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NAME [to-unit]]
[from-uniti[to-unit]]on and calculation program
DESCRIPTIONunit [to-unit]]
SYNOPTheounitstprogram 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
transformation 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 program 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
dimensions. 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 several external data files. You can use the
extensive data files that come with the 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 files.
You can change the default behavior of units with various options
given on the command line. See Invoking Units for a description of the
available options.
ADDITIONAL DOCUMENTATION
This manual is also available in PDF and HTML:
INTERACTING WITH UNITS
To invoke units for interactive use, type units at your shell prompt.
The program will print something like this:
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Currency exchange rates from FloatRates (USD base) on 2023-07-08 3612
units, 109 prefixes, 122 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
complete 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
number 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
obvious 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
dimensions, then units will display the conversion results with an
extra note indicating that reciprocal conversion has been done:
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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
display 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,
simply 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. If the ultimate
definition and the fully reduced form are identical, the latter is not
shown:
You have: B You want:
Definition: byte = 8 bit
The fully reduced form is shown if it and the ultimate definition are
equivalent but not identical:
You have: N You want:
Definition: newton = kg m / s 2 = 1 kg m / s 2
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
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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.
Conformable 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
historical information about the unit. If your pager allows, you may
want to scroll backwards, e.g. with b, because sometimes a longer
comment about a unit or group of units will appear before the
definition. You can generally quit out of the pager 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.
Many command-line options can be set by typing set option=value;
typing set option will show the value for that option. Typing set
will show a list of options that can be set; options set to other than
default values will have a prepended *. See Setting Options
Interactively for more information.
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.
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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
allowed, 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
option, 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 option,
conformable units are shown without definitions; with the previous
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 several units data files:
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definitions.units, elements.units, currency.units, and cpi.units,
which are usually located in the /usr/share/units directory. If you
invoke units with the -V option, it will print the location of these
files. The default main file includes 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.
Physical Constants
Many constants of nature are defined, including these:
pi ratio of circumference of a circle to its 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 numerous other constants. Also
included are the densities of various 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.
Atomic Masses of the Elements
The data file elements.units includes atomic masses for most elements
and most known isotopes. If the mole fractions of constituent
isotopes are known, an elemental mass is calculated from the sum of
the products of the mole fractions and the masses of the constituent
isotopes. If the mole fractions are not known, the mass of the most
stable isotope-if known-is given as the elemental mass. For
radioactive elements with atomic numbers 95 or greater, the mass
number of the most stable isotope is not specified, because the list
of studied isotopes is still incomplete. If no stable isotope is
known, no elemental mass is given, and you will need to choose the
most appropriate isotope.
The data are obtained from the US National Institute for Standards and
Technology (NIST): https://physics.nist.gov/cgi-
bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii2&isotype=all.
The elements.units file can be generated from these data using the
elemcvt command included with the distribution.
Currency Exchange Rates and Consumer Price
The data file currency.units includes currency conversion rates; the
file cpi.units includes the US Consumer Price Index (CPI), published
by the US Bureau of Labor Statistics. The data are updated monthly by
the BLS; see Updating Currency Exchange Rates and CPI for information
on updating currency.units and cpi.units.
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English Customary Units
English customary units differ in various ways among 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 Imperial 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 values are the US definitions. If you wish to force
different definitions, 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
International 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, pole, perch, 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 differed from the international values by about 2 ppm.
The 1959 redefinition of the foot was legally binding in the US but
allowed continued use of the previous definition of the foot for
geodetic surveying. It was assumed that this use would be temporary,
but use persisted, leading to confusion and errors, and it was at odds
with the intent of uniform standards. Since January 1, 2023, the US
survey foot has been officially deprecated (85 FR 62698), with its use
limited to historical and legacy applications.
The units program has always used the international values for these
units; the legacy 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 obtain 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.
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The pre-1959 UK values for these units can be obtained with the prefix
UK.
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 US acre was officially defined in terms of the US survey foot, but
units has used a definition based on the international foot; the units
definition is now the same as the official US value. If you want the
previous US acre, use USacre and similarly use USacrefoot for the
previous US version of that unit. The difference between these units
is about 4 parts per million.
Miscellaneous Notes on Unit Definitions
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
exactly 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 default
units data files; the main data file is extensively annotated.
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. Additionally, units supports some extensions, including high
priority multiplication using a space, and a high priority numerical
division operator (|) that can simplify some expressions.
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You multiply units using a space or an asterisk (*). The next example
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,
hyphenated 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
using 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
denominator: J / mol K. The * and / operators have the same
precedence, 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
advantageous. 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
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exponent: cm3 is equivalent to cm 3; if the exponent is more than one
digit, the is required. You can also use ** as an exponent
operator.
