘You want:’ prompt.
The program will display a list of named units that are conformable
with the unit that you entered at the ‘You have:’ prompt above. Con-
formable unit combinations will not appear on this list.
Typing help at either prompt displays a short help message. You can
also type help followed by a unit name. This will invoke a pager on
the units data base at the point where that unit is defined. You can
read the definition and comments that may give more details or histori-
cal information about the unit. (You can generally quit out of the
page by pressing ‘q’.)
Typing search text will display a list of all of the units whose names
contain text as a substring along with their definitions. This may
help in the case where you aren't sure of the right unit name.
USING UNITS NON-INTERACTIVELY
The units program can perform units conversions non-interactively from
the command line. To do this, type the command, type the original unit
expression, and type the new units you want. If a units expression
contains non-alphanumeric characters, you may need to protect it from
interpretation by the shell using single or double quote characters.
If you type
units "2 liters" quarts
then units will print
* 2.1133764
/ 0.47317647
and then exit. The output tells you that 2 liters is about 2.1 quarts,
or alternatively that a quart is about 0.47 times 2 liters.
units does not require a space between a numerical value and the unit,
so the previous example can be given as
units 2liters quarts
to avoid having to quote the first argument.
If the conversion is successful, units will return success (zero) to
the calling environment. If you enter non-conformable units, then
units will print a message giving the reduced form of each unit and it
will return failure (nonzero) to the calling environment.
If the ‘--conformable’ option is given, only one unit expression is al-
lowed, and units will print all units conformable with that expression;
it is equivalent to giving ? at the ‘You want:’ prompt. For example,
units --conformable gauss
B_FIELD tesla
Gs gauss
T tesla
gauss abvolt sec / cm^2
stT stattesla
statT stattesla
stattesla statWb/cm^2
tesla Wb/m^2
If you give more than one unit expression with the ‘--conformable’ op-
tion, the program will exit with an error message and return failure.
This option has no effect in interactive mode.
If the ‘--terse’ (‘-t’) option is given with the ‘--conformable’ op-
tion, conformable units are shown without definitions; with the previ-
ous example, this would give
units --terse --conformable gauss
B_FIELD
Gs
T
gauss
stT
statT
stattesla
tesla
When the ‘--conformable’ option is not given and you invoke units with
only one argument, units will print the definition of the specified
unit. It will return failure if the unit is not defined and success if
the unit is defined.
UNIT DEFINITIONS
The conversion information is read from a units data file that is
called ‘definitions.units’ and is usually located in the
‘/usr/share/units’ directory. If you invoke units with the ‘-V’ op-
tion, it will print the location of this file. The default file in-
cludes definitions for all familiar units, abbreviations and metric
prefixes. It also includes many obscure or archaic units. Many common
spelled-out numbers (e.g., ‘seventeen’) are recognized.
Many constants of nature are defined, including these:
pi ratio of circumference to diameter
c speed of light
e charge on an electron
force acceleration of gravity
mole Avogadro's number
water pressure per unit height of water
Hg pressure per unit height of mercury
au astronomical unit
k Boltzman's constant
mu0 permeability of vacuum
epsilon0 permittivity of vacuum
G Gravitational constant
mach speed of sound
The standard data file includes atomic masses for all of the elements
and numerous other constants. Also included are the densities of vari-
ous ingredients used in baking so that ‘2 cups flour_sifted’ can be
converted to ‘grams’. This is not an exhaustive list. Consult the
units data file to see the complete list, or to see the definitions
that are used.
The ‘pound’ is a unit of mass. To get force, multiply by the force
conversion unit ‘force’ or use the shorthand ‘lbf’. (Note that ‘g’ is
already taken as the standard abbreviation for the gram.) The unit
‘ounce’ is also a unit of mass. The fluid ounce is ‘fluidounce’ or
‘floz’. When British capacity units differ from their US counterparts,
such as the British Imperial gallon, the unit is defined both ways with
‘br’ and ‘us’ prefixes. Your locale settings will determine the value
of the unprefixed unit. Currency is prefixed with its country name:
‘belgiumfranc’, ‘britainpound’.
When searching for a unit, if the specified string does not appear ex-
actly as a unit name, then the units program will try to remove a
trailing ‘s’, ‘es’. Next units will replace a trailing ‘ies’ with ‘y’.
If that fails, units will check for a prefix. The database includes
all of the standard metric prefixes. Only one prefix is permitted per
unit, so ‘micromicrofarad’ will fail. However, prefixes can appear
alone with no unit following them, so ‘micro*microfarad’ will work, as
will ‘micro microfarad’.
To find out which units and prefixes are available, read the standard
units data file, which is extensively annotated.
English Customary Units
English customary units differ in various ways in different regions.
In Britain a complex system of volume measurements featured different
gallons for different materials such as a wine gallon and ale gallon
that different by twenty percent. This complexity was swept away in
1824 by a reform that created an entirely new gallon, the British Impe-
rial gallon defined as the volume occupied by ten pounds of water.
Meanwhile in the USA the gallon is derived from the 1707 Winchester
wine gallon, which is 231 cubic inches. These gallons differ by about
twenty percent. By default if units runs in the ‘en_GB’ locale you
will get the British volume measures. If it runs in the ‘en_US’ locale
you will get the US volume measures. In other locales the default val-
ues are the US definitions. If you wish to force different defini-
tions, then set the environment variable UNITS_ENGLISH to either ‘US’
or ‘GB’ to set the desired definitions independent of the locale.
Before 1959, the value of a yard (and other units of measure defined in
terms of it) differed slightly among English-speaking countries. In
1959, Australia, Canada, New Zealand, the United Kingdom, the United
States, and South Africa adopted the Canadian value of 1 yard =
0.9144 m (exactly), which was approximately halfway between the values
used by the UK and the US; it had the additional advantage of making
1 inch = 2.54 cm (exactly). This new standard was termed the Interna-
tional Yard. Australia, Canada, and the UK then defined all customary
lengths in terms of the International Yard (Australia did not define
the furlong or rod); because many US land surveys were in terms of the
pre-1959 units, the US continued to define customary surveyors' units
(furlong, chain, rod, and link) in terms of the previous value for the
foot, which was termed the US survey foot. The US defined a US survey
mile as 5280 US survey feet, and defined a statute mile as a US survey
mile. The US values for these units differ from the international val-
ues by about 2 ppm.
The units program uses the international values for these units; the US
values can be obtained by using either the ‘US’ or the ‘survey’ prefix.
In either case, the simple familiar relationships among the units are
maintained, e.g., 1 ‘furlong’ = 660 ‘ft’, and 1 ‘USfurlong’ = 660
‘USft’, though the metric equivalents differ slightly between the two
cases. The ‘US’ prefix or the ‘survey’ prefix can also be used to ob-
tain the US survey mile and the value of the US yard prior to 1959,
e.g., ‘USmile’ or ‘surveymile’ (but not ‘USsurveymile’). To get the US
value of the statute mile, use either ‘USstatutemile’ or ‘USmile’.
Except for distances that extend over hundreds of miles (such as in the
US State Plane Coordinate System), the differences in the miles are
usually insignificant:
You have: 100 surveymile - 100 mile
You want: inch
* 12.672025
/ 0.078913984
The pre-1959 UK values for these units can be obtained with the prefix
‘UK’.
In the US, the acre is officially defined in terms of the US survey
foot, but units uses a definition based on the international foot. If
you want the official US acre use ‘USacre’ and similarly use
‘USacrefoot’ for the official US version of that unit. The difference
between these units is about 4 parts per million.
UNIT EXPRESSIONS
Operators
You can enter more complicated units by combining units with operations
such as multiplication, division, powers, addition, subtraction, and
parentheses for grouping. You can use the customary symbols for these
operators when units is invoked with its default options. Addition-
ally, units supports some extensions, including high priority multipli-
cation using a space, and a high priority numerical division operator
(‘|’) that can simplify some expressions.
You multiply units using a space or an asterisk (‘*’). The next exam-
ple shows both forms:
You have: arabicfoot * arabictradepound * force
You want: ft lbf
* 0.7296
/ 1.370614
You can divide units using the slash (‘/’) or with ‘per’:
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
You can use parentheses for grouping:
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
White space surrounding operators is optional, so the previous example
could have used ‘(1/2)kg/(kg/meter)’. As a consequence, however, hy-
phenated spelled-out numbers (e.g., ‘forty-two’) cannot be used;
‘forty-two’ is interpreted as ‘40 - 2’.
Multiplication using a space has a higher precedence than division us-
ing a slash and is evaluated left to right; in effect, the first ‘/’
character marks the beginning of the denominator of a unit expression.
This makes it simple to enter a quotient with several terms in the de-
nominator: ‘J / mol K’. The ‘*’ and ‘/’ operators have the same prece-
dence, and are evaluated left to right; if you multiply with ‘*’, you
must group the terms in the denominator with parentheses:
‘J / (mol * K)’.
The higher precedence of the space operator may not always be advanta-
geous. For example, ‘m/s s/day’ is equivalent to ‘m / s s day’ and has
dimensions of length per time cubed. Similarly, ‘1/2 meter’ refers to
a unit of reciprocal length equivalent to 0.5/meter, perhaps not what
you would intend if you entered that expression. The get a half meter
you would need to use parentheses: ‘(1/2) meter’. The ‘*’ operator is
convenient for multiplying a sequence of quotients. For example,
‘m/s * s/day’ is equivalent to ‘m/day’. Similarly, you could write
‘1/2 * meter’ to get half a meter.
The units program supports another option for numerical fractions: you
can indicate division of numbers with the vertical bar (‘|’), so if you
wanted half a meter you could write ‘1|2 meter’. You cannot use the
vertical bar to indicate division of non-numerical units (e.g., ‘m|s’
results in an error message).
Powers of units can be specified using the ‘^’ character, as shown in
the following example, or by simple concatenation of a unit and its ex-
ponent: ‘cm3’ is equivalent to ‘cm^3’; if the exponent is more than one
digit, the ‘^’ is required. You can also use ‘**’ as an exponent oper-
ator.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
Concatenation only works with a single unit name: if you write
‘(m/s)2’, units will treat it as multiplication by 2. When a unit in-
cludes a prefix, exponent operators apply to the combination, so
‘centimeter3’ gives cubic centimeters. If you separate the prefix from
the unit with any multiplication operator (e.g., ‘centi meter^3’), the
prefix is treated as a separate unit, so the exponent applies only to
the unit without the prefix. The second example is equivalent to
‘centi * (meter^3)’, and gives a hundredth of a cubic meter, not a cu-
bic centimeter. The units program is limited internally to products of
99 units; accordingly, expressions like ‘meter^100’ or ‘joule^34’ (rep-
resented internally as ‘kg^34 m^68 / s^68’) will fail.
The ‘|’ operator has the highest precedence, so you can write the
square root of two thirds as ‘2|3^1|2’. The ‘^’ operator has the sec-
ond highest precedence, and is evaluated right to left, as usual:
You have: 5 * 2^3^2
You want:
Definition: 2560
With a dimensionless base unit, any dimensionless exponent is meaning-
ful (e.g., ‘pi^exp(2.371)’). Even though angle is sometimes treated as
dimensionless, exponents cannot have dimensions of angle:
You have: 2^radian
^
Exponent not dimensionless
If the base unit is not dimensionless, the exponent must be a rational
number p/q, and the dimension of the unit must be a power of q, so
‘gallon^2|3’ works but ‘acre^2|3’ fails. An exponent using the slash
(‘/’) operator (e.g., ‘gallon^(2/3)’) is also acceptable; the parenthe-
ses are needed because the precedence of ‘^’ is higher than that of
‘/’. Since units cannot represent dimensions with exponents greater
than 99, a fully reduced exponent must have q < 100. When raising a
non-dimensionless unit to a power, units attempts to convert a decimal
exponent to a rational number with q < 100. If this is not possible
units displays an error message:
You have: ft^1.234
Base unit not dimensionless; rational exponent required
A decimal exponent must match its rational representation to machine
precision, so ‘acre^1.5’ works but ‘gallon^0.666’ does not.
Sums and Differences of Units
You may sometimes want to add values of different units that are out-
side the SI. You may also wish to use units as a calculator that keeps
track of units. Sums of conformable units are written with the ‘+’
character, and differences with the ‘-’ character.
You have: 2 hours + 23 minutes + 32 seconds
You want: seconds
* 8612
/ 0.00011611705
You have: 12 ft + 3 in
You want: cm
* 373.38
/ 0.0026782366
You have: 2 btu + 450 ft lbf
You want: btu
* 2.5782804
/ 0.38785542
The expressions that are added or subtracted must reduce to identical
expressions in primitive units, or an error message will be displayed:
You have: 12 printerspoint - 4 heredium
^
Illegal sum of non-conformable units
If you add two values of vastly different scale you may exceed the
available precision of floating point (about 15 digits). The effect is
that the addition of the smaller value makes no change to the larger
value; in other words, the smaller value is treated as if it were zero.
