Units: A Unit Conversion Program
1 Overview of
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.1
Temperature conversions require a special syntax.
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.
2 Android port of
The Android version serves as a front-end to the standard GNU
units program which has been recompiled with the Android Native Development Kit. Thus, much of the original functionality of
units is maintained.
units was originally written by Adrian Mariano.
The Android port works much like standard
units invoked in interactive mode (see below). Enter expressions for your known values in the You have entry box, and target conversion expressions in the You want entry box. Press the Convert button. Conversion and other information (formatted based on flags/options as described below) appear in the editable “Results” box.
Entry history: you can press your device’s Back key in the You have, You want, and Results boxes to cycle back through your entries. Press Back twice in rapid succession to make the “back” function behave as it ordinarily does. You can turn off this functionality viaPreferences if you don’t like it. The application keeps track of your previous 100 entries in each of the entry boxes, and maintains this history even if you leave the application or turn off your phone.
Flags/Options: with some exceptions, many of the original command-line options are available in the Android version. These options can be changed using the Flag/Options settings under the Preferences menu. For simplicity, the Android version sets the
--terse option initially by default. You can remove or change this option if it does not suit you.
Autocompletion: you can turn on autocompletion with the Autocomplete threshold preferences item. Select the number of characters entered that will trigger a drop-down list of recognized units of measures and functions beginning with those characters. Autocompletion is off by default.
You can also enter
search xxx (where
xxx is some string of characters) in the You have box to search for units of measures and functions. For example, to search for units of measure that contain the string “amp”, enter
search amp and then press Convert. The Results box will contain:
abamp abampere abampere 10 A amp ampere ampere A amphora 8 congii amphorae amphora intamp intampere intampere 0.999835 A statamp statampere statampere 10 A cm / s c thermalampere W/K
Share: this menu item allows you to select a sharing application (e.g., email, text message), and copy a
units result to that application for transmission. The applications available for sharing results depend on what you have installed on your device.
You can specify custom units files using the
-f command-line option (set in Preferences->Flags/Options). You can also edit and/or replace the
units.dat file in its default directory (this location may vary based on your platform):
If you use the
-f option, you have to specify the full path to where you installed your custom units file. For example, you could install your custom units file on your sdcard (a device’s optional memory card), and then use this file by including the following Preferences->Flags/Options:
-f /mnt/sdcard/myunits.dat -f ""
(Note the use of the
-f "" flag, which loads the default units file in addition to your custom units file – this is almost always what you want to do.) If you edit or use your own custom unit file, you should check it (
--check) using a non-Android version of
units before use with the Android port. A couple of custom data files are included with the distribution as examples. Using
-f /mnt/sdcard/gnuunits_med.dat -f ""
you can perform some limited medically-oriented conversions, such as converting between traditional (U.S.) and SI units of measure for various lab values::
You have: 78 mg/mL glucose You want: mmol/L Results: 4.3294849
If you use
-f /mnt/sdcard/gnuunits_fun.dat -f ""
you get access to some bonus definitions and conversions, for example, “2000 mockingbird = 2 kilomockingbird,” and others:
You have: 1 paradigm You want: Results: Definition: 4 nickels You have: 1 unit_of_suspense_in_mystery_novel You want: Results: Definition: 1 whod_unit You have: 1 gigolo You want: picolos Results: 1e+21 picolos You have: 2 megacycles You want: bicycles Results: 1e6 bicycles You have: 1 megaphone You want: microphones Results: 1e12 microphones You have: 1 milliHelen_Of_Troy You want: Results: Definition: 1 amount_of_face_that_can_launch_one_ship
(This file also allows use of the proposed
hella- SI prefix for values of 10^27. Using this prefix, you can determine that ”1 hellaHelen_Of_Troy” could launch 10^30 ships (“1000 hella ships”).
(Many of the conversions in
gnuunits_fun.dat are adapted from the “Q Files, a subsidiary of Evil Mad Scientist Laboratories (see
http://windell.oskay.net/humor/qqqfiles/quarks1.html), which in turn notes that the original information was taken from “The Bent of Tau Beta Pi, Spring 1988″).
License and warranty:
Be cautious when using this software. Conversion values have not been verified and tested rigorously, and may be outdated or inaccurate.
You can redistribute this software and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program (see end of this document). You can also find the license at
The documentation that follows is primarily the original
units documentation, edited lightly to reflect the Android port.