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 includes 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 cubic
centimeter. The units program is limited internally to products of 99
units; accordingly, expressions like meter 100 or joule 34
(represented 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 second 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
meaningful (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 parentheses 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.
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Sums and Differences of Units
You may sometimes want to add values of different units that are
outside 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
Invalid 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 necessary
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
Invalid 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
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(3e+2) yC or (3 e)+(2 yC). This ambiguity is resolved 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
example, 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
conversion 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
angle.
The ln and log functions give natural log and log base 10
respectively. 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
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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
underscore (_). 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-
diameter 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
example could have used 2_. If _ follows a non-numerical unit symbol,
however, the space is required:
You have: m_
Parse error
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
after invocation) generates an error:
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You have: _
No previous result; _ not set
Accordingly, _ serves no purpose when units is invoked non-
interactively.
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
dimensional consistency when converting lengthy unit expressions. For
example, 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. You might want 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
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20 November 2024
You have: 8 lb ft ft 3 ft 3 / pi 2 ft 3 s 2 in 5 You want: psi
* 43.533969
/ 0.022970568
Variables Assigned at Run Time
Unit definitions are fixed once units has finished reading the units
data file(s), but at run time you can assign unit expressions to
variables whose names begin with an underscore, using the syntax
_name = <unit expression>
This can help manage a long calculation by saving intermediate
quantities as variables that you can use later. For example, to
determine the shot-noise-limited signal-to-noise ratio (SNR) of an
imaging system using a heliumneon laser, you could do
You have: _lambda = 632.8 nm # laser wavelength You have:
_nu = c / _lambda # optical frequency You have:
_photon_energy = h * _nu You have: _power = 550 uW You have:
_photon_count = _power * 500 ns / _photon_energy You have: _snr =
sqrt(_photon_count) You have: _snr You want:
Definition: sqrt(_photon_count) = 29597.922
Except for beginning with an underscore, runtime variables follow the
same naming rules as units. Because names beginning with _ are
reserved for these variables and unit names cannot begin with _,
runtime variables can never hide unit definitions. Runtime variables
are undefined until you make an assignment to them, so if you give a
name beginning with an underscore and no assignment has been made, you
get an error message.
When you assign a unit expression to a runtime variable, units checks
the expression to determine whether it is valid, but the resulting
definition is stored as a text string that is not reduced to primitive
units. The text will be processed anew each time you use the variable
in a conversion or calculation; this means that if your definition
depends on other runtime variables (or the special variable _), the
result of calculating with your variable will change if any of those
variables change. A dependence need not be direct.
Continuing the example of the laser above, suppose you have done the
calculation as shown. You now wonder what happens if you switch to an
argon laser:
You have: _lambda = 454.6 nm You have: _snr You want:
Definition: sqrt(_photon_count) = 25086.651
If you then change the power:
You have: _power = 1 mW You have: _snr You want:
Definition: sqrt(_photon_count) = 33826.834
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Instead of having to reenter or edit a lengthy expression when you
perform another calculation, you need only enter values that change;
in this respect, runtime variables are similar to a spreadsheet.
The more times a variable appears in an expression that depends on it,
the greater the benefit of having a calculation using that expression
reflect changes to that variable. For example, the length of
daylight-the time the Sun is above the horizon-at a given latitude and
declination of the Sun is given by
L = acos((sin h - sin U sin D) /
(cos U cos D))
where L is the day length, h is the altitude, U is the latitude, and D
is the Sun s declination.
The result above is in sidereal time; the length in solar time is
obtained by multiplying by
siderealday / day
By convention, the Sun s altitude at rise or set is -50' to allow for
atmospheric refraction and the semidiameter of its disk. At the
summer solstice in the northern hemisphere, the Sun s declination is
approximately 23.44o; to find the length of the longest day of the
year for a latitude of 55o, you could do
You have: _alt = -50 arcmin You have: _lat = 55 deg You have: _decl =
23.44 deg You have: _num = sin(_alt) - sin(_lat) sin(_decl) You have:
_denom = cos(_lat) cos(_decl) You have: _sday = 2 (acos(_num / _denom)
/ circle) 24 hr You have: _day = _sday siderealday / day You have:
_day You want: hms
17 hr + 19 min + 34.895151 sec
At the winter solstice, the Sun s declination is approximately
-23.44o, so you could calculate the length of the shortest day of the
year using:
You have: _decl = -23.44 deg You have: _day You want: hms
7 hr + 8 min + 40.981084 sec
Latitude and declination each appear twice in the expression for _day;
the result in the examples above is updated by changing only the value
of the declination.