You have: lightyear + cm
No warning is given, however. As usual, the precedence for ‘+’ and ‘-’
is lower than that of the other operators. A fractional quantity such
as 2 1/2 cups can be given as ‘(2+1|2) cups’; the parentheses are nec-
essary because multiplication has higher precedence than addition. If
you omit the parentheses, units attempts to add ‘2’ and ‘1|2 cups’, and
you get an error message:
You have: 2+1|2 cups
^
Illegal sum or difference of non-conformable units
The expression could also be correctly written as ‘(2+1/2) cups’. If
you write ‘2 1|2 cups’ the space is interpreted as multiplication so
the result is the same as ‘1 cup’.
The ‘+’ and ‘-’ characters sometimes appears in exponents like
‘3.43e+8’. This leads to an ambiguity in an expression like ‘3e+2 yC’.
The unit ‘e’ is a small unit of charge, so this can be regarded as
equivalent to ‘(3e+2) yC’ or ‘(3 e)+(2 yC)’. This ambiguity is re-
solved by always interpreting ‘+’ and ‘-’ as part of an exponent if
possible.
Numbers as Units
For units, numbers are just another kind of unit. They can appear as
many times as you like and in any order in a unit expression. For ex-
ample, to find the volume of a box that is 2 ft by 3 ft by 12 ft in
steres, you could do the following:
You have: 2 ft 3 ft 12 ft
You want: stere
* 2.038813
/ 0.49048148
You have: $ 5 / yard
You want: cents / inch
* 13.888889
/ 0.072
And the second example shows how the dollar sign in the units conver-
sion can precede the five. Be careful: units will interpret ‘$5’ with
no space as equivalent to ‘dollar^5’.
Built-in Functions
Several built-in functions are provided: ‘sin’, ‘cos’, ‘tan’, ‘asin’,
‘acos’, ‘atan’, ‘sinh’, ‘cosh’, ‘tanh’, ‘asinh’, ‘acosh’, ‘atanh’,
‘exp’, ‘ln’, ‘log’, ‘abs’, ‘round’, ‘floor’, ‘ceil’, ‘factorial’,
‘Gamma’, ‘lnGamma’, ‘erf’, and ‘erfc’; the function ‘lnGamma’ is the
natural logarithm of the ‘Gamma’ function.
The ‘sin’, ‘cos’, and ‘tan’ functions require either a dimensionless
argument or an argument with dimensions of angle.
You have: sin(30 degrees)
You want:
Definition: 0.5
You have: sin(pi/2)
You want:
Definition: 1
You have: sin(3 kg)
^
Unit not dimensionless
The other functions on the list require dimensionless arguments. The
inverse trigonometric functions return arguments with dimensions of an-
gle.
The ‘ln’ and ‘log’ functions give natural log and log base 10 respec-
tively. To obtain logs for any integer base, enter the desired base
immediately after ‘log’. For example, to get log base 2 you would
write ‘log2’ and to get log base 47 you could write ‘log47’.
You have: log2(32)
You want:
Definition: 5
You have: log3(32)
You want:
Definition: 3.1546488
You have: log4(32)
You want:
Definition: 2.5
You have: log32(32)
You want:
Definition: 1
You have: log(32)
You want:
Definition: 1.50515
You have: log10(32)
You want:
Definition: 1.50515
If you wish to take roots of units, you may use the ‘sqrt’ or
‘cuberoot’ functions. These functions require that the argument have
the appropriate root. You can obtain higher roots by using fractional
exponents:
You have: sqrt(acre)
You want: feet
* 208.71074
/ 0.0047913202
You have: (400 W/m^2 / stefanboltzmann)^(1/4)
You have:
Definition: 289.80882 K
You have: cuberoot(hectare)
^
Unit not a root
Previous Result
You can insert the result of the previous conversion using the under-
score (‘_’). It is useful when you want to convert the same input to
several different units, for example
You have: 2.3 tonrefrigeration
You want: btu/hr
* 27600
/ 3.6231884e-005
You have: _
You want: kW
* 8.0887615
/ 0.12362832
Suppose you want to do some deep frying that requires an oil depth of
2 inches. You have 1/2 gallon of oil, and want to know the largest-di-
ameter pan that will maintain the required depth. The nonlinear unit
‘circlearea’ gives the radius of the circle (see Other Nonlinear Units,
for a more detailed description) in SI units; you want the diameter in
inches:
You have: 1|2 gallon / 2 in
You want: circlearea
0.10890173 m
You have: 2 _
You want: in
* 8.5749393
/ 0.1166189
In most cases, surrounding white space is optional, so the previous ex-
ample could have used ‘2_’. If ‘_’ follows a non-numerical unit sym-
bol, however, the space is required:
You have: m_
^
Parse error
When ‘_’ is followed by a digit, the operation is multiplication rather
than exponentiation, so that ‘_2’, is equivalent to ‘_ * 2’ rather than
‘_^2’.
You can use the ‘_’ symbol any number of times; for example,
You have: m
You want:
Definition: 1 m
You have: _ _
You want:
Definition: 1 m^2
Using ‘_’ before a conversion has been performed (e.g., immediately af-
ter invocation) generates an error:
You have: _
^
No previous result; '_' not set
Accordingly, ‘_’ serves no purpose when units is invoked non-interac-
tively.
If units is invoked with the ‘--verbose’ option (see Invoking Units),
the value of ‘_’ is not expanded:
You have: mile
You want: ft
mile = 5280 ft
mile = (1 / 0.00018939394) ft
You have: _
You want: m
_ = 1609.344 m
_ = (1 / 0.00062137119) m
You can give ‘_’ at the ‘You want:’ prompt, but it usually is not very
useful.
Complicated Unit Expressions
The units program is especially helpful in ensuring accuracy and dimen-
sional consistency when converting lengthy unit expressions. For exam-
ple, one form of the Darcy-Weisbach fluid-flow equation is
Delta P = (8 / pi)^2 (rho fLQ^2) / d^5,
where Delta P is the pressure drop, rho is the mass density, f is the
(dimensionless) friction factor, L is the length of the pipe, Q is the
volumetric flow rate, and d is the pipe diameter. It might be desired
to have the equation in the form
Delta P = A1 rho fLQ^2 / d^5
that accepted the user’s normal units; for typical units used in the
US, the required conversion could be something like
You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5)
You want: psi
* 43.533969
/ 0.022970568
The parentheses allow individual terms in the expression to be entered
naturally, as they might be read from the formula. Alternatively, the
multiplication could be done with the ‘*’ rather than a space; then
parentheses are needed only around ‘ft^3/s’ because of its exponent:
You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5
You want: psi
* 43.533969
/ 0.022970568
Without parentheses, and using spaces for multiplication, the previous
conversion would need to be entered as
You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5
You want: psi
* 43.533969
/ 0.022970568
Backwards Compatibility: ‘*’ and ‘-’
The original units assigned multiplication a higher precedence than di-
vision using the slash. This differs from the usual precedence rules,
which give multiplication and division equal precedence, and can be
confusing for people who think of units as a calculator.
The star operator (‘*’) included in this units program has, by default,
the same precedence as division, and hence follows the usual precedence
rules. For backwards compatibility you can invoke units with the
‘--oldstar’ option. Then ‘*’ has a higher precedence than division,
and the same precedence as multiplication using the space.
Historically, the hyphen (‘-’) has been used in technical publications
to indicate products of units, and the original units program treated
it as a multiplication operator. Because units provides several other
ways to obtain unit products, and because ‘-’ is a subtraction operator
in general algebraic expressions, units treats the binary ‘-’ as a sub-
traction operator by default. For backwards compatibility use the
‘--product’ option, which causes units to treat the binary ‘-’ operator
as a product operator. When ‘-’ is a multiplication operator it has
the same precedence as multiplication with a space, giving it a higher
precedence than division.
When ‘-’ is used as a unary operator it negates its operand. Regard-
less of the units options, if ‘-’ appears after ‘(’ or after ‘+’, then
it will act as a negation operator. So you can always compute 20 de-
grees minus 12 minutes by entering ‘20 degrees + -12 arcmin’. You must
use this construction when you define new units because you cannot know
what options will be in force when your definition is processed.
NONLINEAR UNIT CONVERSIONS
Nonlinear units are represented using functional notation. They make
possible nonlinear unit conversions such as temperature.
Temperature Conversions
Conversions between temperatures are different from linear conversions
between temperature increments—see the example below. The absolute
temperature conversions are handled by units starting with ‘temp’, and
you must use functional notation. The temperature-increment conver-
sions are done using units starting with ‘deg’ and they do not require
functional notation.
You have: tempF(45)
You want: tempC
7.2222222
You have: 45 degF
You want: degC
* 25
/ 0.04
Think of ‘tempF(x)’ not as a function but as a notation that indicates
that x should have units of ‘tempF’ attached to it. See Defining Non-
linear Units. The first conversion shows that if it’s 45 degrees
Fahrenheit outside, it’s 7.2 degrees Celsius. The second conversion
indicates that a change of 45 degrees Fahrenheit corresponds to a
change of 25 degrees Celsius. The conversion from ‘tempF(x)’ is to ab-
solute temperature, so that
You have: tempF(45)
You want: degR
* 504.67
/ 0.0019814929
gives the same result as
You have: tempF(45)
You want: tempR
* 504.67
/ 0.0019814929
But if you convert ‘tempF(x)’ to ‘degC’, the output is probably not
what you expect:
You have: tempF(45)
You want: degC
* 280.37222
/ 0.0035666871
The result is the temperature in K, because ‘degC’ is defined as ‘K’,
the Kelvin. For consistent results, use the ‘tempX’ units when convert-
ing to a temperature rather than converting a temperature increment.
The ‘tempC()’ and ‘tempF()’ definitions are limited to positive abso-
lute temperatures, and giving a value that would result in a negative
absolute temperature generates an error message:
You have: tempC(-275)
^
Argument of function outside domain
Other Nonlinear Units
Some other examples of nonlinear units are numerous different ring
sizes and wire gauges, the grit sizes used for abrasives, the decibel
scale, shoe size, scales for the density of sugar (e.g., baume). The
standard data file also supplies units for computing the area of a cir-
cle and the volume of a sphere. See the standard units data file for
more details. Wire gauges with multiple zeroes are signified using
negative numbers where two zeroes is ‘-1’. Alternatively, you can use
the synonyms ‘g00’, ‘g000’, and so on that are defined in the standard
units data file.
You have: wiregauge(11)
You want: inches
* 0.090742002
/ 11.020255
You have: brwiregauge(g00)
You want: inches
* 0.348
/ 2.8735632
You have: 1 mm
You want: wiregauge
18.201919
You have: grit_P(600)
You want: grit_ansicoated
342.76923
The last example shows the conversion from P graded sand paper, which
is the European standard and may be marked “P600” on the back, to the
USA standard.
You can compute the area of a circle using the nonlinear unit,
‘circlearea’. You can also do this using the circularinch or cir-
cleinch. The next example shows two ways to compute the area of a cir-
cle with a five inch radius and one way to compute the volume of a
sphere with a radius of one meter.
You have: circlearea(5 in)
You want: in2
* 78.539816
/ 0.012732395
You have: 10^2 circleinch
You want: in2
* 78.539816
/ 0.012732395
You have: spherevol(meter)
You want: ft3
* 147.92573
/ 0.0067601492
The inverse of a nonlinear conversion is indicated by prefixing a tilde
(‘~’) to the nonlinear unit name:
You have: ~wiregauge(0.090742002 inches)
You want:
Definition: 11
You can give a nonlinear unit definition without an argument or paren-
theses, and press Enter at the ‘You want:’ prompt to get the definition
of a nonlinear unit; if the definition is not valid for all real num-
bers, the range of validity is also given. If the definition requires
specific units this information is also displayed:
You have: tempC
Definition: tempC(x) = x K + stdtemp
defined for x >= -273.15
You have: ~tempC
Definition: ~tempC(tempC) = (tempC +(-stdtemp))/K
defined for tempC >= 0 K
You have: circlearea
Definition: circlearea(r) = pi r^2
r has units m
To see the definition of the inverse use the ‘~’ notation. In this
case the parameter in the functional definition will usually be the
name of the unit. Note that the inverse for ‘tempC’ shows that it re-
quires units of ‘K’ in the specification of the allowed range of val-
ues. Nonlinear unit conversions are described in more detail in Defin-
ing Nonlinear Units.
