Information about Si Derived Unit

SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.

Dimensionless derived units

The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the BIPM to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.

Dimensionless SI units

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Name	Symbol	Quantity	Definition
radian	rad	angle	The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are radians in a circle.
steradian	sr	solid angle	The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are steradians on a sphere.

Derived units with special names

Base units can be put together to derive units of measurement for other quantities. In addition to the two dimensionless derived units rad and sr there are 20 derived units having special names:

Named units derived from SI base units

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Name	Symbol	Quantity	Expression in terms of other units	Expression in terms of SI base units
hertz	Hz	frequency	1/s	s−1
newton	N	force, weight	m∙kg/s2	m∙kg∙s−2
joule	J	energy, work, heat	N∙m	m2∙kg∙s−2
watt	W	power, radiant flux	J/s	m2∙kg∙s−3
pascal	Pa	pressure, stress	N/m2	m−1∙kg∙s−2
lumen	lm	luminous flux	cd∙sr	cd
lux	lx	illuminance	lm/m2	m−2∙cd
coulomb	C	electric charge or electric flux	s∙A	s∙A
volt	V	voltage, electrical potential difference, electromotive force	W/A = J/C	m2∙kg∙s−3∙A−1
ohm	Ω	electric resistance, impedance, reactance	V/A	m2∙kg∙s−3∙A−2
farad	F	electric capacitance	C/V	m−2∙kg−1∙s4∙A2
weber	Wb	magnetic flux	J/A	m2∙kg∙s−2∙A−1
tesla	T	magnetic field	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
siemens	S	electrical conductance	1/O	m−2∙kg−1∙s3∙A2
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
Celsius	C	thermodynamic temperature	TC = TK − 273.16

Other quantities and units

Compound units derived from SI units
Name	Symbol	Quantity	Expression in terms of SI base units
square metre	m2	area	m2
cubic metre	m3	volume	m3
metre per second	m/s	speed, velocity	ms−1
metre per second squared	m/s2	acceleration	ms−2
metre per second cubed	m/s3	jerk	ms−3
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
reciprocal metre	m−1	wavenumber	m−1
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
coulomb per cubic metre	C/m3	electric charge density	m−3sA
ampere per square metre	A/m2	electric current density	Am−2
siemens per metre	S/m	conductivity	kg−1m−3s3A2
siemens square metre per mole	Sm2/mol	molar conductivity	kg-1s3mol−1A2
farad per metre	F/m	permittivity	kg−1m−3s4A2
henry per metre	H/m	permeability	kgms−2A−2
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
coulomb per kilogram	C/kg	exposure (X and gamma rays)	kg−1sA
gray per second	Gy/s	absorbed dose rate	m2s−3
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See also

• SI
• SI base unit
• SI prefix
• 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)