It may seem easier-and less subject to error-to simply specify the new
value of _decl as the negative of the current value (e.g.,
_decl = -_decl). This doesn t work; when you make an assignment with
the = operator, the definition is stored as entered, including
possible dependencies on variables. But if you attempt an assignment
that is ultimately self-referential, the current definition is
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20 November 2024
retained, and you get an error message. For example,
You have: _decl = 23.44 deg You have: _decl = -_decl Circular unit
definition
You can overcome this by using the := operator, which reduces the
right hand side to primitive units before making the assignment,
eliminating any dependencies on variables. Returning to the example
above,
You have: _decl = 23.44 deg You have: _decl = -_decl Circular unit
definition You have: _decl := -_decl You have: _decl You want: deg
* -23.44
/ -0.042662116
This works to much the same effect as if the assignment had been
entered literally, e.g.,
You have: _decl = -23.44 deg
but the actual definition is in primitive units-in this case, radians:
You have: _decl = 23.44 deg You have: _decl := -_decl You have: _decl
You want:
Definition: -0.40910517666747087 radian = -0.40910518 radian
Definitions are text strings, and a redefinition using := is given
with enough digits maintain the full precision of the current
definition when converted back to a number; because it is a string,
all digits are displayed when showing the definition, regardless of
the numerical display precision, so you may see more digits than
expected.
A runtime variable must be assigned before it can be used in an
assignment; in the first of the three examples above, giving the
general equation before the values for _alt, _lat, and _decl had been
assigned would result in an error message.
Backwards Compatibility: * and -
The original units assigned multiplication a higher precedence than
division 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.
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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
subtraction 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. Regardless
of the units options, if - appears after ( or after +, then it will
act as a negation operator. So you can always compute 20 degrees
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
conversions 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
Nonlinear 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
absolute 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
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20 November 2024
/ 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 converting to
a temperature rather than converting a temperature increment.
The tempC() and tempF() definitions are limited to positive absolute
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
US Consumer Price Index
units includes the US Consumer Price Index published by the US Bureau
of Labor Statistics. Several functions that use this value are
provided: cpi, cpi_now, inflation_since, and dollars_in.
The cpi function gives the CPI for a specified decimal year. A
decimal year is given as the year plus the fractional part of the
year; because of leap years and the different lengths of months,
calculating an exact value for the fractional part can be tedious, but
for the purposes of CPI, an approximate value is usually adequate.
For example, 1 January 2000 is 2000.0, 1 April 2000 is 2000.25, 1 July
2000 is 2000.4986, and 1 October 2000 is 2000.75. Note also that the
CPI data update monthly; values in between months are linearly
interpolated.
In the middle of 1975, the CPI was
You have: cpi(1975.5) You want:
Definition: 53.6
The value of the CPI for a month is usually published sometime around
the 20th day of the following month; the latest value of the CPI is
available with cpi_now. On 7 January 2024, the value was
You have: cpi_now You want:
Definition: UScpi_now = 307.051
This means that the CPI was 307.015 on 1 December 2023. The cpi_now
variable can only present the most recent data available, so it can
lag the current CPI by several weeks. The decimal year of the last
update is available with cpi_lastdate.
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The inflation_since function provides a convenient way to determine
the inflation factor from a specified decimal year to the latest value
in the CPI table. For example, on 7 January 2024:
You have: inflation_since(1970) You want:
Definition: 8.1445889
In other words, goods that cost 1 US$ in 1970 would cost 8.14 US$ on
1 December 2023.
The inflation_since function can be used to determine an annual rate
of inflation. The earliest US CPI data are from about 1913.1; the
approximate time between then and 7 January 2024 is 110.9 years. The
approximate annual inflation rate for that period is then
You have: inflation_since(1913.1) 1|110.9 - 1 You want: %
* 3.1548115
/ 0.31697614
The inflation rate for any time period can be found from the ratio of
the CPI at the end of the period to that of the beginning:
You have: (cpi(1982)/cpi(1972)) 1|10 - 1 You want: %
* 8.6247033
/ 0.11594602
The period 19721982 was indeed one of high inflation.
The dollars_in function is similar to inflation_since but its output
is in US$ rather than dimensionless:
You have: dollars_in(1970) You want:
Definition: 8.1445889 US$
A typical use might be
You have: 250 dollars_in(1970) You want: $
* 2036.1472
/ 0.00049112362
Because dollars_in includes the units, you should not include them at
the You have: prompt. You can also use dollars_in to convert between
two specified years:
You have: 250 dollars_in(1970) You want: dollars_in(1950)
* 156.49867
/ 0.0063898305
which shows that 250 US$ in 1970 would have equivalent purchasing
power to 156 US$ in 1950.