UNIT LISTS: CONVERSION TO SUMS OF UNITS
Outside of the SI, it is sometimes desirable to convert a single unit
to a sum of units—for example, feet to feet plus inches. The conver-
sion from sums of units was described in Sums and Differences of Units,
and is a simple matter of adding the units with the ‘+’ sign:
You have: 12 ft + 3 in + 3|8 in
You want: ft
* 12.28125
/ 0.081424936
Although you can similarly write a sum of units to convert to, the re-
sult will not be the conversion to the units in the sum, but rather the
conversion to the particular sum that you have entered:
You have: 12.28125 ft
You want: ft + in + 1|8 in
* 11.228571
/ 0.089058524
The unit expression given at the ‘You want:’ prompt is equivalent to
asking for conversion to multiples of ‘1 ft + 1 in + 1|8 in’, which is
1.09375 ft, so the conversion in the previous example is equivalent to
You have: 12.28125 ft
You want: 1.09375 ft
* 11.228571
/ 0.089058524
In converting to a sum of units like miles, feet and inches, you typi-
cally want the largest integral value for the first unit, followed by
the largest integral value for the next, and the remainder converted to
the last unit. You can do this conversion easily with units using a
special syntax for lists of units. You must list the desired units in
order from largest to smallest, separated by the semicolon (‘;’) char-
acter:
You have: 12.28125 ft
You want: ft;in;1|8 in
12 ft + 3 in + 3|8 in
The conversion always gives integer coefficients on the units in the
list, except possibly the last unit when the conversion is not exact:
You have: 12.28126 ft
You want: ft;in;1|8 in
12 ft + 3 in + 3.00096 * 1|8 in
The order in which you list the units is important:
You have: 3 kg
You want: oz;lb
105 oz + 0.051367866 lb
You have: 3 kg
You want: lb;oz
6 lb + 9.8218858 oz
Listing ounces before pounds produces a technically correct result, but
not a very useful one. You must list the units in descending order of
size in order to get the most useful result.
Ending a unit list with the separator ‘;’ has the same effect as re-
peating the last unit on the list, so ‘ft;in;1|8 in;’ is equivalent to
‘ft;in;1|8 in;1|8 in’. With the example above, this gives
You have: 12.28126 ft
You want: ft;in;1|8 in;
12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in
in effect separating the integer and fractional parts of the coeffi-
cient for the last unit. If you instead prefer to round the last coef-
ficient to an integer you can do this with the ‘--round’ (‘-r’) option.
With the previous example, the result is
You have: 12.28126 ft
You want: ft;in;1|8 in
12 ft + 3 in + 3|8 in (rounded down to nearest 1|8 in)
When you use the ‘-r’ option, repeating the last unit on the list has
no effect (e.g., ‘ft;in;1|8 in;1|8 in’ is equivalent to ‘ft;in;1|8
in’), and hence neither does ending a list with a ‘;’. With a single
unit and the ‘-r’ option, a terminal ‘;’ does have an effect: it causes
units to treat the single unit as a list and produce a rounded value
for the single unit. Without the extra ‘;’, the ‘-r’ option has no ef-
fect on single unit conversions. This example shows the output using
the ‘-r’ option:
You have: 12.28126 ft
You want: in
* 147.37512
/ 0.0067854058
You have: 12.28126 ft
You want: in;
147 in (rounded down to nearest in)
Each unit that appears in the list must be conformable with the first
unit on the list, and of course the listed units must also be conform-
able with the unit that you enter at the ‘You have:’ prompt.
You have: meter
You want: ft;kg
^
conformability error
ft = 0.3048 m
kg = 1 kg
You have: meter
You want: lb;oz
conformability error
1 m
0.45359237 kg
In the first case, units reports the disagreement between units appear-
ing on the list. In the second case, units reports disagreement be-
tween the unit you entered and the desired conversion. This conforma-
bility error is based on the first unit on the unit list.
Other common candidates for conversion to sums of units are angles and
time:
You have: 23.437754 deg
You want; deg;arcmin;arcsec
23 deg + 26 arcmin + 15.9144 arcsec
You have: 7.2319 hr
You want: hr;min;sec
7 hr + 13 min + 54.84 sec
Some applications for unit lists may be less obvious. Suppose that you
have a postal scale and wish to ensure that it’s accurate at 1 oz, but
have only metric calibration weights. You might try
You have: 1 oz
You want: 100 g;50 g; 20 g;10 g;5 g;2 g;1 g;
20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g
You might then place one each of the 20 g, 5 g, 2 g, and 1 g weights on
the scale and hope that it indicates close to
You have: 20 g + 5 g + 2 g + 1 g
You want: oz;
0.98767093 oz
Appending ‘;’ to ‘oz’ forces a one-line display that includes the unit;
here the integer part of the result is zero, so it is not displayed.
If a non-empty list item differs vastly in scale from the quantity from
which the list is to be converted, you may exceed the available preci-
sion of floating point (about 15 digits), in which case you will get a
warning, e.g.,
You have: lightyear
You want: mile;100 inch;10 inch;mm;micron
5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision limit)
Cooking Measure
In North America, recipes for cooking typically measure ingredients by
volume, and use units that are not always convenient multiples of each
other. Suppose that you have a recipe for 6 and you wish to make a
portion for 1. If the recipe calls for 2 1/2 cups of an ingredient,
you might wish to know the measurements in terms of measuring devices
you have available, you could use units and enter
You have: (2+1|2) cup / 6
You want: cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp
1|3 cup + 1 tbsp + 1 tsp
By default, if a unit in a list begins with fraction of the form 1|x
and its multiplier is an integer, the fraction is given as the product
of the multiplier and the numerator; for example,
You have: 12.28125 ft
You want: ft;in;1|8 in;
12 ft + 3 in + 3|8 in
In many cases, such as the example above, this is what is wanted, but
sometimes it is not. For example, a cooking recipe for 6 might call
for 5 1/4 cup of an ingredient, but you want a portion for 2, and your
1-cup measure is not available; you might try
You have: (5+1|4) cup / 3
You want: 1|2 cup;1|3 cup;1|4 cup
3|2 cup + 1|4 cup
This result might be fine for a baker who has a 1 1/2-cup measure (and
recognizes the equivalence), but it may not be as useful to someone
with more limited set of measures, who does want to do additional cal-
culations, and only wants to know “How many 1/2-cup measures to I need
to add?” After all, that’s what was actually asked. With the
‘--show-factor’ option, the factor will not be combined with a unity
numerator, so that you get
You have: (5+1|4) cup / 3
You want: 1|2 cup;1|3 cup;1|4 cup
3 * 1|2 cup + 1|4 cup
A user-specified fractional unit with a numerator other than 1 is never
overridden, however—if a unit list specifies ‘3|4 cup;1|2 cup’, a re-
sult equivalent to 1 1/2 cups will always be shown as ‘2 * 3|4 cup’
whether or not the ‘--show-factor’ option is given.
Unit List Aliases
A unit list such as
cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp
can be tedious to enter. The units program provides shorthand names
for some common combinations:
hms hours, minutes, seconds
dms angle: degrees, minutes, seconds
time years, days, hours, minutes and seconds
usvol US cooking volume: cups and smaller
ftin feet, inches and 1/8 inches
inchfine inches subdivided to 1/64 inch
Using these shorthands, or unit list aliases, you can do the following
conversions:
You have: anomalisticyear
You want: time
1 year + 25 min + 3.4653216 sec
You have: 1|6 cup
You want: usvol
2 tbsp + 2 tsp
You can define your own unit list aliases; see Defining Unit List
Aliases.
You cannot combine a unit list alias with other units: it must appear
alone at the ‘You want:’ prompt.
You can display the definition of a unit list alias by entering it at
the ‘You have:’ prompt:
You have: dms
Definition: unit list, deg;arcmin;arcsec
When you specify compact output with ‘--compact’, ‘--terse’ or ‘-t’ and
perform conversion to a unit list, units lists the conversion factors
for each unit in the list, separated by semicolons.
You have: year
You want: day;min;sec
365;348;45.974678
Unlike the case of regular output, zeros are included in this output
list:
You have: liter
You want: cup;1|2 cup;1|4 cup;tbsp
4;0;0;3.6280454
ALTERNATIVE UNIT SYSTEMS
CGS Units
The SI—an extension of the MKS (meter–kilogram–second) system—has
largely supplanted the older CGS (centimeter–gram–second) system, but
CGS units are still used in a few specialized fields, especially in
physics where they lead to a more elegant formulation of Maxwell’s
equations. Conversions between SI and CGS involving mechanical units
are straightforward, involving powers of 10 (e.g., 1 m = 100 cm). Con-
versions involving electromagnetic units are more complicated, and
units supports four different systems of CGS units: electrostatic units
(ESU), electromagnetic units (EMU), the Gaussian system and the Heavi-
side–Lorentz system. The differences between these systems arise from
different choices made for proportionality constants in electromagnetic
equations. Coulomb’s law gives electrostatic force between two charges
separated by a distance delim $$ r:
F = k_C q_1 q_2 / r^2.
Ampere’s law gives the electromagnetic force per unit length between
two current-carrying conductors separated by a distance r:
F/l = 2 k_A I_1 I_2 / r.
The two constants, k_C and k_A, are related by the square of the speed
of light: k_A = k_C / c^2.
In the SI, the constants have dimensions, and an additional base unit,
the ampere, measures electric current. The CGS systems do not define
new base units, but express charge and current as derived units in
terms of mass, length, and time. In the ESU system, the constant for
Coulomb’s law is chosen to be unity and dimensionless, which defines
the unit of charge. In the EMU system, the constant for Ampere’s law
is chosen to be unity and dimensionless, which defines a unit of cur-
rent. The Gaussian system usually uses the ESU units for charge and
current; it chooses another constant so that the units for the electric
and magnetic fields are the same. The Heaviside–Lorentz system is “ra-
tionalized” so that factors of 4{pi} do not appear in Maxwell’s equa-
tions. The SI system is similarly rationalized, but the other CGS sys-
tems are not. In the Heaviside–Lorentz (HLU) system the factor of
4{pi} appears in Coulomb’s law instead; this system differs from the
Gaussian system by factors of the square root of 4{pi}
The dimensions of electrical quantities in the various CGS systems are
different from the SI dimensions for the same units; strictly, conver-
sions between these systems and SI are not possible. But units in dif-
ferent systems relate to the same physical quantities, so there is a
correspondence between these units. The units program defines the
units so that you can convert between corresponding units in the vari-
ous systems.
The CGS definitions involve cm^(1/2) and g^(1/2), which is problematic
because units does not normally support fractional roots of base units.
The ‘--units’ (‘-u’) option allows selection of a CGS unit system and
works around this restriction by introducing base units for the square
roots of length and mass: ‘sqrt_cm’ and ‘sqrt_g’. The centimeter then
becomes ‘sqrt_cm^2’ and the gram, ‘sqrt_g^2’. This allows working from
equations using the units in the CGS system, and enforcing dimensional
conformity within that system. Recognized CGS arguments to the
‘--units’ option are ‘gauss[ian]’, ‘esu’, ‘emu’, ‘lhu’; the argument is
case insensitive. You can also give ‘si’ which just enforces the de-
fault SI mode and displays ‘(SI)’ at the ‘You have:’ prompt to empha-
size the units mode. Some other types of units are also supported as
described below. Giving an unrecognized system generates a warning,
and units uses SI units.
The changes resulting from the ‘--units’ option are actually controlled
by the UNITS_SYSTEM environment variable. If you frequently work with
one of the supported CGS units systems, you may set this environment
variable rather than giving the ‘--units’ option at each invocation.
As usual, an option given on the command line overrides the setting of
the environment variable. For example, if you would normally work with
Gaussian units but might occasionally work with SI, you could set
UNITS_SYSTEM to ‘gaussian’ and specify SI with the ‘--units’ option.
Unlike the argument to the ‘--units’ option, the value of UNITS_SYSTEM
is case sensitive, so setting a value of ‘EMU’ will have no effect
other than to give an error message and set SI units.
The CGS definitions appear as conditional settings in the standard
units data file, which you can consult for more information on how
these units are defined, or on how to define an alternate units system.
The ESU system derives the electromagnetic units from its unit of
charge, the statcoulomb, which is defined from Coulomb’s law. The
statcoulomb equals dyne^(1/2) cm, or cm^(3/2) g^(1/2) s^(−1). The unit
of current, the statampere, is statcoulomb sec, analogous to the rela-
tionship in SI. Other electrical units are then derived in a manner
similar to that for SI units; the units use the SI names prefixed by
‘stat-’, e.g., ‘statvolt’ or ‘statV’. The prefix ‘st-’ is also recog-
nized (e.g., ‘stV’).
The EMU system derives the electromagnetic units from its unit of cur-
rent, the abampere, which is defined in terms of Ampere’s law. The
abampere is equal to dyne^(1/2), or cm^(1/2) g^(1/2) s^(−1). delim off
The unit of charge, the abcoulomb, is abampere sec, again analogous to
the SI relationship. Other electrical units are then derived in a man-
ner similar to that for SI units; the units use the SI names prefixed
by ‘ab-’, e.g., ‘abvolt’ or ‘abV’. The magnetic field units include
the gauss, the oersted and the maxwell.
