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12.3 Predefined Units

The definitions of many units have changed over the years. For example, the meter was originally defined in 1791 as one ten-millionth of the distance from the equator to the north pole. In order to be more precise, the definition was adjusted several times, and now a meter is defined as the distance that light will travel in a vacuum in 1/299792458 of a second; consequently, the speed of light in a vacuum is exactly 299792458 m/s. Many other units have been redefined in terms of fundamental physical processes; a second, for example, is currently defined as 9192631770 periods of a certain radiation related to the cesium-133 atom. The only SI unit that is not based on a fundamental physical process (although there are efforts to change this) is the kilogram, which was originally defined as the mass of one liter of water, but is now defined as the mass of the International Prototype Kilogram (IPK), a cylinder of platinum-iridium kept at the Bureau International des Poids et Mesures in Sèvres, France. (There are several copies of the IPK throughout the world.) The British imperial units, once defined in terms of physical objects, were redefined in 1963 in terms of SI units. The US customary units, which were the same as British units until the British imperial system was created in 1824, were also defined in terms of the SI units in 1893. Because of these redefinitions, conversions between metric, British Imperial, and US customary units can often be done precisely.

Since the exact definitions of many kinds of units have evolved over the years, and since certain countries sometimes have local differences in their definitions, it is a good idea to examine Calc's definition of a unit before depending on its exact value. For example, there are three different units for gallons, corresponding to the US (gal), Canadian (galC), and British (galUK) definitions. Also, note that oz is a standard ounce of mass, ozt is a Troy ounce, and ozfl is a fluid ounce.

The temperature units corresponding to degrees Kelvin and Centigrade (Celsius) are the same in this table, since most units commands treat temperatures as being relative. The calc-convert-temperature command has special rules for handling the different absolute magnitudes of the various temperature scales.

The unit of volume “liters” can be referred to by either the lower-case l or the upper-case L.

The unit A stands for Amperes; the name Ang is used for Angstroms.

The unit pt stands for pints; the name point stands for a typographical point, defined by ‘72 point = 1 in’. This is slightly different than the point defined by the American Typefounder's Association in 1886, but the point used by Calc has become standard largely due to its use by the PostScript page description language. There is also texpt, which stands for a printer's point as defined by the TeX typesetting system: ‘72.27 texpt = 1 in’. Other units used by TeX are available; they are texpc (a pica), texbp (a “big point”, equal to a standard point which is larger than the point used by TeX), texdd (a Didot point), texcc (a Cicero) and texsp (a scaled TeX point, all dimensions representable in TeX are multiples of this value).

When Calc is using the TeX or LaTeX language mode (see TeX and LaTeX Language Modes), the TeX specific unit names will not use the ‘tex’ prefix; the unit name for a TeX point will be ‘pt’ instead of ‘texpt’, for example. To avoid conflicts, the unit names for pint and parsec will simply be ‘pint’ and ‘parsec’ instead of ‘pt’ and ‘pc’.

The unit e stands for the elementary (electron) unit of charge; because algebra command could mistake this for the special constant ‘e’, Calc provides the alternate unit name ech which is preferable to e.

The name g stands for one gram of mass; there is also gf, one gram of force. (Likewise for lb, pounds, and lbf.) Meanwhile, one “‘g’” of acceleration is denoted ga.

The unit ton is a U.S. ton of ‘2000 lb’, and t is a metric ton of ‘1000 kg’.

The names s (or sec) and min refer to units of time; arcsec and arcmin are units of angle.

Some “units” are really physical constants; for example, c represents the speed of light, and h represents Planck's constant. You can use these just like other units: converting ‘.5 c’ to ‘m/s’ expresses one-half the speed of light in meters per second. You can also use this merely as a handy reference; the u g command gets the definition of one of these constants in its normal terms, and u b expresses the definition in base units.

Two units, pi and alpha (the fine structure constant, approximately 1/137) are dimensionless. The units simplification commands simply treat these names as equivalent to their corresponding values. However you can, for example, use u c to convert a pure number into multiples of the fine structure constant, or u b to convert this back into a pure number. (When u c prompts for the “old units,” just enter a blank line to signify that the value really is unitless.)