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Other Nonlinear Units
Some other examples of nonlinear units are numerous different ring
sizes and wire gauges, screw gauges, pipe and tubing sizes, 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 circle and the volume of a sphere.
See the standard units data file for more details.
Diameters of American wire sizes can be found using the wiregauge()
function or its alias awg():
You have: wiregauge(11) You want: inches
* 0.090742002
/ 11.020255 You have: 1 mm You want: wiregauge
18.201919
Wire and screw gauges with multiple zeroes are signified using
negative numbers, where two zeroes (00; 2/0) is -1, three zeros (000;
3/0) is -2, and so on. Alternatively, you can use the synonyms g00,
g000, or g2_0, g3_0, and so on that are defined in the standard units
data file.
You have: brwiregauge(g00) You want: inches
* 0.348
/ 2.8735632
In North America, wire sizes larger than 0000 (4/0) are usually given
in terms of area, either in kcmil or the older initialism MCM
(thousand circular mils). Outside of North America, all wire sizes
are usually given in terms of area in mm 2. Wire area can be obtained
using wiregaugeA() or its alias awgA():
You have: awgA(g6_0) You want: kcmil
* 336.45718
/ 0.0029721464 You have: awgA(12) You want: mm 2
* 3.3087729
/ 0.30222685
The closest standard metric sizes are 2.5 mm 2 and 4 mm 2; in general,
there isn t an exact correlation between American and metric wire
sizes.
Though based on the long-established iron pipe size (IPS) given in
inches, nominal pipe size (NPS) is a dimensionless quantity that
corresponds to the inch size. Pipe size can be equivalently specified
using metric diam[u00E8]tre nominal (DN), which roughly corresponds to
the diameter in mm. For a given pipe size, outside diameter is
constant while inside diameter varies with schedule. For example, for
NPS 2[u00BD] pipe,
- 21 - Formatted: December 27, 2024
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20 November 2024
You have: npsOD(2+1|2) You want: in
* 2.875
/ 0.34782609 You have: nps40(2+1|2) You want: in
* 2.469
/ 0.40502228 You have: nps80(2+1|2) You want: in
* 2.323
/ 0.43047783
Pipe size can be given equivalently in terms of the metric DN by using
the DN() function, which converts nominal metric size to nominal inch
size:
You have: npsOD(DN(65)) You want: mm
* 73.025
/ 0.01369394 You have: _ You want: in
* 2.875
/ 0.34782609
Unlike with wire sizes, actual NPS and metric DN pipe dimensions are
the same.
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
circleinch. The next example shows two ways to compute the area of a
circle 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
parentheses, and press Enter at the You want: prompt to get the
definition of a nonlinear unit; if the definition is not valid for all
- 22 - Formatted: December 27, 2024
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20 November 2024
real numbers, 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 requires
units of K in the specification of the allowed range of values.
Nonlinear unit conversions are described in more detail in Defining
Nonlinear Units.
UNIT LISTS: CONVERSION TO SUMS OF
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
conversion 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
result 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
typically 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 (;) character:
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20 November 2024
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
repeating 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
coefficient for the last unit. If you instead prefer to round the
last coefficient 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 effect 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
conformable with the unit that you enter at the You have: prompt.
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20 November 2024
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
appearing on the list. In the second case, units reports disagreement
between the unit you entered and the desired conversion. This
conformability 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
precision 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
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20 November 2024
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
calculations, 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
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.
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 time: hours, minutes, seconds dms angle: degrees,
minutes, seconds time time: years, days, hours, minutes and
seconds usvol US cooking volume: cups and smaller uswt US
weight: pounds and ounces ftin length: feet, inches and 1/8
inches ftin2 length: feet, inches and 1/2 inches ftin4
length: feet, inches and 1/4 inches ftin8 length: feet, inches
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20 November 2024
and 1/8 inches ftin16 length: feet, inches and 1/16 inches ftin32
length: feet, inches and 1/32 inches ftin64 length: feet, inches
and 1/64 inches inchfine length: 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
Suppose you want to drill a clearance hole for a #10 screw and have
about 1/64 inch clearance; you could try
You have: screwgauge(10) + 1|64 in You want: ftin64
13.16 * 1|64 in You have: _ You want: ftin32
6.58 * 1|32 in
If a slightly tight fit is acceptable, a 13/64-inch drill would do the
job; if not, a 7/32-inch drill would work with a slightly looser fit.
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 (meterkilogramsecond) system-has
largely supplanted the older CGS (centimetergramsecond) 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
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equations. Conversions between SI and CGS involving mechanical units
are straightforward, involving powers of 10 (e.g., 1 m = 100 cm).