The Gaussian units system, which was also known as the Symmetric Sys-
tem, uses the same charge and current units as the ESU system (e.g.,
‘statC’, ‘statA’); it differs by defining the magnetic field so that it
has the same units as the electric field. The resulting magnetic field
units are the same ones used in the EMU system: the gauss, the oersted
and the maxwell.
The Heaviside–Lorentz system appears to lack named units. We define
five basic units, ‘hlu_charge’, ‘hlu_current’, ‘hlu_volt’, ‘hlu_efield’
and ‘hlu_bfield’ for conversions with this system. It is important to
remember that with all of the CGS systems, the units may look the same
but mean something different. The HLU system and Gaussian systems both
measure magnetic field using the same CGS dimensions, but the amount of
magnetic field with the same units is different in the two systems.
The CGS systems define units that measure the same thing but may have
conflicting dimensions. Furthermore, the dimensions of the electromag-
netic CGS units are never compatible with SI. But if you measure
charge in two different systems you have measured the same physical
thing, so there is a correspondence between the units in the different
systems, and units supports conversions between corresponding units.
When running with SI, units defines all of the CGS units in terms of
SI. When you select a CGS system, units defines the SI units and the
other CGS system units in terms of the system you have selected.
(Gaussian) You have: statA
You want: abA
* 3.335641e-11
/ 2.9979246e+10
(Gaussian) You have: abA
You want: sqrt(dyne)
conformability error
2.9979246e+10 sqrt_cm^3 sqrt_g / s^2
1 sqrt_cm sqrt_g / s
In the above example, units converts between the current units statA
and abA even though the abA, from the EMU system, has incompatible di-
mensions. This works because in Gaussian mode, the abA is defined in
terms of the statA, so it does not have the correct definition for EMU;
consequently, you cannot convert the abA to its EMU definition.
One challenge of conversion is that because the CGS system has fewer
base units, quantities that have different dimensions in SI may have
the same dimension in a CGS system. And yet, they may not have the
same conversion factor. For example, the unit for the E field and B
fields are the same in the Gaussian system, but the conversion factors
to SI are quite different. This means that correct conversion is only
possible if you keep track of what quantity is being measured. You
cannot convert statV/cm to SI without indicating which type of field
the unit measures. To aid in dimensional analysis, units defines vari-
ous dimension units such as LENGTH, TIME, and CHARGE to be the appro-
priate dimension in SI. The electromagnetic dimensions such as B_FIELD
or E_FIELD may be useful aids both for conversion and dimensional
analysis in CGS. You can convert them to or from CGS in order to per-
form SI conversions that in some cases will not work directly due to
dimensional incompatibilities. This example shows how the Gaussian
system uses the same units for all of the fields, but they all have
different conversion factors with SI.
(Gaussian) You have: statV/cm
You want: E_FIELD
* 29979.246
/ 3.335641e-05
(Gaussian) You have: statV/cm
You want: B_FIELD
* 0.0001
/ 10000
(Gaussian) You have: statV/cm
You want: H_FIELD
* 79.577472
/ 0.012566371
(Gaussian) You have: statV/cm
You want: D_FIELD
* 2.6544187e-07
/ 3767303.1
The next example shows that the oersted cannot be converted directly to
the SI unit of magnetic field, A/m, because the dimensions conflict.
We cannot redefine the ampere to make this work because then it would
not convert with the statampere. But you can still do this conversion
as shown below.
(Gaussian) You have: oersted
You want: A/m
conformability error
1 sqrt_g / s sqrt_cm
29979246 sqrt_cm sqrt_g / s^2
(Gaussian) You have: oersted
You want: H_FIELD
* 79.577472
/ 0.012566371
Natural Units
Like the CGS units, “natural” units are an alternative to the SI system
used primarily physicists in different fields, with different systems
tailored to different fields of study. These systems are “natural” be-
cause the base measurements are defined using physical constants in-
stead of arbitrary values such as the meter or second. In different
branches of physics, different physical constants are more fundamental,
which has given rise to a variety of incompatible natural unit systems.
The supported systems are the “natural” units (which seem to have no
better name) used in high energy physics and cosmology, the Planck
units, often used my scientists working with gravity, and the Hartree
atomic units are favored by those working in physical chemistry and
condensed matter physics.
You can select the various natural units using the ‘--units’ option in
the same way that you select the CGS units. The “natural” units come
in two types, a rationalized system derived from the Heaviside–Lorentz
units and an unrationalized system derived from the Gaussian system.
You can select these using ‘natural’ and ‘natural-gauss’ respectively.
For conversions in SI mode, several unit names starting with ‘natural’
are available. This “natural” system is defined by setting {hbar}, c
and the Boltzman constant to 1. Only a single base unit remains: the
electron volt.
The Planck units exist in a variety of forms, and units supports two.
Both supported forms are rationalized, in that factors of 4{pi} do not
appear in Maxwell’s equations. However, Planck units can also differ
based on how the gravitational constant is treated. This system is
similar to the natural units in that c, {hbar}, and Boltzman’s constant
are set to 1, but in this system, Newton’s gravitational constant, G is
also fixed. In the “reduced” Planck system, delim $$ 8{pi}G = 1
whereas in the unreduced system G = 1. The reduced system eliminates
factors of 8{pi} delim off from the Einstein field equations for gravi-
tation, so this is similar to the process of forming rationalized units
to simplify Maxwell’s equations. To obtain the unreduced system use
the name ‘planck’ and for the reduced Planck units, ‘planck-red’.
Units such as ‘planckenergy’ and ‘planckenergy_red’ enable you to con-
vert the unreduced and reduced Planck energy unit in SI mode between
the various systems. In Planck units, all measurements are dimension-
less.
The final natural unit system is the Hartree atomic units. Like the
Planck units, all measurements in the Hartree units are dimensionless,
but this system is defined by defined from completely different physi-
cal constants: the electron mass, Planck’s constant, the electron
charge, and the Coulomb constant are the defining physical quantities,
which are all set to unity. To invoke this system with the ‘--units’
option use the name ‘hartree’.
Prompt Prefix
If a unit system is specified with the ‘--units’ option, the selected
system’s name is prepended to the ‘You have:’ prompt as a reminder,
e.g.,
(Gaussian) You have: stC
You want:
Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s
You can suppressed the prefix by including a line
!prompt
with no argument in a site or personal units data file. The prompt can
be conditionally suppressed by including such a line within ‘!var’ ...
‘!endvar’ constructs, e.g.,
!var UNITS_SYSTEM gaussian gauss
!prompt
!endvar
This might be appropriate if you normally use Gaussian units and find
the prefix distracting but want to be reminded when you have selected a
different CGS system.
LOGGING CALCULATIONS
The ‘--log’ option allows you to save the results of calculations in a
file; this can be useful if you need a permanent record of your work.
For example, the fluid-flow conversion in Complicated Unit Expressions,
is lengthy, and if you were to use it in designing a piping system, you
might want a record of it for the project file. If the interactive
session
# Conversion factor A1 for pressure drop
# dP = A1 rho f L Q^2/d^5
You have: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units
You want: psi
* 43.533969
/ 0.022970568
were logged, the log file would contain
### Log started Fri Oct 02 15:55:35 2015
# Conversion factor A1 for pressure drop
# dP = A1 rho f L Q^2/d^5
From: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units
To: psi
* 43.533969
/ 0.022970568
The time is written to the log file when the file is opened.
The use of comments can help clarify the meaning of calculations for
the log. The log includes conformability errors between the units at
the ‘You have:’ and ‘You want:’ prompts, but not other errors, includ-
ing lack of conformability of items in sums or differences or among
items in a unit list. For example, a conversion between zenith angle
and elevation angle could involve
You have: 90 deg - (5 deg + 22 min + 9 sec)
^
Illegal sum or difference of non-conformable units
You have: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
You want: dms
84 deg + 37 arcmin + 51 arcsec
You have: _
You want: deg
* 84.630833
/ 0.011816024
You have:
The log file would contain
From: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
To: deg;arcmin;arcsec
84 deg + 37 arcmin + 51 arcsec
From: _
To: deg
* 84.630833
/ 0.011816024
The initial entry error (forgetting that minutes have dimension of
time, and that arcminutes must be used for dimensions of angle) does
not appear in the output. When converting to a unit list alias, units
expands the alias in the log file.
The ‘From:’ and ‘To:’ tags are written to the log file even if the
‘--quiet’ option is given. If the log file exists when units is in-
voked, the new results are appended to the log file. The time is writ-
ten to the log file each time the file is opened. The ‘--log’ option
is ignored when units is used non-interactively.
INVOKING UNITS
You invoke units like this:
units [options] [from-unit [to-unit]]
If the from-unit and to-unit are omitted, the program will use interac-
tive prompts to determine which conversions to perform. See Interac-
tive Use. If both from-unit and to-unit are given, units will print
the result of that single conversion and then exit. If only from-unit
appears on the command line, units will display the definition of that
unit and exit. Units specified on the command line may need to be
quoted to protect them from shell interpretation and to group them into
two arguments. Note also that the ‘--quiet’ option is enabled by de-
fault if you specify from-unit on the command line. See Command Line
Use.
The default behavior of units can be changed by various options given
on the command line. In most cases, the options may be given in either
short form (a single ‘-’ followed by a single character) or long form
(‘--’ followed by a word or hyphen-separated words). Short-form op-
tions are cryptic but require less typing; long-form options require
more typing but are more explanatory and may be more mnemonic. With
long-form options you need only enter sufficient characters to uniquely
identify the option to the program. For example, ‘--out %f’ works, but
‘--o %f’ fails because units has other long options beginning with ‘o’.
However, ‘--q’ works because ‘--quiet’ is the only long option begin-
ning with ‘q’.
Some options require arguments to specify a value (e.g., ‘-d 12’ or
‘--digits 12’). Short-form options that do not take arguments may be
concatenated (e.g., ‘-erS’ is equivalent to ‘-e -r -S’); the last op-
tion in such a list may be one that takes an argument (e.g., ‘-ed 12’).
With short-form options, the space between an option and its argument
is optional (e.g., ‘-d12’ is equivalent to ‘-d 12’). Long-form options
may not be concatenated, and the space between a long-form option and
its argument is required. Short-form and long-form options may be in-
termixed on the command line. Options may be given in any order, but
when incompatible options (e.g., ‘--output-format’ and ‘--exponential’)
are given in combination, behavior is controlled by the last option
given. For example, ‘-o%.12f -e’ gives exponential format with the de-
fault eight significant digits).
The following options are available:
-c, --check
Check that all units and prefixes defined in the units data file
reduce to primitive units. Print a list of all units that can-
not be reduced. Also display some other diagnostics about sus-
picious definitions in the units data file. Only definitions
active in the current locale are checked. You should always run
units with this option after modifying a units data file.
--check-verbose, --verbose-check
Like the ‘--check’ option, this option prints a list of units
that cannot be reduced. But to help find unit definitions that
cause endless loops, it lists the units as they are checked. If
units hangs, then the last unit to be printed has a bad defini-
tion. Only definitions active in the current locale are
checked.
-d ndigits, --digits ndigits
Set the number of significant digits in the output to the value
specified (which must be greater than zero). For example,
‘-d 12’ sets the number of significant digits to 12. With expo-
nential output units displays one digit to the left of the deci-
mal point and eleven digits to the right of the decimal point.
On most systems, the maximum number of internally meaningful
digits is 15; if you specify a greater number than your system’s
maximum, units will print a warning and set the number to the
largest meaningful value. To directly set the maximum value,
give an argument of max (e.g., ‘-d max’). Be aware, of course,
that “significant” here refers only to the display of numbers;
if results depend on physical constants not known to this preci-
sion, the physically meaningful precision may be less than that
shown. The ‘--digits’ option conflicts with the
‘--output-format’ option.
-e, --exponential
Set the numeric output format to exponential (i.e., scientific
notation), like that used in the Unix units program. The de-
fault precision is eight significant digits (seven digits to the
right of the decimal point); this can be changed with the
‘--digits’ option. The ‘--exponential’ option conflicts with
the ‘--output-format’ option.
-o format, --output-format format
This option affords complete control over the numeric output
format using the specified format. The format is a single float-
ing point numeric format for the printf() function in the C pro-
gramming language. All compilers support the format types ‘g’
and ‘G’ to specify significant digits, ‘e’ and ‘E’ for scien-
tific notation, and ‘f’ for fixed-point decimal. The ISO C99
standard introduced the ‘F’ type for fixed-point decimal and the
‘a’ and ‘A’ types for hexadecimal floating point; these types
are allowed with compilers that support them. The default for-
mat is ‘%.8g’; for greater precision, you could specify
‘-o %.15g’. See Numeric Output Format and the documentation for
printf() for more detailed descriptions of the format specifica-
tion. The ‘--output-format’ option affords the greatest control
of the output appearance, but requires at least rudimentary
knowledge of the printf() format syntax. If you don’t want to
bother with the printf() syntax, you can specify greater preci-
sion more simply with the ‘--digits’ option or select exponen-
tial format with ‘--exponential’. The ‘--output-format’ option
is incompatible with the ‘--exponential’ and ‘--digits’ options.
