units Version 1.69
units
The units program converts quantities expressed in various scales
to their equivalents in other scales. The units program can
handle multiplicative scale changes as well as nonlinear
conversions such as Fahrenheit to Celsius.
The units are defined in an external data file. You can use the extensive data file that comes with this program, or you can provide your own data file to suit your needs.
You can use the program interactively with prompts, or you can use it from the command line.
unitsTo invoke units for interactive use, type units at your shell prompt. The program will print something like this:
2131 units, 53 prefixes, 24 functions
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 type of units you want to convert
to. To convert to feet, you would type feet.
The answer 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 .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 .03048 dekameters.
But the number given the other direction is inexact.
If you try to 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 which measure reciprocal
dimensions, then units will display the conversion results with an extra
note indicating that reciprocal conversion has been done:
You have: 6 ohms
You want: siemens
reciprocal conversion
* 0.16666667
/ 6
Reciprocal conversion can be suppressed by using the `--strict' option. As usual, use the `--verbose' option to get more comprehensible output:
You have: tex
You want: typp
reciprocal conversion
1 / tex = 496.05465 typp
1 / tex = (1 / 0.0020159069) typp
You have: 20 mph
You want: sec/mile
reciprocal conversion
1 / 20 mph = 180 sec/mile
1 / 20 mph = (1 / 0.0055555556) sec/mile
If you enter incompatible unit types, the units program will
print a message indicating that the units are not conformable and
it will 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 return 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.
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 units expression, and type the new units you want.
You will probably need to protect the units expressions from
interpretation by the shell using single quote characters.
If you type
units '2 liters' 'quarts'
then units will print
* 2.1133764
/ 0.47317647
and then exit. The output tells you that 2 liters is about 2.1 quarts, or alternatively that a quart is about 0.47 times 2 liters.
If the conversion is successful, then units will return success (0)
to the calling environment. If units is given non-conformable
units to convert, it will print a message giving the reduced form of
each unit and it will return failure (nonzero) to the calling environment.
When units is invoked with only one argument, it will print out
the definition of the specified unit. It will return failure if the
unit is not defined and success if the unit is defined.
In order to enter more complicated units or fractions, you will need to use operations such as powers, products and division. Powers of units can be specified using the `^' character as shown in the following example, or by simple concatenation: `cm3' is equivalent to `cm^3'. If the exponent is more than one digit, the `^' is required.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfoot-arabictradepound-force
You want: ft lbf
* 0.7296
/ 1.370614
Multiplication of units can be specified by using spaces, a hyphen (`-') or an asterisk (`*'). Division of units is indicated by the slash (`/') or by `per'.
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
Multiplication has a higher precedence than division and is evaluated left to right, so `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 .5/meter, which is probably not what you would intend if you entered that expression. You can indicate division of numbers with the vertical dash (`|'). This operator has very high precedence, higher even than the exponent operator.
You have: 1|2 inch
You want: cm
* 1.27
/ 0.78740157
Parentheses can be used for grouping as desired.
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
Prefixes are defined separately from base units. In order to get centimeters, the units database defines `centi-' and `c-' as prefixes. Prefixes can appear alone with no unit following them. An exponent applies only to the immediately preceding unit and its prefix so that `cm^3' or `centimeter^3' refer to cubic centimeters but `centi-meter^3' refers to hundredths of cubic meters. Only one prefix is permitted per unit, so `micromicrofarad' will fail, but `micro-microfarad' will work.
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 which 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 dollars^5.
Outside of the SI system, it is often desirable to add values of different units together. Sums of conformable units are written 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 which are added together must reduce to identical expressions in primitive units, or an error message will be displayed:
You have: 12 printerspoint + 4 heredium
^
Illegal sum of non-conformable units
Because `-' is used for products, it cannot also be used to form differences of units. If a `-' appears after `(' or after `+' then it will act as a negation operator. So you can compute 20 degrees minus 12 minutes by entering `20 degrees + -12 arcmin'. The `+' character is sometimes used in exponents like `3.43e+8'. This leads to an ambiguity in an expression like `3e+2 yC'. The unit `e' is a small unit of charge, so this can be regarded as equivalent to `(3e+2) yC' or `(3 e)+(2 yC)'. This ambiguity is resolved by always interpreting `+' as part of an exponent if possible.
Several built in functions are provided: `sin', `cos', `tan', `ln', `log', `log2', `exp', `acos', `atan' and `asin'. 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.