Conversions 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
HeavisideLorentz 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
current. 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 HeavisideLorentz
system is rationalized so that factors of 4{pi} do not appear in
Maxwell s equations. The SI system is similarly rationalized, but the
other CGS systems are not. In the HeavisideLorentz (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,
conversions between these systems and SI are not possible. But units
in different 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
various 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
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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
default SI mode and displays (SI) at the You have: prompt to emphasize
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
relationship 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
recognized (e.g., stV).
The EMU system derives the electromagnetic units from its unit of
current, 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 manner 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
System, 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.
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The HeavisideLorentz 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
electromagnetic 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
dimensions. 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
various dimension units such as LENGTH, TIME, and CHARGE to be the
appropriate 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 perform 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.
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(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
because the base measurements are defined using physical constants
instead 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 by 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 HeavisideLorentz
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
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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 gravitation, 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 convert the unreduced and reduced Planck energy unit in
SI mode between the various systems. In Planck units, all
measurements are dimensionless.
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
physical 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.
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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, including
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)
Invalid 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.
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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 invoked, the
new results are appended to the log file. The time is written 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
interactive prompts to determine which conversions to perform. See
Interactive 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 default 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
options 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
beginning 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 option
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
intermixed 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 default eight significant digits).
Many options can be set interactively; this can be especially helpful
for Windows users who start units from a shortcut. See Setting
Options Interactively for more information.
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The following options are available:
-c, --check
Check that all units and prefixes defined in units data files
reduce to primitive units. Display a list of all units that
cannot be reduced and a list of units with circular definitions.
Also display some other diagnostics about suspicious 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.
Some errors may hide other errors, so you should run units with
this option again after correcting any errors, and keep doing so
until there are no errors.
--check-verbose, --verbose-check
Like the --check option, this option displays a list of units
that cannot be reduced. But it also lists the units as they are
checked. Because the --check option now catches circular unit
definitions that previously caused units to hang, this option is
no longer necessary. It is retained only for compatibility with
previous versions.
-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 exponential
output, units displays one digit to the left of the decimal 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 precision,
the physically meaningful precision may be less than that shown.
The --digits option is incompatible with the --output-format
option; if you give them both, the format is controlled by the
last option given.
-e, --exponential
Set the numeric output format to exponential (i.e., scientific
notation), like that used in the Unix units program. The default
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 is incompatible with the --
output-format option; if you give them both, the format is
controlled by the last option given.
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-o format, --output-format format
This option affords complete control over the numeric output
format using the specified format. The format is a single
floating point numeric format for the printf function in the C
programming language. All compilers support the format types g
and G to specify significant digits, e and E for scientific
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 format is %.8g;
for greater precision, you could specify -o %.15g. Unlike with
the --digits option, you can specify any desired precision,
though not all digits may be meaningful. See Numeric Output
Format and the documentation for printf for more detailed
descriptions of the format specification. 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 precision more simply with the --digits
option or select exponential format with --exponential. The --
output-format option is incompatible with the --exponential and
--digits options; if you give either in combination with --
output-format, the format is controlled by the last option given.
-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
option, 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 main 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 conversions 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
filename to the empty string (-H ""). This option has no effect
if readline is not available.
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-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
integer.
-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 example,
the results for a cooking recipe might show 3 * 1|2 cup as
3|2 cup. With the --show-factor option, a result equivalent 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 specifies 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
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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
library has been included, tell whether UTF-8 support has been
included; give the locale, the location of the default main 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 program,
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 systems 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 main 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
supported units systems are: gauss[ian], esu, emu, hlu, natural,
natural-gauss, hartree, planck, planck-red, and si. See
Alternative Unit Systems for further information about these unit
systems.
-l locale, --locale locale
Force a specified locale such as en_GB to get British definitions
by default. This overrides the locale determined from system
settings or environment variables. See Locale for a description
of locale format.
-n, --nolists
Disable conversion to unit lists.
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-s, --strict
Suppress conversion of units to their reciprocal units. For
example, 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
conversion, 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 conversion
line.
-t, --terse
Print only a single conversion factor without any clutter, or if
you request a definition, prints just the definition (including
its units). This option can be used when calling units from
another program so that the output is easy to parse. The command
units --terse mile m produces the output 1690.344. This option
has the combined effect of these options: --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 default
if you invoke units with a unit expression on the command line.
SETTING OPTIONS INTERACTIVELY
Many command-line options can also be set interactively, obviating the
need to quit and restart units to change the values. This can be
especially helpful for Windows users who start units from a shortcut.