-f filename, --file filename
Instruct units to load the units file filename. You can specify
up to 25 units files on the command line. When you use this op-
tion, units will load only the files you list on the command
line; it will not load the standard file or your personal units
file unless you explicitly list them. If filename is the empty
string (‘-f ""’), the default units file (or that specified by
UNITSFILE) will be loaded in addition to any others specified
with ‘-f’.
-L logfile, --log logfile
Save the results of calculations in the file logfile; this can
be useful if it is important to have a record of unit conver-
sions or other calculations that are to be used extensively or
in a critical activity such as a program or design project. If
logfile exits, the new results are appended to the file. This
option is ignored when units is used non-interactively. See
Logging Calculations for a more detailed description and some
examples.
-H filename, --history filename
Instruct units to save history to filename, so that a record of
your commands is available for retrieval across different units
invocations. To prevent the history from being saved set file-
name to the empty string (‘-H ""’). This option has no effect
if readline is not available.
-h, --help
Print out a summary of the options for units.
-m, --minus
Causes ‘-’ to be interpreted as a subtraction operator. This is
the default behavior.
-p, --product
Causes ‘-’ to be interpreted as a multiplication operator when
it has two operands. It will act as a negation operator when it
has only one operand: ‘(-3)’. By default ‘-’ is treated as a
subtraction operator.
--oldstar
Causes ‘*’ to have the old-style precedence, higher than the
precedence of division so that ‘1/2*3’ will equal ‘1/6’.
--newstar
Forces ‘*’ to have the new (default) precedence that follows the
usual rules of algebra: the precedence of ‘*’ is the same as the
precedence of ‘/’, so that ‘1/2*3’ will equal ‘3/2’.
-r, --round
When converting to a combination of units given by a unit list,
round the value of the last unit in the list to the nearest in-
teger.
-S, --show-factor
When converting to a combination of units specified in a list,
always show a non-unity factor before a unit that begins with a
fraction with a unity denominator. By default, if the unit in a
list begins with fraction of the form 1|x and its multiplier is
an integer other than 1, the fraction is given as the product of
the multiplier and the numerator (e.g., ‘3|8 in’ rather than ‘3
* 1|8 in’). In some cases, this is not what is wanted; for ex-
ample, the results for a cooking recipe might show ‘3 * 1|2 cup’
as ‘3|2 cup’. With the ‘--show-factor’ option, a result equiva-
lent to 1.5 cups will display as ‘3 * 1|2 cup’ rather than
‘3|2 cup’. A user-specified fractional unit with a numerator
other than 1 is never overridden, however—if a unit list speci-
fies ‘3|4 cup;1|2 cup’, a result equivalent to 1 1/2 cups will
always be shown as ‘2 * 3|4 cup’ whether or not the
‘--show-factor’ option is given.
--conformable
In non-interactive mode, show all units conformable with the
original unit expression. Only one unit expression is allowed;
if you give more than one, units will exit with an error message
and return failure.
-v, --verbose
Give slightly more verbose output when converting units. When
combined with the ‘-c’ option this gives the same effect as
‘--check-verbose’. When combined with ‘--version’ produces a
more detailed output, equivalent to the ‘--info’ option.
-V, --version
Print the program version number, tell whether the readline li-
brary has been included, tell whether UTF-8 support has been in-
cluded; give the locale, the location of the default units data
file, and the location of the personal units data file; indicate
if the personal units data file does not exist.
When given in combination with the ‘--terse’ option, the program
prints only the version number and exits.
When given in combination with the ‘--verbose’ option, the pro-
gram, the ‘--version’ option has the same effect as the ‘--info’
option below.
-I, --info
Print the information given with the ‘--version’ option, show
the pathname of the units program, show the status of the
UNITSFILE and MYUNITSFILE environment variables, and additional
information about how units locates the related files. On sys-
tems running Microsoft Windows, the status of the UNITSLOCALE
environment variable and information about the related locale
map are also given. This option is usually of interest only to
developers and administrators, but it can sometimes be useful
for troubleshooting.
Combining the ‘--version’ and ‘--verbose’ options has the same
effect as giving ‘--info’.
-U, --unitsfile
Print the location of the default units data file and exit; if
the file cannot be found, print “Units data file not found”.
-u units-system, --units units-system
Specify a CGS units system or natural units system. The sup-
ported units systems are: gauss[ian], esu, emu, hlu, natural,
natural-gauss, hartree, planck, planck-red, and si. See Alterna-
tive Unit Systems for further information about these unit sys-
tems.
-l locale, --locale locale
Force a specified locale such as ‘en_GB’ to get British defini-
tions by default. This overrides the locale determined from
system settings or environment variables. See Locale for a de-
scription of locale format.
-n, --nolists
Disable conversion to unit lists.
-s, --strict
Suppress conversion of units to their reciprocal units. For ex-
ample, units will normally convert hertz to seconds because
these units are reciprocals of each other. The strict option
requires that units be strictly conformable to perform a conver-
sion, and will give an error if you attempt to convert hertz to
seconds.
-1, --one-line
Give only one line of output (the forward conversion); do not
print the reverse conversion. If a reciprocal conversion is
performed, then units will still print the “reciprocal conver-
sion” line.
-t, --terse
Print only a single conversion factor. This option can be used
when calling units from another program so that the output is
easy to parse. This option has the combined effect of these op-
tions: ‘--strict’ ‘--quiet’ ‘--one-line’ ‘--compact’. When
combined with ‘--version’ it produces a display showing only the
program name and version number.
--compact
Give compact output featuring only the conversion factor; the
multiplication and division signs are not shown, and there is no
leading whitespace. If you convert to a unit list, then the
output is a semicolon separated list of factors. This turns off
the ‘--verbose’ option.
-q, --quiet, --silent
Suppress the display of statistics about the number of units
loaded, any messages printed by the units database, and the
prompting of the user for units. This option does not affect
how units displays the results. This option is turned on by de-
fault if you invoke units with a unit expression on the command
line.
SCRIPTING WITH UNITS
Despite its numerous options, units cannot cover every conceivable
unit-conversion task. For example, suppose we have found some mysteri-
ous scale, but cannot figure out the units in which it is reporting.
We reach into our pocket, place a 3.75-gram coin on the scale, and ob-
serve the scale reading ‘0.120’. How do we quickly determine the
units? Or we might wonder if a unit has any “synonyms,” i.e., other
units with the same value.
The capabilities of units are easily extended with simple scripting.
Both questions above involve conformable units; on a system with Unix-
like utilities, conversions to conformable units could be shown accom-
plished with the following script:
#!/bin/sh
progname=`basename $0 .sh`
umsg="Usage: $progname [<number>] unit"
if [ $# -lt 1 ]
then
echo "$progname: missing quantity to convert"
echo "$umsg"
exit 1
fi
for unit in `units --conformable "$*" | cut -f 1 -d ' '`
do
echo "$*" # have -- quantity to convert
echo $unit # want -- conformable unit
done | units --terse --verbose
When units is invoked with no non-option arguments, it reads have/want
pairs, on alternating lines, from its standard input, so the task can
be accomplished with only two invocations of units. This avoids the
computational overhead of needlessly reprocessing the units database
for each conformable unit, as well as the inherent system overhead of
process invocation.
By itself, the script is not very useful. But it could be used in com-
bination with other commands to address specific tasks. For example,
running the script through a simple output filter could help solve the
scale problem above. If the script is named conformable, running
$ conformable 3.75g | grep 0.120
gives
3.75g = 0.1205653 apounce
3.75g = 0.1205653 fineounce
3.75g = 0.1205653 ozt
3.75g = 0.1205653 tradewukiyeh
3.75g = 0.1205653 troyounce
So we might conclude that the scale is calibrated in troy ounces.
We might run
$ units --verbose are
Definition: 100 m^2 = 100 m^2
and wonder if ‘are’ has any synonyms, value. To find out, we could run
$ conformable are | grep "= 1 "
are = 1 a
are = 1 are
OUTPUT STYLES
The output can be tweaked in various ways using command line options.
With no options, the output looks like this
$ units
Currency exchange rates from FloatRates (USD base) on 2019-02-20
3070 units, 109 prefixes, 109 nonlinear units
You have: 23ft
You want: m
* 7.0104
/ 0.14264521
You have: m
You want: ft;in
3 ft + 3.3700787 in
This is arguably a bit cryptic; the ‘--verbose’ option makes clear what
the output means:
$ units --verbose
Currency exchange rates from FloatRates (USD base) on 2019-02-20
3070 units, 109 prefixes, 109 nonlinear units
You have: 23 ft
You want: m
23 ft = 7.0104 m
23 ft = (1 / 0.14264521) m
You have: meter
You want: ft;in
meter = 3 ft + 3.3700787 in
The ‘--quiet’ option suppresses the clutter displayed when units
starts, as well as the prompts to the user. This option is enabled by
default when you give units on the command line.
$ units --quiet
23 ft
m
* 7.0104
/ 0.14264521
$ units 23ft m
* 7.0104
/ 0.14264521
The remaining style options allow you to display only numerical values
without the tab or the multiplication and division signs, or to display
just a single line showing the forward conversion:
$ units --compact 23ft m
7.0104
0.14264521
$ units --compact m 'ft;in'
3;3.3700787
$ units --one-line 23ft m
* 7.0104
$ units --one-line 23ft 1/m
reciprocal conversion
* 0.14264521
$ units --one-line 23ft kg
conformability error
7.0104 m
1 kg
Note that when converting to a unit list, the ‘--compact’ option dis-
plays a semicolon separated list of results. Also be aware that the
‘one-line’ option doesn't live up to its name if you execute a recipro-
cal conversion or if you get a conformability error. The former case
can be prevented using the ‘--strict’ option, which suppresses recipro-
cal conversions. Similarly you can suppress unit list conversion using
‘--nolists’. It is impossible to prevent the three line error output.
$ units --compact --nolists m 'ft;in'
Error in 'ft;in': Parse error
$ units --one-line --strict 23ft 1/m
The various style options can be combined appropriately. The ultimate
combination is the ‘--terse’ option, which combines ‘--strict’,
‘--quiet’, ‘--one-line’, and ‘--compact’ to produce the minimal output,
just a single number for regular conversions and a semicolon separated
list for conversion to unit lists. This will likely be the best choice
for programs that want to call units and then process its result.
$ units --terse 23ft m
7.0104
$ units --terse m 'ft;in'
3;3.3700787
$ units --terse 23ft 1/m
conformability error
7.0104 m
1 / m
ADDING YOUR OWN DEFINITIONS
Units Data Files
The units and prefixes that units can convert are defined in the units
data file, typically ‘/usr/share/units/definitions.units’. If you
can’t find this file, run units --version to get information on the
file locations for your installation. Although you can extend or mod-
ify this data file if you have appropriate user privileges, it’s usu-
ally better to put extensions in separate files so that the definitions
will be preserved if you update units.
You can include additional data files in the units database using the
‘!include’ command in the standard units data file. For example
!include /usr/local/share/units/local.units
might be appropriate for a site-wide supplemental data file. The loca-
tion of the ‘!include’ statement in the standard units data file is im-
portant; later definitions replace earlier ones, so any definitions in
an included file will override definitions before the ‘!include’ state-
ment in the standard units data file. With normal invocation, no warn-
ing is given about redefinitions; to ensure that you don’t have an un-
intended redefinition, run units -c after making changes to any units
data file.
If you want to add your own units in addition to or in place of stan-
dard or site-wide supplemental units data files, you can include them
in the ‘.units’ file in your home directory. If this file exists it is
read after the standard units data file, so that any definitions in
this file will replace definitions of the same units in the standard
data file or in files included from the standard data file. This file
will not be read if any units files are specified on the command line.
(Under Windows the personal units file is named ‘unitdef.units’.) Run-
ning units -V will display the location and name of your personal units
file.
The units program first tries to determine your home directory from the
HOME environment variable. On systems running Microsoft Windows, if
HOME does not exist, units attempts to find your home directory from
HOMEDRIVE, HOMEPATH and USERPROFILE. You can specify an arbitrary file
as your personal units data file with the MYUNITSFILE environment vari-
able; if this variable exists, its value is used without searching your
home directory. The default units data files are described in more de-
tail in Data Files.