3 Interacting with
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 queries for You want. You should type the type to convert to. To convert to feet, you would type feet.
The answer will be displayed in two ways (note: the Android port sets the –terse option by default. Remove this option if you want more verbose output as indicated in the following examples). 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.
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
You have: 6 ohms You want: siemens reciprocal conversion * 0.16666667 / 6
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
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.
Some named units are treated as dimensionless in some situations. These include the radian and steradian. These units will be treated as equal to 1 in units conversions. Power is equal to torque times angular velocity. This conversion can only be performed if the radian is dimensionless.
You have: (14 ft lbf) (12 radians/sec) You want: watts * 227.77742 / 0.0043902509
Note that named dimensionaless units are not treated as dimensionless in other contexts. They cannot be used as exponents so for example, meter^radian is not allowed. If you want a list of options you can type ? at the You want: prompt. The program will display a list of named units which are conformable with the unit that you entered at the You have: prompt above. Note that conformable unit combinations will not appear on this list.
4 Unit expressions
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. An exponent like 2^3^2 is evaluated right to left. The ^ operator has the second highest precedence.
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, or an asterisk (*). If
units is invoked with the –product option then the hyphen (-) also acts as a multiplication operator. 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 the highest precedence so the square root of two thirds could be written 2|3^1|2.
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, as will micro microfarad.. 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. You may also wish to use
units as a calculator that keeps track of units. 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
Historically - has been used for products of units, which complicates its iterpretation in
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. This behavior can be altered using the –product option which causes
units to treat the binary - operator as a product operator. Note that when - is a multiplication operator it has the same precedence as *, but when - is a subtraction operator it has the lower precedence as the addition operator.
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. The + character sometimes appears in exponents like 3.43e+8. This leads to an ambiguity in an expression like 3e+2 yC. The unit e is a small unit of charge, so this can be regarded as equivalent to (3e+2) yC or (3 e)+(2 yC). This ambiguity is 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
Temperature Conversion Example
Nonlinear units are represented using functional notation. They make possible nonlinear unit conversions such temperature. This is different from the linear units that convert temperature differences. Note the difference below. The absolute temperature conversions are handled by units starting with temp, and you must use functional notation. The temperature differences 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 which indicates that x should have units of tempF attached to it. See Nonlinear units. The first conversion shows that if it’s 45 degrees Fahrehneit outside it’s 7.2 degrees Celsius. The second conversions indicates that a change of 45 degrees Fahrenheit corresponds to a change of 25 degrees Celsius. Some other examples of nonlinears units are ring size and wire gauge. There are numerous different gauges and ring sizes. See the units database for more details. Note that wire gauges with multiple zeroes are signified using negative numbers where two zeroes is -1. Alternatively, you can use the synonyms g00, g000, and so on that are defined in the units database.
You have: wiregauge(11) You want: inches * 0.090742002 / 11.020255 You have: brwiregauge(g00) You want: inches * 0.348 / 2.8735632 You have: 1 mm You want: wiregauge 18.201919
The program uses 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 will need to be quoted to protect them from shell interpretation and to group them into two arguments. See Command line use.
The following options allow you to read in an alternative units file or change the output format:
unitsto load the units file
filenameis the empty string (-f ”) then the default units file will be loaded. This enables you to load the default file plus a personal units file. Up to 25 units files may be specified on the command line.
unitswill 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.
unitswill print still print the reciprocal conversion line.
unitsfrom another program so that the output is easy to parse. This option has the combined effect of these options: –strict –quiet –one-line –compact.
6 Unit definitions
The conversion information is read from a units data file which is called units.dat. 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.
7 Defining new units
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. A file can be included by giving the command !include followed by the file’s name. The file will be sought in the same directory as the parent file unless a full path is given. Unit names must not contain any of the operator characters +, -, *, /, |, ^ or the parentheses. They cannot begin with a digit or a decimal point (.), nor can they end with a digit (except for zero). Be careful to define new units in terms of old ones so that a reduction leads to the primitive units, which are marked with ! characters. Dimensionless units are indicated by using the string !dimensionless for the unit definition. When adding new units, be sure to use the -c option to check that the new units reduce properly. If you create a loop in the units 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. If you define any units which contain + characters, 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. To compute the difference of foo and bar write foo+(-bar) or even foo+-bar. 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 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 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.