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. Higher roots can be obtained 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
Functions can also be used for nonlinear unit conversions such as Fahrenheit to Celsius:
You have: tempF(45)
You want: tempC
7.2222222
Inverse funtions can be obtained with the `~' operator, so the same temperature conversion could be done as:
You have: ~tempC(tempF(45))
You want:
Definition: 7.2222222
units
You invoke units like this:
units options [from-unit [to-unit]]
If the from-unit and to-unit are omitted, then the program
will use interactive prompts to determine which conversions to perform.
See section Interacting with units.
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 will need
to be quoted to protect them from shell interpretation and to group
them into two arguments. See section Using units non-interactively.
The following options allow you to read in an alternative units file, check your units file, or change the output format:
units hangs, then the last unit to be printed has a bad
definition.
units.
The conversion information is read from a units data file which
is called `units.dat' and is probably located in
the `/usr/local/share' directory.
If you invoke units with the `-V' option, it will print
the location of this file.
The default
file includes definitions for all familiar units, abbreviations and
metric prefixes. It also includes many obscure or archaic units.
Many constants of nature are defined, including these:
pi ratio of circumference to diameter c speed of light e charge on an electron force acceleration of gravity mole Avogadro's number water pressure per unit height of water Hg pressure per unit height of mercury au astronomical unit k Boltzman's constant mu0 permeability of vacuum epsilon0 permitivity of vacuum G Gravitational constant mach speed of sound
The database includes atomic masses for all of the elements and 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.
The unit `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'. British capacity units that differ from their US counterparts, such as the British Imperial gallon, are prefixed with `br'. Currency is prefixed with its country name: `belgiumfranc', `britainpound'.
The US Survey foot, yard, and mile can be obtained by using the `US' prefix. These units differ slightly from the international length units. They were in general use until 1959, and are still used for geographic surveys. The acre is officially defined in terms of the US Survey foot. If you want an acre defined according to the international foot, use `intacre'. The difference between these units is about 4 parts per million. The British also used a slightly different length measure before 1959. These can be obtained with the prefix `UK'.
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' or a trailing `es'. If that fails, units
will check for a prefix.
All of the standard metric prefixes are defined.
To find out what units and prefixes are available, read the standard units data file.
All of the units and prefixes that units can convert are defined
in the units data file. If you want to add your own units, you can
supply
your own file.
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.
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.
When adding new units, be sure to use the `-c' option to check that
the new units reduce properly. If you define any units which contain
`+' characters, carefully check them because the `-c' option
will not catch non-conformable sums.
If you create a loop in the units definitions, then units will
hang when invoked with the `-c' options. You will need to
use the `--check-verbose' option which prints out each unit as it
checks them. The program will still hang, but the last unit printed
will be the unit which caused the infinite loop.
Here is an example of a short units file that defines some basic units:
m ! # The meter is a primitive unit sec ! # The second is a 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 0.0254 m # Inch defined in terms of meters ft 12 inches # The foot defined in terms of inches mile 5280 ft # And the mile
A unit which 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'.
Functions can be useful for performing nonlinear unit conversions. For example, temperature conversions between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conversions factors. In order to make nonlinear conversions available, you must specify a function definition along with its inverse in the units database.
Here is an example function definition:
tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
A function definition begins with the function name followed immediately
(with no spaces) by a `(' character. In parentheses is the name of
the parameter. Next is an optional specification of what units this
function requires. In the example above, the `tempF' function
requires an input argument conformable with `1'. The inverse
function requires an input argument conformable with `K'. The sole
purpose of the expression in brackets to enable units to perform
error checking on function arguments.
Next the function definition appears. In the example above, the `tempF' function is defined by
tempF(x) = (x+(-32)) degF + stdtemp
This means that the `tempF' function regards its argument as a temperature in Fahrenheit and converts it to an absolute temperature.
In order to make conversions to Fahrenheit possible, you must also specify the inverse. 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, but then conversions to the unit will be impossible.
Sometimes you may be interested in a piecewise linear unit such as wire gauge. Piecewise linear functions can be defined by specifying the function's value on a list of points. The function will be evaluated using 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 function. The definition of such a function is indicated by the embedded `[' character. After the bracket, you should indicate the units to be attached to this function. No spaces can appear before the `]' character, so a definition like `foo[kg meters]' is illegal; instead write `foo[kg*meters]'. The definition of the function consists of a list of pairs optionally separated by commas. 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 line this may be more readable if written using continuation characters as
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1
With the preceeding 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 function that is not strictly
monotonic, then the inverse will not be well defined. If the inverse is
requested for such a function, units will return the smallest
inverse.
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 the 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 the
? key then units will display a list of all the units which
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 unitname, you can hit the tab key
and units will provide the rest of the unit name. If units
beeps, it means that there is no unique completion. Pressing the tab
key a second time will print the list of all completions.
units
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