International System of Units

The International System of Units (commonly abbreviated to SI from its French name Système Internationale d'Unités) is the international system of units of measurement established under the Metre Convention. It is based on seven "base units", with a potentially limitless number of "derived units".

The definitions of the base units and other fundamental aspects of the system are approved by the General Conference on Weights and Measures (CGPM), a diplomatic conference which meets every four years, based on recommendations from the International Committee for Weights and Measures (CIPM). The CIPM is also charged with agreeing many of the technical details of the system, such as the methods of realization of units and other details of conventional measurement techniques.

Base units

Unit name	Unit symbol	Physical quantity	Notes
metre	m	length
kilogram	kg	mass
second	s	time
ampere	A	electric current
kelvin	K	thermodynamic temperature
candela	cd	luminous intensity
mole	mol	amount of substance

The six original base units were selected in 1956 by the 9th CGPM (the mole was added in 1972). They represent a conventional choice: the choice made in the International System of Units is not the only possible choice of base units, nor is there any physical significance that the ampere was chosen as the base for electromagnetic units rather than, e.g., the coulomb.

The inclusion of the candela as a base unit is for both historical and practical reasons. There is an obvious technical need to classify many everyday light sources on the basis of their effect on the human eye. This is acheived by multiplying the radient intensity (measured in watts per steradian) by a standard luminosity function that models the response of the human eye: the result is the candela, which is also the base for a series of other luminosity units.

Derived units

A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second (m s⁻¹) as a unit of speed. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared (m s⁻²) is the coherent SI derived unit for acceleration, whereas the centimetre per second squared is a valid derived SI unit but is not coherent because of the factor of 10⁻² implied by the prefix "centi" (see below).

The number of possible derived units is without practical limit, but certain coherent derived units have special names and symbols within the SI.

Name	Symbol	Physical quantity	Definition	Notes
becquerel	Bq	activity	s−1
coulomb	C	electric charge	s A
farad	F	capacitance	m−2 kg−1 s4 A2 = C/V
gray	Gy	absorbed dose	m2 s−2 = J/kg
henry	H	inductance	m2 kg s−2 A−2 = Wb/A
hertz	Hz	frequency	s−1
joule	J	energy work amount of heat	m2 kg s−2 = N m
katal	kat	catalytic activity	s−1 mol
lumen	lm	luminous flux	cd sr = cd
lux	lx	illuminance	m−2 cd = lm/m2
newton	N	force	m kg s−2
ohm	Ω	electric resistance	m2 kg s−3 A−2 = V/A
pascal	Pa	pressure stress	m−1 kg s−2 = N/m2
siemens	S	electric conductance	m−2 kg−1 s3 A2 = A/V
sievert	Sv	dose equivalent	m2 s−2 = J/kg
tesla	T	magnetic flux density	kg s−2 A−1 = Wb/m2
volt	V	electric potential difference electromotive force	m2 kg s−3 A−1 = W/A = J/C
watt	W	power radiant flux	m2 kg s−3 = J/s
weber	Wb	magnetic flux	m2 kg s−2 A−1 = V s
degree Celsius	°C	Celsius temperature	K
radian	rad	plane angle	m/m = 1
steradian	sr	solid angle	m2/m2 = 1

Multiples and submultiples

Multiples				Submultiples
Symbol	Prefix				Prefix	Symbol
da	deca	101		10−1	deci	d
h	hecto	102		10−2	centi	c
k	kilo	103		10−3	milli	m
M	mega	106		10−6	micro	µ
G	giga	109		10−9	nano	n
T	tera	1012		10−12	pico	p
P	peta	1015		10−15	femto	f
E	exa	1018		10−18	atto	a
Z	zetta	1021		10−21	zepto	z
Y	yotta	1024		10−24	yocto	y

Units used with the SI

There are several sets of units which are not SI units but which have some degree of acceptance for use with the International System of Units.

Common units with exact conversion factors

Name	Symbol	Physical quantity	Value	Notes
minute	min	time	1 min = 60 s
hour	h	time	1 h = 60 min = 3600 s
day	d	time	1 d = 86 400 s
degree	°	plane angle	1° = (π/180) rad
minute	′	plane angle	1′ = (1/60)° = (π/10 800) rad
second	″	plane angle	1″ = (1/60)′ = (π/648 000) rad
hectare	ha	area	1 ha = 1 hm2 = 0.01 km2 = 104 m2
litre	L, l	volume	1 L = 1 l = 1 dm3 = 103 cm3 = 10−3 m3
tonne	t	mass	1 t = 1000 kg

Units with empirical conversion factors

Name	Symbol	Physical quantity	Value	Notes
electronvolt	eV	energy	1 eV = 1.602 176 487(40) × 10−19 J
dalton	Da	mass	1 Da = 1 u = 1.660 538 782(83) × 10−27 kg
atomic mass unit	u
astronomical unit	ua	length	1 ua = 149 597 870 700(3) m

External links

• International Bureau of Weights and Measures (BIPM)