Defining New Units and Prefixes
A unit is specified on a single line by giving its name and an equiva-
lence. Comments start with a ‘#’ character, which can appear anywhere
in a line. The backslash character (‘\’) acts as a continuation char-
acter if it appears as the last character on a line, making it possible
to spread definitions out over several lines if desired. A file can be
included by giving the command ‘!include’ followed by the file’s name.
The ‘!’ must be the first character on the line. The file will be
sought in the same directory as the parent file unless you give a full
path. The name of the file to be included cannot contain spaces or the
comment character ‘#’.
Unit names must not contain any of the operator characters ‘+’, ‘-’,
‘*’, ‘/’, ‘|’, ‘^’, ‘;’, ‘~’, the comment character ‘#’, or parenthe-
ses. They cannot begin or end with an underscore (‘_’), a comma (‘,’)
or a decimal point (‘.’). The figure dash (U+2012), typographical mi-
nus ('-’; U+2212), and en dash ('--’; U+2013) are converted to the op-
erator ‘-’, so none of these characters can appear in unit names.
Names cannot begin with a digit, and if a name ends in a digit other
than zero or one, the digit must be preceded by a string beginning with
an underscore, and afterwards consisting only of digits, decimal
points, or commas. For example, ‘foo_2’, ‘foo_2,1’, or ‘foo_3.14’ are
valid names but ‘foo2’ or ‘foo_a2’ are invalid. The underscore is nec-
essary because without it, units cannot determine whether ‘foo2’ is a
unit name or represents ‘foo^2’. Zero and one are exceptions because
units never interprets them as exponents.
You could define nitrous oxide as
N2O nitrogen 2 + oxygen
but would need to define nitrogen dioxide as
NO_2 nitrogen + oxygen 2
Be careful to define new units in terms of old ones so that a reduction
leads to the primitive units, which are marked with ‘!’ characters.
Dimensionless units are indicated by using the string ‘!dimensionless’
for the unit definition.
When adding new units, be sure to use the ‘-c’ option to check that the
new units reduce properly. If you create a loop in the units defini-
tions, then units will hang when invoked with the ‘-c’ option. You
will need to use the ‘--check-verbose’ option, which prints out each
unit as it is checked. The program will still hang, but the last unit
printed will be the unit that caused the infinite loop.
If you define any units that contain ‘+’ characters in their defini-
tions, carefully check them because the ‘-c’ option will not catch non-
conformable sums. Be careful with the ‘-’ operator as well. When used
as a binary operator, the ‘-’ character can perform addition or multi-
plication depending on the options used to invoke units. To ensure
consistent behavior use ‘-’ only as a unary negation operator when
writing units definitions. To multiply two units leave a space or use
the ‘*’ operator with care, recalling that it has two possible prece-
dence values and may require parentheses to ensure consistent behavior.
To compute the difference of ‘foo’ and ‘bar’ write ‘foo+(-bar)’ or even
‘foo+-bar’.
You may wish to intentionally redefine a unit. When you do this, and
use the ‘-c’ option, units displays a warning message about the redefi-
nition. You can suppress these warnings by redefining a unit using a
‘+’ at the beginning of the unit name. Do not include any white space
between the ‘+’ and the redefined unit name.
Here is an example of a short data file that defines some basic units:
m ! # The meter is a primitive unit
sec ! # The second is a primitive unit
rad !dimensionless # A dimensionless primitive unit
micro- 1e-6 # Define a prefix
minute 60 sec # A minute is 60 seconds
hour 60 min # An hour is 60 minutes
inch 72 m # Inch defined incorrectly terms of meters
ft 12 inches # The foot defined in terms of inches
mile 5280 ft # And the mile
+inch 0.0254 m # Correct redefinition, warning suppressed
A unit that ends with a ‘-’ character is a prefix. If a prefix defini-
tion contains any ‘/’ characters, be sure they are protected by paren-
theses. If you define ‘half- 1/2’, then ‘halfmeter’ would be equiva-
lent to ‘1 / (2 meter)’.
Defining Nonlinear Units
Some unit conversions of interest are nonlinear; for example, tempera-
ture conversions between the Fahrenheit and Celsius scales cannot be
done by simply multiplying by conversion factors.
When you give a linear unit definition such as ‘inch 2.54 cm’ you are
providing information that units uses to convert values in inches into
primitive units of meters. For nonlinear units, you give a functional
definition that provides the same information.
Nonlinear units are represented using a functional notation. It is
best to regard this notation not as a function call but as a way of
adding units to a number, much the same way that writing a linear unit
name after a number adds units to that number. Internally, nonlinear
units are defined by a pair of functions that convert to and from lin-
ear units in the database, so that an eventual conversion to primitive
units is possible.
Here is an example nonlinear unit definition:
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
(x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
A nonlinear unit definition comprises a unit name, a formal parameter
name, two functions, and optional specifications for units, the domain,
and the range (the domain of the inverse function). The functions tell
units how to convert to and from the new unit. To produce valid re-
sults, the arguments of these functions need to have the correct dimen-
sions and be within the domains for which the functions are defined.
The definition begins with the unit name followed immediately (with no
spaces) by a ‘(’ character. In the parentheses is the name of the for-
mal parameter. Next is an optional specification of the units required
by the functions in the definition. In the example above, the
‘units=[1;K]’ specification indicates that the ‘tempF’ function re-
quires an input argument conformable with ‘1’ (i.e., the argument is
dimensionless), and that the inverse function requires an input argu-
ment conformable with ‘K’. For normal nonlinear units definition, the
forward function will always take a dimensionless argument; in general,
the inverse function will need units that match the quantity measured
by your nonlinear unit. Specifying the units enables units to perform
error checking on function arguments, and also to assign units to do-
main and range specifications, which are described later.
Next the function definitions appear. In the example above, the
‘tempF’ function is defined by
tempF(x) = (x+(-32)) degF + stdtemp
This gives a rule for converting ‘x’ in the units ‘tempF’ to linear
units of absolute temperature, which makes it possible to convert from
tempF to other units.
To enable conversions to Fahrenheit, you must give a rule for the in-
verse conversions. The inverse will be ‘x(tempF)’ and its definition
appears after a ‘;’ character. In our example, the inverse is
x(tempF) = (tempF+(-stdtemp))/degF + 32
This inverse definition takes an absolute temperature as its argument
and converts it to the Fahrenheit temperature. The inverse can be
omitted by leaving out the ‘;’ character and the inverse definition,
but then conversions to the unit will not be possible. If the inverse
definition is omitted, the ‘--check’ option will display a warning. It
is up to you to calculate and enter the correct inverse function to ob-
tain proper conversions; the ‘--check’ option tests the inverse at one
point and prints an error if it is not valid there, but this is not a
guarantee that your inverse is correct.
With some definitions, the units may vary. For example, the definition
square(x) x^2
can have any arbitrary units, and can also take dimensionless argu-
ments. In such a case, you should not specify units. If a definition
takes a root of its arguments, the definition is valid only for units
that yield such a root. For example,
squirt(x) sqrt(x)
is valid for a dimensionless argument, and for arguments with even pow-
ers of units.
Some definitions may not be valid for all real numbers. In such cases,
units can handle errors better if you specify an appropriate domain and
range. You specify the domain and range as shown below:
baume(d) units=[1;g/cm^3] domain=[0,130.5] range=[1,10] \
(145/(145-d)) g/cm^3 ; (baume+-g/cm^3) 145 / baume
In this example the domain is specified after ‘domain=’ with the end-
points given in brackets. In accord with mathematical convention,
square brackets indicate a closed interval (one that includes its end-
points), and parentheses indicate an open interval (one that does not
include its endpoints). An interval can be open or closed on one or
both ends; an interval that is unbounded on either end is indicated by
omitting the limit on that end. For example, a quantity to which deci-
bel (dB) is applied may have any value greater than zero, so the range
is indicated by ‘(0,)’:
decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel)
If the domain or range is given, the second endpoint must be greater
than the first.
The domain and range specifications can appear independently and in any
order along with the units specification. The values for the domain
and range endpoints are attached to the units given in the units speci-
fication, and if necessary, the parameter value is adjusted for compar-
ison with the endpoints. For example, if a definition includes
‘units=[1;ft]’ and ‘range=[3,)’, the range will be taken as 3 ft to in-
finity. If the function is passed a parameter of ‘900 mm’, that value
will be adjusted to 2.9527559 ft, which is outside the specified range.
If you omit the units specification from the previous example, units
can not tell whether you intend the lower endpoint to be 3 ft or 3 mi-
crofurlongs, and can not adjust the parameter value of 900 mm for com-
parison. Without units, numerical values other than zero or plus or
minus infinity for domain or range endpoints are meaningless, and ac-
cordingly they are not allowed. If you give other values without
units, then the definition will be ignored and you will get an error
message.
Although the units, domain, and range specifications are optional, it’s
best to give them when they are applicable; doing so allows units to
perform better error checking and give more helpful error messages.
Giving the domain and range also enables the ‘--check’ option to find a
point in the domain to use for its point check of your inverse defini-
tion.
You can make synonyms for nonlinear units by providing both the forward
and inverse functions; inverse functions can be obtained using the ‘~’
operator. So to create a synonym for ‘tempF’ you could write
fahrenheit(x) units=[1;K] tempF(x); ~tempF(fahrenheit)
This is useful for creating a nonlinear unit definition that differs
slightly from an existing definition without having to repeat the orig-
inal functions. For example,
dBW(x) units=[1;W] range=[0,) dB(x) W ; ~dB(dBW/W)
If you wish a synonym to refer to an existing nonlinear unit without
modification, you can do so more simply by adding the synonym with ap-
pended parentheses as a new unit, with the existing nonlinear unit—
without parentheses—as the definition. So to create a synonym for
‘tempF’ you could write
fahrenheit() tempF
The definition must be a nonlinear unit; for example, the synonym
fahrenheit() meter
will result in an error message when units starts.
You may occasionally wish to define a function that operates on units.
This can be done using a nonlinear unit definition. For example, the
definition below provides conversion between radius and the area of a
circle. This definition requires a length as input and produces an
area as output, as indicated by the ‘units=’ specification. Specifying
the range as the nonnegative numbers can prevent cryptic error mes-
sages.
circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
Defining Piecewise Linear Units
Sometimes you may be interested in a piecewise linear unit such as many
wire gauges. Piecewise linear units can be defined by specifying con-
versions to linear units on a list of points. Conversion at other
points will be done by linear interpolation. A partial definition of
zinc gauge is
zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1
In this example, ‘zincgauge’ is the name of the piecewise linear unit.
The definition of such a unit is indicated by the embedded ‘[’ charac-
ter. After the bracket, you should indicate the units to be attached
to the numbers in the table. No spaces can appear before the ‘]’ char-
acter, so a definition like ‘foo[kg meters]’ is invalid; instead write
‘foo[kg*meters]’. The definition of the unit consists of a list of
pairs optionally separated by commas. This list defines a function for
converting from the piecewise linear unit to linear units. The first
item in each pair is the function argument; the second item is the
value of the function at that argument (in the units specified in
brackets). In this example, we define ‘zincgauge’ at five points. For
example, we set ‘zincgauge(1)’ equal to ‘0.002 in’. Definitions like
this may be more readable if written using continuation characters
as
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1
With the preceding definition, the following conversion can be per-
formed:
You have: zincgauge(10)
You want: in
* 0.02
/ 50
You have: .01 inch
You want: zincgauge
5
If you define a piecewise linear unit that is not strictly monotonic,
then the inverse will not be well defined. If the inverse is requested
for such a unit, units will return the smallest inverse.
After adding nonlinear units definitions, you should normally run
units --check to check for errors. If the ‘units’ keyword is not
given, the ‘--check’ option checks a nonlinear unit definition using a
dimensionless argument, and then checks using an arbitrary combination
of units, as well as the square and cube of that combination; a warning
is given if any of these tests fail. For example,
Warning: function 'squirt(x)' defined as 'sqrt(x)'
failed for some test inputs:
squirt(7(kg K)^1): Unit not a root
squirt(7(kg K)^3): Unit not a root
Running units --check will print a warning if a non-monotonic piecewise
linear unit is encountered. For example, the relationship between ANSI
coated abrasive designation and mean particle size is non-monotonic in
the vicinity of 800 grit:
ansicoated[micron] \
. . .
600 10.55 \
800 11.5 \
1000 9.5 \
Running units --check would give the error message
Table 'ansicoated' lacks unique inverse around entry 800
Although the inverse is not well defined in this region, it’s not re-
ally an error. Viewing such error messages can be tedious, and if
there are enough of them, they can distract from true errors. Error
checking for nonlinear unit definitions can be suppressed by giving the
‘noerror’ keyword; for the examples above, this could be done as
squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt^2
ansicoated[micron] noerror \
. . .
Use the ‘noerror’ keyword with caution. The safest approach after
adding a nonlinear unit definition is to run units --check and confirm
that there are no actual errors before adding the ‘noerror’ keyword.