Typing set will display a list of all options that can be set
interactively, as well as the current and possible values; options set
to other than default values have an asterisk (*) prepended. For
example,
You have: set
q[uiet] = no (y|n) do/don t suppress prompting
o[neline] = no (y|n) do/don t suppress the second line of
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output
st[rict] = no (y|n) do/don t suppress reciprocal unit
conversion
(e.g. Hz<->s)
t[erse] = no (y|n) do/don t give very terse output
c[ompact] = no (y|n) do/don t suppress printing tab, SETFLAG,
and /
characters in results
v[erbose] = 1 (0|1|2) amount of information shown
*d[igits] = 9 number of significant digits in output
e[ponential] = no (y|n) do/don t use exponential ("scientific")
notation
*f[ormat] = %.9g printf(3) format specification
u[nitlists] = yes (y|n) do/don t allow conversion to unit lists
r[ound] = no (y|n) do/don t round last element of unit list
output
to an integer
sh[owfactor] = no (y|n) do/don t show non-unity factor before 1|x
in multi-unit output
Characters within the square brackets are optional, so settings can be
changed by entering only one or two characters.
The syntax for setting options is set option = value; the spaces
around the = sign are optional.
Some settings are Boolean, enabled by entering yes (or just y) and
disabled by entering no (or just n). For example,
You have: set quiet = y
quiet = yes
Other settings take an integer value; for example,
You have: set d=11
digits = 11
format = %.11g
The format setting takes a string, the format specification for the
printf function in the C programming language; for example,
You have: set format = %.9g
format = %.9g
Typing set option will display the current value of option, for
example
You have: set u
unitlists = yes You have: set d
digits = 8
format = %.8g
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For the digits and exponential options, the value of format is also
shown.
SCRIPTING WITH UNITS
Despite its numerous options, units cannot cover every conceivable
unit-conversion task. For example, suppose we have found some
mysterious 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 observe 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
accomplished 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
combination 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
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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 2023-
07-08 3612 units, 109 prefixes, 122 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 2023-07-08 3612 units, 109 prefixes, 122 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
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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
displays 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
reciprocal conversion or if you get a conformability error. The
former case can be prevented using the --strict option, which
suppresses reciprocal 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 $ units --
terse 1 mile 1609.344 m $ units --terse mile 5280 ft = 1609.344 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 modify
this data file if you have appropriate user privileges, it s usually
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
location of the !include statement in the standard units data file is
important; later definitions replace earlier ones, so any definitions
in an included file will override definitions before the !include
statement in the standard units data file. With normal invocation, no
warning is given about redefinitions; to ensure that you don t have an
unintended redefinition, run units -c after making changes to any
units data file.
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If you want to add your own units in addition to or in place of
standard 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.) Running 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 variable; if this variable exists, its value is used
without searching your home directory. The default units data files
are described in more detail in Data Files.
Defining New Units and Prefixes
A unit is specified on a single line by giving its name and an
equivalence. Comments start with a # character, which can appear
anywhere in a line. The backslash character (\) acts as a
continuation character 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 cannot begin or end with an underscore (_), a comma (,) or
a decimal point (.). Names must not contain any of the operator
characters +, -, *, /, |, , ;, , the comment character #, or
parentheses. To facilitate copying and pasting from documents,
several typographical characters are converted to operators: the
figure dash (U+2012), minus (-; U+2212), and en dash (; U+2013) are
converted to the operator -; the multiplication sign (x; U+00D7), N-
ary times operator (U+2A09), dot operator (; U+22C5), and middle dot
(; U+00B7) are converted to the operator *; the division sign
([u00F7]; U+00F7) is converted to the operator /; and the fraction
slash (U+2044) is converted to the operator |; accordingly, 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 necessary
because without it, units cannot determine whether foo2 is a unit name
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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 and that there are no circular definitions
that lead to endless loops. Because some errors may hide other
errors, you should run units with the -c option again after correcting
any errors, and keep doing so until no errors are displayed.
If you define any units that contain + characters in their
definitions, 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
multiplication 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
precedence 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
redefinition. 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
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A unit that ends with a - character is a prefix. If a prefix
definition contains any / characters, be sure they are protected by
parentheses. If you define half- 1/2, then halfmeter would be
equivalent to 1 / (2 meter).
Defining Nonlinear Units
Some unit conversions of interest are nonlinear; for example,
temperature 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
linear 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 results, the arguments of these functions need to have
the correct dimensions 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
formal 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
requires an input argument conformable with 1 (i.e., the argument is
dimensionless), and that the inverse function requires an input
argument 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 domain and range specifications, which are described later.
