COS - Standards Used
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Units of Measurement
|mole||mol||amount of substance|
A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.
The International Organisation for Standardisation
document ISO 31 contains recommendations for the use of the
International System of Units; together with IEC 60027 for
A new standard ISO 80000 is now in progress to combine both standards in a joint standard in which the quantities and equations used with SI are to be referred as the International System of Quantities (ISQ).
It is a widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide. In most countries, the notations used in mathematics and science textbooks at schools and universities follow closely the guidelines given by these standards.
Very few of the above prefixes appear in scientific work, as scientific notation of some value to a power of 10 is normally used with a base unit, example 5.8 x 109 grams would not be expressed as 5.8 gigagram but 5.8 x 106 kg. Mega, giga and tera are used more in computing where the they are not exact anyway - a kilobyte being 1024 bytes rather than a 1000 bytes, but we will not start going down that road here. In Astronomy the largest measurements are distances and these can be in units based on special multiples of the base distance unit, e.g. light year, parsec, astronomical unit. This is mainly because of the large numbers involved and some of these units fit neatly into equations with other derived units to produce meaningful results.
|Name||Symbol||Quantity||Expression in terms of other units||Expression in terms of SI base units|
|joule||J||energy, work, heat||Nm = CV = Ws||m2kgs-2|
|watt||W||power, radiant flux, luminosity||Js-1 = VA||m2kgs-3|
|volt||V||voltage, electrical potential difference, electromotive force||W/A = J/C||m2kgs-3A-1|
|tesla||T||magnetic field||Vs/m2 = Wb/m2 = N/(Am)||kgs-2A-1|
|henry||H||inductance||Vs/A = Wb/A||m2kgs-2A-2|
|degree Celsius||C||temperature||K - 273.15||K|
Compound units derived from SI units
|Name||Symbol||Quantity||Expression in terms
of SI base units
|metre per second||m/s||speed, velocity||ms-1|
|cubic metre per second||m3/s||volumetric flow||m3s-1|
|metre per second squared||m/s2||acceleration||ms-2|
|metre per second cubed||m/s3||jerk||ms-3|
|metre per quartic second||m/s4||snap||ms-4|
|radian per second||rad/s||angular velocity||s-1|
|newton second||Ns||momentum, impulse||kgms-1|
|newton metre second||Nms||angular momentum||kgm2s-1|
|newton metre||Nm||torque, moment of force||kgm2s-2|
|kilogram per cubic metre||kg/m3||density, mass density||kgm-3|
|cubic metre per kilogram||m3/kg||specific volume||kg-1m3|
|mole per cubic metre||mol/m3||amount (-of-substance) concentration||m-3mol|
|cubic metre per mole||m3/mol||molar volume||m3mol-1|
|joule per kelvin||J/K||heat capacity, entropy||kgm2s-2K-1|
|joule per kelvin mole||J/(Kmol)||molar heat capacity, molar entropy||kgm2s-2K-1mol-1|
|joule per kilogram kelvin||J/(Kkg)||specific heat capacity, specific entropy||m2s-2K-1|
|joule per mole||J/mol||molar energy||kgm2s-2mol-1|
|joule per kilogram||J/kg||specific energy||m2s-2|
|joule per cubic metre||J/m3||energy density||kgm-1s-2|
|newton per metre||N/m = J/m2||surface tension||kgs-2|
|watt per square metre||W/m2||heat flux density, irradiance||kgs-3|
|watt per metre kelvin||W/(mK)||thermal conductivity||kgms-3K-1|
|square metre per second||m2/s||kinematic viscosity, diffusion coefficient||m2s-1|
|pascal second||Pas = Ns/m2||dynamic viscosity||kgm-1s-1|
|siemens per metre||S/m||conductivity||kg-1m-3s3A2|
|siemens square metre per mole||Sm2/mol||molar conductivity||kg-1s3mol-1A2|
|volt per metre||V/m||electric field strength||kgms-3A-1|
|ampere per metre||A/m||magnetic field strength||Am-1|
|candela per square metre||cd/m2||luminance||cdm-2|
The following units are not SI units but are "accepted for use with the International System."
|Name||Symbol||Quantity||Equivalent SI unit|
|minute||min||time (multiple unit)||1 min = 60 s|
|hour||h||time (multiple unit)||1 h = 60 min = 3600 s|
|day||d||time (multiple unit)||1 d = 24 h = 1440 min = 86400 s|
|degree of arc||angle (non unitary unit)||1 = (p/180) rad|
|minute of arc||'||angle (non unitary unit)||1' = (1/60) = (p/10800) rad|
|second of arc||?||angle (non unitary unit)||1? = (1/60)' = (1/3600) = (p/648000) rad|
|square degree||deg or sq.deg.||solid angle||1 deg = (p/180) sr. This unit is mostly used in astronomy and optic (its usage is strongly discouraged in all other domains, including in cartography). The whole sphere covers a solid angle (seen from its centre) of (129600/p) deg (approx. 41252.961 deg) and is the solid angle covered by a conic section of a sphere, whose opening apex is exactly 360 (note that the measure of a solid angle in square degrees is not proportional (and does not vary polynomially with) the measure of the associated planar angle in degrees of opening of its associated cone. In cartography, you can't simply multiply a difference of longitudes and a difference of latitudes, both expressed in degrees to get an exact measure of a solid angle in square degrees (this will just be an approximation only if these differences are very small, below one minute of arc each, and the covered area is very near the equator, i.e. at very low latitudes where the small area will be nearly rectangular instead of being nearly trapezoidal in median latitudes, or nearly a disc sector near the poles).|
|litre||l or L||volume (simple decimal multiple unit)||1 dm3 = 0.001 m3|
|tonne||t||mass (simple decimal multiple unit)||1 t = 103 kg = 1 Mg|
|Name||Symbol||Quantity||Equivalent SI unit|
|electronvolt||eV||energy||1 eV = 1.60217733 (49) 10-19 J|
|atomic mass unit||u||mass||1 u = 1.6605402 (10) 10-27 kg|
|astronomical unit||AU||length||1 AU = 1.49597870691 (30) 1011 m|
|Name||Symbol||Quantity||Equivalent SI unit|
|ngstrm, angstrom||length||1 = 0.1 nm = 10-10 m|
|bar||bar||pressure||1 bar = 105 Pa|
|millibar||mbar||pressure||1 mbar = 1 hPa = 100 Pa (was used in atmospheric meteorology, the preferred unit is now the hectopascal)|
|atmosphere||atm||pressure||1 atm = 1013.25 mbar = 1013.25 hPa] = 1.01325105 Pa (commonly used in atmospheric meteorology, in oceanology and for pressures within liquids, or in the industry for pressures within containers of liquified gas)|
Values for constants in calculations follow
standards recommended by the National Physical Laboratory (www.npl.co.uk)
and Kaye & Laby Online is a valuable resource.
These are sourced from CODATA Task Group on Fundamental Constants (Committee on Data for Science and Technology)
The latest values are available from the CODATA fundamental constants page at the American National Institute of Standards and Technology's web site (NIST)