Defining Unit List Aliases
Unit list aliases are treated differently from unit definitions, be-
cause they are a data entry shorthand rather than a true definition for
a new unit. A unit list alias definition begins with ‘!unitlist’ and
includes the alias and the definition; for example, the aliases in-
cluded in the standard units data file are
!unitlist hms hr;min;sec
!unitlist time year;day;hr;min;sec
!unitlist dms deg;arcmin;arcsec
!unitlist ftin ft;in;1|8 in
!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
Unit list aliases are only for unit lists, so the definition must in-
clude a ‘;’. Unit list aliases can never be combined with units or
other unit list aliases, so the definition of ‘time’ shown above could
not have been shortened to ‘year;day;hms’.
As usual, be sure to run units --check to ensure that the units listed
in unit list aliases are conformable.
NUMERIC OUTPUT FORMAT
By default, units shows results to eight significant digits. You can
change this with the ‘--exponential’, ‘--digits’, and ‘--output-format’
options. The first sets an exponential format (i.e., scientific nota-
tion) like that used in the original Unix units program, the second al-
lows you to specify a different number of significant digits, and the
last allows you to control the output appearance using the format for
the printf() function in the C programming language. If you only want
to change the number of significant digits or specify exponential for-
mat type, use the ‘--digits’ and ‘--exponential’ options. The
‘--output-format’ option affords the greatest control of the output ap-
pearance, but requires at least rudimentary knowledge of the printf()
format syntax. See Invoking Units for descriptions of these options.
Format Specification
The format specification recognized with the ‘--output-format’ option
is a subset of that for printf(). The format specification has the
form %[flags][width][.precision]type; it must begin with ‘%’, and must
end with a floating-point type specifier: ‘g’ or ‘G’ to specify the
number of significant digits, ‘e’ or ‘E’ for scientific notation, and
‘f’ for fixed-point decimal. The ISO C99 standard added the ‘F’ type
for fixed-point decimal and the ‘a’ and ‘A’ types for hexadecimal
floating point; these types are allowed with compilers that support
them. Type length modifiers (e.g., ‘L’ to indicate a long double) are
inapplicable and are not allowed.
The default format for units is ‘%.8g’; for greater precision, you
could specify ‘-o %.15g’. The ‘g’ and ‘G’ format types use exponential
format whenever the exponent would be less than -4, so the value
0.000013 displays as ‘1.3e-005’. These types also use exponential no-
tation when the exponent is greater than or equal to the precision, so
with the default format, the value 5e7 displays as ‘50000000’ and the
value 5e8 displays as ‘5e+008’. If you prefer fixed-point display, you
might specify ‘-o %.8f’; however, small numbers will display very few
significant digits, and values less than 0.5e-8 will show nothing but
zeros.
The format specification may include one or more optional flags: ‘+’,
‘ ’ (space), ‘#’, ‘-’, or ‘0’ (the digit zero). The digit-grouping
flag ‘'’ is allowed with compilers that support it. Flags are followed
by an optional value for the minimum field width, and an optional pre-
cision specification that begins with a period (e.g., ‘.6’). The field
width includes the digits, decimal point, the exponent, thousands sepa-
rators (with the digit-grouping flag), and the sign if any of these are
shown.
Flags
The ‘+’ flag causes the output to have a sign (‘+’ or ‘-’). The space
flag ‘ ’ is similar to the ‘+’ flag, except that when the value is pos-
itive, it is prefixed with a space rather than a plus sign; this flag
is ignored if the ‘+’ flag is also given. The ‘+’ or ‘ ’ flag could be
useful if conversions might include positive and negative results, and
you wanted to align the decimal points in exponential notation. The
‘#’ flag causes the output value to contain a decimal point in all
cases; by default, the output contains a decimal point only if there
are digits (which can be trailing zeros) to the right of the point.
With the ‘g’ or ‘G’ types, the ‘#’ flag also prevents the suppression
of trailing zeros. The digit-grouping flag ‘'’ shows a thousands sepa-
rator in digits to the left of the decimal point. This can be useful
when displaying large numbers in fixed-point decimal; for example, with
the format ‘%f’,
You have: mile
You want: microfurlong
* 8000000.000000
/ 0.000000
the magnitude of the first result may not be immediately obvious with-
out counting the digits to the left of the decimal point. If the thou-
sands separator is the comma (‘,’), the output with the format ‘%'f’
might be
You have: mile
You want: microfurlong
* 8,000,000.000000
/ 0.000000
making the magnitude readily apparent. Unfortunately, few compilers
support the digit-grouping flag.
With the ‘-’ flag, the output value is left aligned within the speci-
fied field width. If a field width greater than needed to show the
output value is specified, the ‘0’ (zero) flag causes the output value
to be left padded with zeros until the specified field width is
reached; for example, with the format ‘%011.6f’,
You have: troypound
You want: grain
* 5760.000000
/ 0000.000174
The ‘0’ flag has no effect if the ‘-’ (left align) flag is given.
Field Width
By default, the output value is left aligned and shown with the minimum
width necessary for the specified (or default) precision. If a field
width greater than this is specified, the value shown is right aligned,
and padded on the left with enough spaces to provide the specified
field width. A width specification is typically used with fixed-point
decimal to have columns of numbers align at the decimal point; this ar-
guably is less useful with units than with long columnar output, but it
may nonetheless assist in quickly assessing the relative magnitudes of
results. For example, with the format ‘%12.6f’,
You have: km
You want: in
* 39370.078740
/ 0.000025
You have: km
You want: rod
* 198.838782
/ 0.005029
You have: km
You want: furlong
* 4.970970
/ 0.201168
Precision
The meaning of “precision” depends on the format type. With ‘g’ or
‘G’, it specifies the number of significant digits (like the ‘--digits’
option); with ‘e’, ‘E’, ‘f’, or ‘F’, it specifies the maximum number of
digits to be shown after the decimal point.
With the ‘g’ and ‘G’ format types, trailing zeros are suppressed, so
the results may sometimes have fewer digits than the specified preci-
sion (as indicated above, the ‘#’ flag causes trailing zeros to be dis-
played).
The default precision is 6, so ‘%g’ is equivalent to ‘%.6g’, and would
show the output to six significant digits. Similarly, ‘%e’ or ‘%f’
would show the output with six digits after the decimal point.
The C printf() function allows a precision of arbitrary size, whether
or not all of the digits are meaningful. With most compilers, the max-
imum internal precision with units is 15 decimal digits (or 13 hexadec-
imal digits). With the ‘--digits’ option, you are limited to the maxi-
mum internal precision; with the ‘--output-format’ option, you may
specify a precision greater than this, but it may not be meaningful.
In some cases, specifying excess precision can result in rounding arti-
facts. For example, a pound is exactly 7000 grains, but with the for-
mat ‘%.18g’, the output might be
You have: pound
You want: grain
* 6999.9999999999991
/ 0.00014285714285714287
With the format ‘%.25g’ you might get the following:
You have: 1/3
You want:
Definition: 0.333333333333333314829616256247
In this case the displayed value includes a series of digits that rep-
resent the underlying binary floating-point approximation to 1/3 but
are not meaningful for the desired computation. In general, the result
with excess precision is system dependent. The precision affects only
the display of numbers; if a result relies on physical constants that
are not known to the specified precision, the number of physically
meaningful digits may be less than the number of digits shown.
See the documentation for printf() for more detailed descriptions of
the format specification.
The ‘--output-format’ option is incompatible with the ‘--exponential’
or ‘--digits’ options; if the former is given in combination with ei-
ther of the latter, the format is controlled by the last option given.
LOCALIZATION
Some units have different values in different locations. The localiza-
tion feature accommodates this by allowing a units data file to specify
definitions that depend on the user’s locale.
Locale
A locale is a subset of a user’s environment that indicates the user’s
language and country, and some attendant preferences, such as the for-
matting of dates. The units program attempts to determine the locale
from the POSIX setlocale function; if this cannot be done, units exam-
ines the environment variables LC_CTYPE and LANG. On POSIX systems, a
locale is of the form language_country, where language is the two-char-
acter code from ISO 639-1 and country is the two-character code from
ISO 3166-1; language is lower case and country is upper case. For exam-
ple, the POSIX locale for the United Kingdom is en_GB.
On systems running Microsoft Windows, the value returned by setlocale()
is different from that on POSIX systems; units attempts to map the Win-
dows value to a POSIX value by means of a table in the file
‘locale_map.txt’ in the same directory as the other data files. The
file includes entries for many combinations of language and country,
and can be extended to include other combinations. The
‘locale_map.txt’ file comprises two tab-separated columns; each entry
is of the form
Windows-locale POSIX-locale
where POSIX-locale is as described above, and Windows-locale typically
spells out both the language and country. For example, the entry for
the United States is
English_United States en_US
You can force units to run in a desired locale by using the ‘-l’ op-
tion.
In order to create unit definitions for a particular locale you begin a
block of definitions in a unit datafile with ‘!locale’ followed by a
locale name. The ‘!’ must be the first character on the line. The
units program reads the following definitions only if the current lo-
cale matches. You end the block of localized units with ‘!endlocale’.
Here is an example, which defines the British gallon.
!locale en_GB
gallon 4.54609 liter
!endlocale
Additional Localization
Sometimes the locale isn’t sufficient to determine unit preferences.
There could be regional preferences, or a company could have specific
preferences. Though probably uncommon, such differences could arise
with the choice of English customary units outside of English-speaking
countries. To address this, units allows specifying definitions that
depend on environment variable settings. The environment variables can
be controlled based on the current locale, or the user can set them to
force a particular group of definitions.
A conditional block of definitions in a units data file begins with ei-
ther ‘!var’ or ‘!varnot’ following by an environment variable name and
then a space separated list of values. The leading ‘!’ must appear in
the first column of a units data file, and the conditional block is
terminated by ‘!endvar’. Definitions in blocks beginning with ‘!var’
are executed only if the environment variable is exactly equal to one
of the listed values. Definitions in blocks beginning with ‘!varnot’
are executed only if the environment variable does not equal any of the
list values.
The inch has long been a customary measure of length in many places.
The word comes from the Latin uncia meaning “one twelfth,” referring to
its relationship with the foot. By the 20th century, the inch was of-
ficially defined in English-speaking countries relative to the yard,
but until 1959, the yard differed slightly among those countries. In
France the customary inch, which was displaced in 1799 by the meter,
had a different length based on a french foot. These customary defini-
tions could be accommodated as follows:
!var INCH_UNIT usa
yard 3600|3937 m
!endvar
!var INCH_UNIT canada
yard 0.9144 meter
!endvar
!var INCH_UNIT uk
yard 0.91439841 meter
!endvar
!var INCH_UNIT canada uk usa
foot 1|3 yard
inch 1|12 foot
!endvar
!var INCH_UNIT france
foot 144|443.296 m
inch 1|12 foot
line 1|12 inch
!endvar
!varnot INCH_UNIT usa uk france canada
!message Unknown value for INCH_UNIT
!endvar
When units reads the above definitions it will check the environment
variable INCH_UNIT and load only the definitions for the appropriate
section. If INCH_UNIT is unset or is not set to one of the four values
listed, then units will run the last block. In this case that block
uses the ‘!message’ command to display a warning message. Alterna-
tively that block could set default values.
In order to create default values that are overridden by user settings
the data file can use the ‘!set’ command, which sets an environment
variable only if it is not already set; these settings are only for
the current units invocation and do not persist. So if the example
above were preceded by ‘!set INCH_UNIT france’, then this would make
‘france’ the default value for INCH_UNIT. If the user had set the
variable in the environment before invoking units, then units would use
the user’s value.
To link these settings to the user’s locale you combine the ‘!set’ com-
mand with the ‘!locale’ command. If you wanted to combine the above
example with suitable locales you could do by preceding the above defi-
nition with the following:
!locale en_US
!set INCH_UNIT usa
!endlocale
!locale en_GB
!set INCH_UNIT uk
!endlocale
!locale en_CA
!set INCH_UNIT canada
!endlocale
!locale fr_FR
!set INCH_UNIT france
!endlocale
!set INCH_UNIT france
These definitions set the overall default for INCH_UNIT to ‘france’ and
set default values for four locales appropriately. The overall default
setting comes last so that it only applies when INCH_UNIT was not set
by one of the other commands or by the user.
If the variable given after ‘!var’ or ‘!varnot’ is undefined, then
units prints an error message and ignores the definitions that follow.
Use ‘!set’ to create defaults to prevent this situation from arising.
The ‘-c’ option only checks the definitions that are active for the
current environment and locale, so when adding new definitions take
care to check that all cases give rise to a well defined set of defini-
tions.