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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
inverse 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
obtain 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
arguments. 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
powers 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
endpoints given in brackets. In accord with mathematical convention,
square brackets indicate a closed interval (one that includes its
endpoints), and parentheses indicate an open interval (one that does
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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
decibel (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 specification, and if necessary, the parameter value is adjusted
for comparison with the endpoints. For example, if a definition
includes units=[1;ft] and range=[3,), the range will be taken as 3 ft
to infinity. 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 microfurlongs, and can not adjust the parameter value of 900 mm for
comparison. Without units, numerical values other than zero or plus
or minus infinity for domain or range endpoints are meaningless, and
accordingly 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
definition.
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
original 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
appended parentheses as a new unit, with the existing nonlinear
unit-without parentheses-as the definition. So to create a synonym
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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
messages.
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
conversions 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 [
character. After the bracket, you should indicate the units to be
attached to the numbers in the table. No spaces can appear before the
] character, 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
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With the preceding definition, the following conversion can be
performed:
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
really 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
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that there are no actual errors before adding the noerror keyword.
Defining Unit List Aliases
Unit list aliases are treated differently from unit definitions,
because 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
included 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
include 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 in general
number format. You can change this with the --exponential, --digits,
and --output-format options. The first sets an exponential format
(i.e., scientific notation) like that used in the original Unix units
program, the second allows 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 format type, use the --
digits and --exponential options. The --output-format option affords
the greatest control of the output appearance, 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][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
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displays as 1.3e-005. These types also use exponential notation when
the exponent is greater than or equal to the precision, so with the
default format, the value 5 x 10 7 displays as 50000000 and the value
5 x 10 8 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 5 x 10 -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 precision
specification that begins with a period (e.g., .6). The field width
includes the digits, decimal point, the exponent, thousands separators
(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 positive, 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 separator 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
without counting the digits to the left of the decimal point. If the
thousands 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 specified
field width. If a field width greater than needed to show the output
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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 arguably 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 precision
(as indicated above, the # flag causes trailing zeros to be
displayed).
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
maximum internal precision with units is 15 decimal digits (or 13
hexadecimal digits). With the --digits option, you are limited to the
maximum 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
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artifacts. For example, a pound is exactly 7000 grains, but with the
format %.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
represent 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 either of
the latter, the format is controlled by the last option given.
LOCALIZATION
Some units have different values in different locations. The
localization 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
formatting of dates. The units program attempts to determine the
locale from the POSIX setlocale function; if this cannot be done,
units examines the environment variables LC_CTYPE and LANG. On POSIX
systems, a locale is of the form language_country, where language is
the two-character 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 example, 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
Windows 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
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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 option.
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
locale 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
either !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
officially 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
definitions 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
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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.
Alternatively 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
command with the !locale command. If you wanted to combine the above
example with suitable locales you could do by preceding the above
definition 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 definitions.
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 directory from
the HOMEDRIVE and HOMEPATH environment variables; if these
variables do not exist, units finally tries USERPROFILE-typically
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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 default main units data
file are specific to certain locales.
MYUNITSFILE
Specifies your personal units data file. If this variable
exists, units uses its value rather than searching your home
directory 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
conformable units. The help function browses the units database
and calls the pager using the +nn 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
environment 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
default). This variable seldom needs to be set, but you can use
it to ensure that the locale map file will be found if you
specify a location for the units data file using either the -f
option 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 default main data file
to select CGS measurement systems. Currently supported systems
are esu, emu, gauss[ian], hlu, natural, natural-gauss, planck,
planck-red, hartree and si. The default is si.
DATA FILES
The units program uses four default data files: the main data file,
definitions.units; the atomic masses of the elements, elements.units;
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currency exchange rates, currency.units, and the US Consumer Price
Index, cpi.units. The last three files are loaded by means of
!include directives in the main file (see Database Command Syntax).
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
distribution. 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
locations 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
Windows installations) or C:\Program Files\GNU\units (for 32-bit
installations).
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 main 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 related 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 beginning with !utf8 and ending with !endutf8.
The non-ASCII definitions are loaded only if the platform and the
locale support UTF-8. Platform support is determined when units is
compiled; 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-
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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 ? commands.
Microsoft Windows supports UTF-8 in console applications running in
Windows Terminal; UTF-8 is not supported in applications running in
the older Windows Console Host-see Unicode Support 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 007F
hexadecimal correspond to ASCII encoding. Non-ASCII characters are
simply sequences of bytes, and have no special meanings; for
definitions in supplementary 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 character 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
... !endutf8 blocks-otherwise, they will be ignored.
Except for code examples, typeset material usually uses the Unicode
symbols for mathematical operators. To facilitate copying and pasting
from such sources, several typographical characters are converted to
the ASCII operators used in units: the figure dash (U+2012), minus (-;
U+2212), and en dash (; U+2013) are converted to the operator -; the
multiplication sign (x; U+00D7), N-ary times operator (U+2A09), dot
operator (; U+22C5), and middle dot (; U+00B7) are converted to the
operator *; the division sign ([u00F7]; U+00F7) is converted to the
operator /; and the fraction slash (U+2044) is converted to the
operator |.
