SI derived unit

The International System of Units (SI) specifies a set of seven base units from which all other units of measurement are formed. These other units are called SI derived units and are also considered part of the standard. SI units was after the French Le Système International d'Unités which opted for a universal, unified and self-consistent system of measurement units based on the MKS (metre-kilogram-second) system.

The names of SI units are always written in lowercase. The unit symbols of units named after persons, however, are always spelled with an initial capital letter (e.g., the symbol of hertz is Hz; but metre becomes m).

Derived units with special names

Base units can be combined to derive units of measurement for other quantities. In addition to the two dimensionless derived units radian (rad) and steradian (sr), 20 other derived units have special names.

Named units derived from SI base units

Name	Symbol	Quantity	Expression in terms of other units	Expression in terms of SI base units
hertz	Hz	frequency	1/s	s-1
radian	rad	angle	m·m-1	dimensionless
steradian	sr	solid angle	m2·m-2	dimensionless
newton	N	force, weight	kg·m/s2	kg·m·s−2
pascal	Pa	pressure, stress	N/m2	m−1·kg·s−2
joule	J	energy, work, heat	N·m = C·V = W·s	m2·kg·s−2
watt	W	power, radiant flux	J/s = V·A	m2·kg·s−3
coulomb	C	electric charge or quantity of electricity	s·A	s·A
volt	V	voltage, electrical potential difference, electromotive force	W/A = J/C	m2·kg·s−3·A−1
farad	F	electric capacitance	C/V	m−2·kg−1·s4·A2
ohm	Ω	electric resistance, impedance, reactance	V/A	m2·kg·s−3·A−2
siemens	S	electrical conductance	1/Ω	m−2·kg−1·s3·A2
weber	Wb	magnetic flux	J/A	m2·kg·s−2·A−1
tesla	T	magnetic field strength, magnetic flux density	V·s/m2 = Wb/m2 = N/(A·m)	kg·s−2·A−1
henry	H	inductance	V·s/A = Wb/A	m2·kg·s−2·A−2
Celsius	°C	Celsius temperature	K − 273.15	K − 273.15
lumen	lm	luminous flux	lx·m2	cd·sr
lux	lx	illuminance	lm/m2	m−2·cd·sr
becquerel	Bq	radioactivity (decays per unit time)	1/s	s−1
gray	Gy	absorbed dose (of ionizing radiation)	J/kg	m2·s−2
sievert	Sv	equivalent dose (of ionizing radiation)	J/kg	m2·s−2
katal	kat	catalytic activity	mol/s	s−1·mol

Other common units, such as the litre, are not SI units, but are accepted for use with SI (cf. non-SI units accepted for use with SI).

Supplementary units

Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned and the units were grouped as derived units.

See also

• International Vocabulary of Metrology
• International System of Quantities
• International System of Units
• SI base units
• SI prefixes
• Non-SI units accepted for use with the SI
• Planck units

References

• I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd edition (June 1993), Blackwell Science Inc (p. 72)