ENVIRONMENT VARIABLES
The units program uses the following environment variables:
HOME Specifies the location of your home directory; it is used by
units to find a personal units data file ‘.units’. On systems
running Microsoft Windows, the file is ‘unitdef.units’, and if
HOME does not exist, units tries to determine your home direc-
tory from the HOMEDRIVE and HOMEPATH environment variables; if
these variables do not exist, units finally tries
USERPROFILE—typically ‘C:\Users\username’ (Windows Vista and
Windows 7) or ‘C:\Documents and Settings\username’ (Windows XP).
LC_CTYPE, LANG
Checked to determine the locale if units cannot obtain it from
the operating system. Sections of the standard units data file
are specific to certain locales.
MYUNITSFILE
Specifies your personal units data file. If this variable ex-
ists, units uses its value rather than searching your home di-
rectory for ‘.units’. The personal units file will not be
loaded if any data files are given using the ‘-f’ option.
PAGER Specifies the pager to use for help and for displaying the con-
formable units. The help function browses the units database
and calls the pager using the ‘+n’n syntax for specifying a line
number. The default pager is more; PAGER can be used to specify
alternatives such as less, pg, emacs, or vi.
UNITS_ENGLISH
Set to either ‘US’ or ‘GB’ to choose United States or British
volume definitions, overriding the default from your locale.
UNITSFILE
Specifies the units data file to use (instead of the default).
You can only specify a single units data file using this envi-
ronment variable. If units data files are given using the ‘-f’
option, the file specified by UNITSFILE will be not be loaded
unless the ‘-f’ option is given with the empty string (-
‘units -f ""’).
UNITSLOCALEMAP
Windows only; this variable has no effect on Unix-like systems.
Specifies the units locale map file to use (instead of the de-
fault). This variable seldom needs to be set, but you can use
it to ensure that the locale map file will be found if you spec-
ify a location for the units data file using either the ‘-f’ op-
tion or the UNITSFILE environment variable, and that location
does not also contain the locale map file.
UNITS_SYSTEM
This environment variable is used in the standard data file to
select CGS measurement systems. Currently supported systems are
‘esu’, ‘emu’, ‘gauss[ian]’, and ‘si’. The default is ‘si’.
DATA FILES
The units program uses two default data files: ‘definitions.units’ and
‘currency.units’. The program can also use an optional personal units
data file ‘.units’ (‘unitdef.units’ under Windows) located in the
user’s home directory. The personal units data file is described in
more detail in Units Data Files.
On Unix-like systems, the data files are typically located in
‘/usr/share/units’ if units is provided with the operating system, or
in ‘/usr/local/share/units’ if units is compiled from the source dis-
tribution. Note that the currency file ‘currency.units’ is a symbolic
link to another location.
On systems running Microsoft Windows, the files may be in the same lo-
cations if Unix-like commands are available, a Unix-like file structure
is present (e.g., ‘C:/usr/local’), and units is compiled from the
source distribution. If Unix-like commands are not available, a more
common location is ‘C:\Program Files (x86)\GNU\units’ (for 64-bit Win-
dows installations) or ‘C:\Program Files\GNU\units’ (for 32-bit instal-
lations).
If units is obtained from the GNU Win32 Project
(http://gnuwin32.sourceforge.net/), the files are commonly in
‘C:\Program Files\GnuWin32\share\units’.
If the default units data file is not an absolute pathname, units will
look for the file in the directory that contains the units program; if
the file is not found there, units will look in a directory
../share/units relative to the directory with the units program.
You can determine the location of the files by running units --version.
Running units --info will give you additional information about the
files, how units will attempt to find them, and the status of the re-
lated environment variables.
UNICODE SUPPORT
The standard units data file is in Unicode, using UTF-8 encoding. Most
definitions use only ASCII characters (i.e., code points U+0000 through
U+007F); definitions using non-ASCII characters appear in blocks begin-
ning with ‘!utf8’ and ending with ‘!endutf8’.
The non-ASCII definitions are loaded only if the platform and the lo-
cale support UTF-8. Platform support is determined when units is com-
piled; the locale is checked at every invocation of units. To see if
your version of units includes Unicode support, invoke the program with
the ‘--version’ option.
When Unicode support is available, units checks every line within UTF-8
blocks in all of the units data files for invalid or non-printing UTF-8
sequences; if such sequences occur, units ignores the entire line. In
addition to checking validity, units determines the display width of
non-ASCII characters to ensure proper positioning of the pointer in
some error messages and to align columns for the ‘search’ and ‘?’ com-
mands.
As of early 2019, Microsoft Windows provides limited support for UTF-8
in console applications, and accordingly, units does not support Uni-
code on Windows. The UTF-16 and UTF-32 encodings are not supported on
any platforms.
If Unicode support is available and definitions that contain non-ASCII
UTF-8 characters are added to a units data file, those definitions
should be enclosed within ‘!utf8’ ... ‘!endutf8’ to ensure that they
are only loaded when Unicode support is available. As usual, the ‘!’
must appear as the first character on the line. As discussed in Units
Data Files, it’s usually best to put such definitions in supplemental
data files linked by an ‘!include’ command or in a personal units data
file.
When Unicode support is not available, units makes no assumptions about
character encoding, except that characters in the range 00–7F hexadeci-
mal correspond to ASCII encoding. Non-ASCII characters are simply se-
quences of bytes, and have no special meanings; for definitions in sup-
plementary units data files, you can use any encoding consistent with
this assumption. For example, if you wish to use non-ASCII characters
in definitions when running units under Windows, you can use a charac-
ter set such as Windows “ANSI” (code page 1252 in the US and Western
Europe); if this is done, the console code page must be set to the same
encoding for the characters to display properly. You can even use
UTF-8, though some messages may be improperly aligned, and units will
not detect invalid UTF-8 sequences. If you use UTF-8 encoding when
Unicode support is not available, you should place any definitions with
non-ASCII characters outside ‘!utf8’
Typeset material other than code examples usually uses the Unicode mi-
nus (U+2212) rather than the ASCII hyphen-minus operator (U+002D) used
in units; the figure dash (U+2012) and en dash (U+2013) are also occa-
sionally used. To allow such material to be copied and pasted for in-
teractive use or in units data files, units converts these characters
to U+002D before further processing. Because of this, none of these
characters can appear in unit names.
READLINE SUPPORT
If the readline package has been compiled in, then when units is used
interactively, numerous command line editing features are available.
To check if your version of units includes readline, invoke the program
with the ‘--version’ option.
For complete information about readline, consult the documentation for
the readline package. Without any configuration, units will allow
editing in the style of emacs. Of particular use with units are the
completion commands.
If you type a few characters and then hit ESC followed by ?, then units
will display a list of all the units that start with the characters
typed. For example, if you type metr and then request completion, you
will see something like this:
You have: metr
metre metriccup metrichorsepower metrictenth
metretes metricfifth metricounce metricton
metriccarat metricgrain metricquart metricyarncount
You have: metr
If there is a unique way to complete a unit name, you can hit the TAB
key and units will provide the rest of the unit name. If units beeps,
it means that there is no unique completion. Pressing the TAB key a
second time will print the list of all completions.
The readline library also keeps a history of the values you enter. You
can move through this history using the up and down arrows. The his-
tory is saved to the file ‘.units_history’ in your home directory so
that it will persist across multiple units invocations. If you wish to
keep work for a certain project separate you can change the history
filename using the ‘--history’ option. You could, for example, make an
alias for units to units --history .units_history so that units would
save separate history in the current directory. The length of each
history file is limited to 5000 lines. Note also that if you run sev-
eral concurrent copies of units each one will save its new history to
the history file upon exit.
UPDATING CURRENCY EXCHANGE RATES
The units program database includes currency exchange rates and prices
for some precious metals. Of course, these values change over time,
sometimes very rapidly, and units cannot provide real-time values. To
update the exchange rates, run units_cur, which rewrites the file con-
taining the currency rates, typically ‘/var/lib/units/currency.units’
or ‘/usr/local/com/units/currency.units’ on a Unix-like system or
‘C:Program Files (x86)\:GNU\:units\:definitions.units’ on a Windows
system.
This program requires Python (https://www.python.org); either version 2
or 3 will work. The program must be run with suitable permissions to
write the file. To keep the rates updated automatically, run it using
a cron job on a Unix-like system, or a similar scheduling program on a
different system.
Reliable free sources of currency exchange rates have been annoyingly
ephemeral. The program currently supports several sources:
• FloatRates (https://www/floatrates.com). The US dollar (‘USD’) is
the default base currency. You can change the base currency with
the ‘-b’ option described below. Allowable base currencies are
listed on the FloatRates website. Exchange rates update daily.
• The European Central Bank (https://www.ecb.europa.eu). The base
currency is always the euro (‘EUR’). Exchange rates update daily.
This source offers a more limited list of currencies than the oth-
ers.
• Fixer (https://fixer.io). Registration for a free API key is re-
quired. With a free API key, base currency is the euro; exchange
rates are updated hourly, the service has a limit of 1,000 API
calls per month, and SSL encryption (https protocol) is not avail-
able. Most of these restrictions are eliminated or reduced with
paid plans.
• open exchange rates (https://openexchangerates.org). Registration
for a free API key is required. With a free API key, the base cur-
rency is the US dollar; exchange rates are updated hourly, and
there is a limit of 1,000 API calls per month. Most of these re-
strictions are eliminated or reduced with paid plans.
ExchangeRate-API.com (https://www.exchangerate-api.com). Allows open
access without an API key, with unlimited API requests. Rates update
once a day, and you can choose your base currency. You can optionally
sign up for an API key to access paid benefits such as faster data up-
date rates.
The default source is FloatRates; you can select a different one using
‘-s’ option described below.
Precious metals pricing is obtained from Packetizer (www.packe-
tizer.com). This site updates once per day.
You invoke units_cur like this:
units_cur [options] [outfile]
By default, the output is written to the default currency file de-
scribed above; this is usually what you want, because this is where
units looks for the file. If you wish, you can specify a different
filename on the command line and units_cur will write the data to that
file. If you give ‘-’ for the file it will write to standard output.
The following options are available:
-h, --help
Print a summary of the options for units_cur.
-V, --version
Print the units_cur version number.
-v, --verbose
Give slightly more verbose output when attempting to update cur-
rency exchange rates.
-s source, --source source
Specify the source for currency exchange rates; currently sup-
ported values are ‘floatrates’ (for FloatRates), ‘eubank’ (for
the European Central Bank), ‘fixer’ (for Fixer), and
‘openexchangerates’ (for open exchange rates); the last two re-
quire an API key to be given with the ‘-k’ option.
-b base, --base base
Set the base currency (when allowed by the site providing the
data). base should be a 3-letter ISO currency code, e.g.,
‘USD’. The specified currency will be the primitive currency
unit used by units. You may find it convenient to specify your
local currency. Conversions may be more accurate and you will
be able to convert to your currency by simply hitting Enter at
the ‘You want:’ prompt. This option is ignored if the source
does not allow specifying the base currency. (Currently only
floatrates supports this option.)
-k key, --key key
Set the API key to key for sources that require it.
DATABASE COMMAND SYNTAX
unit definition
Define a regular unit.
prefix- definition
Define a prefix.
funcname(var) noerror units=[in-units,out-units] domain=[x1,x2]
range=[y1,y2] definition(var) ; inverse(funcname)
Define a nonlinear unit or unit function. The four optional
keywords noerror, units=, range= and domain= can appear in any
order. The definition of the inverse is optional.
tabname[out-units] noerror pair-list
Define a piecewise linear unit. The pair list gives the points
on the table listed in ascending order. The noerror keyword is
optional.
!endlocale
End a block of definitions beginning with ‘!locale’
!endutf8
End a block of definitions begun with ‘!utf8’
!endvar
End a block of definitions begun with ‘!var’ or ‘!varnot’
!include file
Include the specified file.
!locale value
Load the following definitions only of the locale is set to
value.
!message text
Display text when the database is read unless the quiet option
(‘-q’) is enabled. If you omit text, then units will display a
blank line. Messages will also appear in the log file.
!prompt text
Prefix the ‘You have:’ prompt with the specified text. If you
omit text, then any existing prefix is canceled.
!set variable value
Sets the environment variable, variable, to the specified value
only if it is not already set.
!unitlist alias definition
Define a unit list alias.
!utf8 Load the following definitions only if units is running with
UTF-8 enabled.
!var envar value-list
Load the block of definitions that follows only if the environ-
ment variable envar is set to one of the values listed in the
space-separated value list. If envar is not set, units prints
an error message and ignores the block of definitions.
!varnot envar value-list
Load the block of definitions that follows only if the environ-
ment variable envar is set to value that is not listed in the
space-separated value list. If envar is not set, units prints
an error message and ignores the block of definitions.
FILES
/usr/share/units/definitions.units — the standard units data file
AUTHOR
units was written by Adrian Mariano
25 August 2022 UNITS(1)
Generated by dwww version 1.15 on Sat Jun 29 02:11:32 CEST 2024.