See

metric system for general information about metric measurements from the French Revolution to the present, and for conversion factors and the use of everyday units.

See

International System of Units for a detailed history of the

SI, the scientific form of the metric system.

See

Standard SI prefixes for the prefixes that indicates multiples and submultiples of SI units.

See under the name of each unit, or the write-up below, for its definition.

The controlling body for the SI is the

BIPM,

*Bureau International des Poids et Mesures*. See their homepage www.bipm.fr for definitive information.

An **SI unit** is one of those with simple names: metre, second, ampere, watt, hertz, and so on; or any other formed by simple multiplication of them, such as the metre per second squared. The kilogram is the SI unit in this strict sense, not the gram.

A **base unit** is one of the seven independent units on which the system is based. The base units are:

metre m
kilogram kg
second s
ampere A
kelvin K
candela cd
mole mol

A **derived unit** is any other SI unit, and is dimensionally equal to some multiplication of base units. The derived units with special names are the following, with their equivalent in other units:

radian rad 1
steradian sr 1
hertz Hz 1/s
newton N m kg/s^2
pascal Pa N/m^2 kg/m s^2
joule J N m m^2 kg/s^2
watt W J/s m^2 kg/s^3
coulomb C A s
volt V W/A m^2 kg/s^3 A
farad F C/V s^4 A^2/m^2 kg
ohm Ω V/A m^2 kg/s^3 A^2
siemens S A/V s^3 A^2/m^2 kg
weber Wb V s m^2 kg/s^2 A
tesla T Wb/m^2 kg/s^2 A
henry H Wb/A m^2 kg/s^2 A^2
degree Celsius °C K
lumen lm cd sr cd
lux lx lm/m^2 cd/m^2
becquerel Bq 1/s
gray Gy J/kg m^2/s^2
sievert Sv J/kg m^2/s^2
katal kat mol/s
neper Np 1

A **unit within the SI** is any one of these or any other formed by adding prefixes, such as the terahertz, or the millimetre per second squared.

Names of units have lower-case initials (newton, kelvin, *not* Newton or Kelvin). Exception: degree Celsius. Units named after people have capital letters starting their symbols. These two rules apply regardless of prefixes. So a millisievert has the symbol mSv.

The symbols are mathematical symbols. They are not abbreviations. They do not take punctuation. They are separated from the preceding number. So 200 m long, not 200m long, and not 200 m. long. Exception: the symbol °C is attached to the number.

Multiplication may be indicated by spacing or a dot, so newton metre is N m or N·m or N.m -- and division may be indicated by the slash or by negative exponents, so metre per second squared is m/s^{2} or m s^{-2} or m.s ^{-2} etc. But they mustn't be joined together: not Nm or ms^{-2}.

The name of the unit of area is the metre squared, and that of volume is the metre cubed. The plural of metre squared is metres squared. If you have four of them, that's four metres squared. By convention, the name "square metre" is allowed as a synonym for "metre squared". Four square metres is identically equal to four metres squared, by definition.

There is a single international spelling for all the units: *metre*, *kilogram*, etc. But in practice local national spellings are also used, e.g. *meter* in USA, *mètre* in France, *metro* in Italy and Spain, *Meter* in German, etc.

The plural of siemens, lux, and hertz is unchanged. The other basic names take S: henrys. The plural of compound names is formed by pluralizing the first part: two degrees Celsius, two metres per second. The plural is used for any number over one: three kelvins, not three kelvin.

Although the kilogram is the base unit, prefixes are added as if gram was: so a thousand kilograms is not a kilokilogram but a megagram.

The radian and steradian were formerly considered to be supplementary units, midway between base and derived. They are now classed as derived units, and are dimensionless.

Another dimensionless unit recently added* is the neper. It is logarithmic in base e. So eight nepers is e times more than seven nepers. It can be used for any suitable logarithmic quantity.

The degree Celsius has also just been admitted as an SI unit. It can take prefixes, e.g. millidegree Celsius (m°C). (A long-obsolete name of the degree Celsius was the degree centigrade, and that of the kelvin was the degree Kelvin. Both these are still sometimes seen, unfortunately.)

There are a number of non-SI units that are accepted for continued use, such as the hour, minute, day, bel and decibel, electronvolt, nautical mile, litre, tonne, hectare, and so on. (The degree Celsius was formerly one of these.)

It is a fundamental principle of metrology that the unit of measurement does not tell you what is being measured. A quantity of 10 m could be a length, a displacement, or a distance; an amount of radiation in joules per kilogram could be either an absorbed dose or an absorbed dose equivalent, and the difference is so important they've been given different unit names, gray and sievert.

* I am not sure of the status of the katal, neper, and bel. The International Committee on Weights and Measures (CIPM) resolved in 1998 to adopt them (katal and neper as SI units, bel as acceptable for use with the SI). A resolution to be presented to the General Conference (CGPM) in 1999 was published. If this was adopted by the 1999 CGPM, they are official. I have not been able to find confirmation that this took place, however. Websites for national physics laboratories note that the CGPM has not yet adopted them, but these pages seem to pre-date the CGPM.

*Later.* The katal was adopted: www.bipm.fr/enus/2_Committees/cgpm21/resolutions.html