Unicode Support on Windows
Microsoft Windows supports UTF-8 in console applications running in
Windows Terminal but not in applications running in the older Windows
Console Host. In Windows Terminal, the code page must be set to 65001
for UTF-8 to be enabled. With the UTF-8 code page, running units -V
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might show
GNU Units version 2.24 Without readline, with UTF-8, locale
English_United States (en_US)
Two values are shown for the locale: the first is the one returned by
the system; the second is the POSIX value to which the system value is
mapped.
With a different code page, the result might be
GNU Units version 2.24 Without readline, with UTF-8 (disabled), locale
English_United States (en_US) To enable UTF-8: set code page to 65001
If units is running in Windows Console Host, regardless of the code
page, the result might be
GNU Units version 2.24 Without readline, with UTF-8 (disabled), locale
English_United States (en_US) To enable UTF-8: run in Windows Terminal
and set code page to 65001
The UTF-8 code page can be set by running chcp 65001.
As of late 2024, the Windows build of units does not identify
characters-typically East Asian-that occupy more than one column, and
error messages involving those characters may not be properly aligned.
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
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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
history 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
several concurrent copies of units each one will save its new history
to the history file upon exit.
UPDATING CURRENCY EXCHANGE RATES AND Cdefinitions.units on a Windows
Cusystem.Exchange Rates units\
The units program databGNU\rency.unitsronnayUnix-like systemaor prices
Thisrprogramirequires)Pythonf3c(https://www.python.org).e Ther program
musttibesrunrwith/suitabledpermissionsotopwriteetheafile.urTonkeepnthe
ratessupdated/automatically,urunnitsusing ahcronrjobiton tae Unix-like
system,ior ahsimilarnschedulingtprogramyonvardifferent system.
Reliable free sources of currency exchange rates have been annoyingly
ephemeral. The program currently supports several sources:
* ExchangeRate-API.com (https://www.exchangerate-api.com).
The default currency server. Allows open access without an API
key, with unlimited API requests. Rates update once a day, the US
dollar (USD) is the default base currency, and you can choose your
base currency with the -b option described below. You can
optionally sign up for an API key to access paid benefits such as
faster data update rates.
* 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 others.
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* Fixer (https://fixer.io).
Registration for a free API key is required. 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 available. 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 currency is the US dollar; exchange rates are updated
hourly, and there is a limit of 1,000 API calls per month. Most
of these restrictions are eliminated or reduced with paid plans.
The default source is FloatRates; you can select a different one using
-s option described below.
Precious metals pricing is obtained from Packetizer
(www.packetizer.com). This site updates once per day.
US Consumer Price Index
The units program includes the US Consumer Price Index (CPI) published
by the US Bureau of Labor Statistics: specifically, the Consumer Price
Index for All Urban Consumers (CPI-U), not seasonally adjusted-Series
CUUR0000SA0. The units_cur command updates the CPI and saves the
result in cpi.units in the same location as currency.units. The data
are obtained via the BLS Public Data API
(https://www.bls.gov/developers/). These data update once a month.
When units_cur runs it will only attempt to update the CPI data if the
current CPI data file is from a previous month, or if the current date
is after the 18th of the month.
Invoking units_cur
You invoke units_cur like this:
units_cur [options] [currency_file] [cpi_file]
By default, the output is written to the default currency and CPI
files described above; this is usually what you want, because this is
where units looks for the files. If you wish, you can specify
different filenames on the command line and units_cur will write the
data to those files. If you give - for a 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.
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-v, --verbose
Give slightly more verbose output when attempting to update
currency exchange rates.
-s source, --source source
Specify the source for currency exchange rates; currently
supported values are floatrates (for FloatRates), eubank (for the
European Central Bank), fixer (for Fixer), and openexchangerates
(for open exchange rates); the last two require 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 currency sources that require it.
--blskey BLSkey
Set the US Bureau of Labor Statistics (BLS) key for fetching CPI
data. Without a BLS key you should be able to fetch the CPI data
exactly one time per day. If you want to use a key you must
request a personal key from BLS.
DATABASE COMMAND SYNTAX
unit definition
Define a regular unit.
prefix- definition
Define a prefix.
range=[y1,y2] definition(var) ; inverse(funcname)
funcname(var) noerror units=[in-units,out-
units] domain=[x1,x2]
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.
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!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
environment 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
environment 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/local/share/units/definitions.units - the standard units data
file
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AUTHOR
units was written by Adrian Mariano
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