8 Defining nonlinear units
Some units conversions of interest are nonlinear; for example, temperature conversions between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conversions 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 which convert to and from linear units in the data file, so that an eventual conversion to primitive units is possible. Here is an example nonlinear unit definition:
tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
A nonlinear unit definition comprises a unit name, a dummy parameter name, two functions, and two corresponding units. The functions tell
units how to convert to and from the new unit. In order to produce valid results, the arguments of these functions need to have the correct dimensions. To facilitate error checking, you may specify the dimensions.
The definition begins with the unit name followed immediately (with no spaces) by a ( character. In parentheses is the name of the parameter. Next is an optional specification of the units required by the functions in this definition. In the example above, the tempF function requires an input argument conformable with 1. For normal nonlinear units definitions the forward function will always take a dimensionless argument. The inverse function requires an input argument conformable with K. In general the inverse function will need units that match the quantity measured by your nonlinear unit. The sole purpose of the expression in brackets to enable
units to perform error checking on function arguments. 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.
In order to make conversions to Fahrenheit possible, 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, but then conversions to the unit will be impossible. If the inverse is omitted then 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 print an error if it is not valid there, but this is not a guarantee that your inverse is correct.
If you wish to make synonyms for nonlinear units, you still need to define 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) [1;K] tempF(x); ~tempF(fahrenheit)
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. Note that this definition requires a length as input and produces an area as output, as indicated by the specification in brackets.
circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)
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 illegal; instead write foo[kg*meters]. The definition of the unit consists of a list of pairs optionally separated by commas. This list defines a function for converting from the piecewise linear unit to linear units. The first item in each pair is the function argument; the second item is the value of the function at that argument (in the units specified in brackets). In this example, we define zincgauge at five points. For example, we set zincgauge(1) equal to 0.002 in. Definitions like this may be more readable if written using continuation characters as
zincgauge[in] \ 1 0.002 \ 10 0.02 \ 15 0.04 \ 19 0.06 \ 23 0.1
With the 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 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. The –check option will print a warning if a non-monotonic piecewise linear unit is encountered.
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A “contributor” is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s “contributor version”. A contributor’s “essential patent claims” are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, “control” includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a “patent license” is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To “grant” such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.
If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.
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The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
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If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.> Copyright (C) <year> <name of author> This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author> This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details.
The hypothetical commands `show w’ and `show c’ should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an “about box”. You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyright disclaimer” for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see <http://www.gnu.org/licenses/>. The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read <http://www.gnu.org/philosophy/why-not-lgpl.html>.
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
units): Invoking units
- addition of units: Unit expressions
- changing nonlinear unit definitions: Nonlinear units
- changing units definitions: Defining new units
- command line options: Invoking units
- command line unit conversion: Command line use
- defining nonlinear units: Nonlinear units
- defining units: Defining new units
- dimensionless units: Defining new units
- dimensionless units: Interactive use
- division of numbers: Unit expressions
- division of units: Unit expressions
- environment variables: Environment vars
- fractions: Unit expressions
- functions of units: Nonlinear units
- functions, built in: Unit expressions
- include files: Defining new units
- incompatible units: Interactive use
- interactive use: Interactive use
- invoking units: Invoking units
- linear interpolation: Nonlinear units
- LOCALE environment variable: Environment vars
- localization: Localization
- multiplication of units: Unit expressions
- non-conformable units: Interactive use
- non-interactive unit conversion: Command line use
- nonlinear unit conversions: Nonlinear units
- nonlinear units, redefinition of: Nonlinear units
- PAGER environment variable: Environment vars
- piecewise linear units: Nonlinear units
- powers: Unit expressions
- products: Unit expressions
- readline, use with
units: Readline support
- reciprocal conversion: Interactive use
- roots: Unit expressions
- square roots: Unit expressions
- strict conversion: Interactive use
- sums of units: Unit expressions
- temperature conversions: Unit expressions
- unit definitions: Unit definitions
- unit expressions: Unit expressions
- unit name completion: Readline support
- units functions: Nonlinear units
- units, piecewise linear: Nonlinear units
- units, redefinition of: Defining new units
- UNITSFILE environment variable: Environment vars
- verbose output: Interactive use
 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.
Copyright © 2010-2011 Keith Flower, and 2004-2006 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved.