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 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/s2 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:

Definition of base SI units
Or "Where did they get that from, anyway?"

The International System of units is explained here. The following is merely a list of the seven primary international standards used to determine the base SI units. Note that with the exception of time/frequency, you are never ever going to see any of these standards. Ever.

Mass: measured in kilograms (kg);
Simply the mass of the international prototype. This prototype is a platinum-iridium mix (90%-10%) kept in a sealed vacuum at the International Bureau of Weights and Measures, Sèvres. It is kept in a vacuum because it was found to be gaining mass due to oxidisation effects.

Length: measured in metres (m);
Length has several definitions. The one most commonly bandied about is the 1983 definition, which is the distance light propagates in a vacuum in 1 / 299,792,458 seconds.
The previous definition from 1960 was "one metre is equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom".
The original definition of the metre was a ten-millionth part of the earth's meridian passing through Paris. This was represented by the distance between two lines engraved on a platinum-iridium bar kept in the International Bureau of Weights and Measures.

Time: measured in seconds (s)
One second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-135 atom.
This standard is the only one accessible to the general public, as it is broadcast on various radio stations, including WWV, WWVB and Radio Rugby. This can be received on specialist clocks and suchlike pieces of equipment.
Frequency is not a base SI unit, but can be derived from time as 1 / s. It is measured in hertz.
What's that? Universal Time? Another node, methinks..

Current: measured in amperes (A);
One ampere is that constant current which, if maintained in two straight parallel conductors of infinite length and negligible cross-section, spaced one metre apart in vacuum, will produce a force of 2x10-7 N per one metre between them. That simple, eh?
Alternately, you can simply get two long conductors, put a large current through them, balance edge effects and other errors and then measure the resulting force between them. When it is 2x10-7N/m, you should have one ampere flowing through your conductors, provided your instruments are precise enough. Thanks to vuo again.

Temperature: measured in kelvin (K);
One kelvin is the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water.
Note that Fahrenheit is not an SI unit. Celsius is a derived SI unit, and is also measured in kelvins, but starting from 273.15 K.

Luminous Intensity: measured in candela (cd);
The luminous intensity in the perpendicular direction of a surface of 1 / 600,000 m2 of a black body at the temperature of freezing platinum under a pressure of 101,325 N/m2.
An alternate definiton, straight from the Bureau International des Poids et Mesures, is "the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian."

Amount of substance: measured in moles (mol);
The amount of substance of a system which contains as many specified elementary particles as there are atoms in 0.012 kg of carbon-12.

Information from the IEE and the BIPM
Background from study notes
Correction to definition of ampere by vuo

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