SI derived unit

SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. SI coherent derived units involve only a trivial proportionality factor, not requiring conversion factors.

The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m²), the SI derived unit of area; and the kilogram per cubic metre (kg/m³ or kg⋅m⁻³), the SI derived unit of density.

The names of SI coherent derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m".^[1]

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Special names

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Named units derived from SI base units^[2]
Name	Symbol	Quantity	Equivalents	SI base unit Equivalents
hertz	Hz	frequency	1/s	s⁻¹
radian	rad	angle	m/m	1
steradian	sr	solid angle	m²/m²	1
newton	N	force, weight	kg⋅m/s²	kg⋅m⋅s⁻²
pascal	Pa	pressure, stress	N/m²	kg⋅m⁻¹⋅s⁻²
joule	J	energy, work, heat	m⋅N, C⋅V, W⋅s	kg⋅m²⋅s⁻²
watt	W	power, radiant flux	J/s, V⋅A	kg⋅m²⋅s⁻³
coulomb	C	electric charge or quantity of electricity	s⋅A, F⋅V	s⋅A
volt	V	voltage, electrical potential difference, electromotive force	W/A, J/C	kg⋅m²⋅s⁻³⋅A⁻¹
farad	F	electrical capacitance	C/V, s/Ω	kg⁻¹⋅m⁻²⋅s⁴⋅A²
ohm	Ω	electrical resistance, impedance, reactance	1/S, V/A	kg⋅m²⋅s⁻³⋅A⁻²
siemens	S	electrical conductance	1/Ω, A/V	kg⁻¹⋅m⁻²⋅s³⋅A²
weber	Wb	magnetic flux	J/A, T⋅m²,V⋅s	kg⋅m²⋅s⁻²⋅A⁻¹
tesla	T	magnetic induction, magnetic flux density	V⋅s/m², Wb/m², N/(A⋅m)	kg⋅s⁻²⋅A⁻¹
henry	H	electrical inductance	V⋅s/A, Ω⋅s, Wb/A	kg⋅m²⋅s⁻²⋅A⁻²
degree Celsius	°C	temperature relative to 273.15 K	K	K
lumen	lm	luminous flux	cd⋅sr	cd
lux	lx	illuminance	lm/m²	cd⋅m⁻²
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.

By field of application

Kinematics

Name	Symbol	Quantity	Expression in terms of SI base units
metre per second	m/s	speed, velocity	m⋅s⁻¹
metre per second squared	m/s²	acceleration	m⋅s⁻²
metre per second cubed	m/s³	jerk, jolt	m⋅s⁻³
metre per second to the fourth	m/s⁴	snap, jounce	m⋅s⁻⁴
radian per second	rad/s	angular velocity	s⁻¹
radian per second squared	rad/s²	angular acceleration	s⁻²
hertz per second	Hz/s	frequency drift	s⁻²
cubic metre per second	m³/s	volumetric flow	m³⋅s⁻¹

Mechanics

Name	Symbol	Quantity	Expression in terms of SI base units
square metre	m²	area	m²
cubic metre	m³	volume	m³
newton-second	N⋅s	momentum, impulse	m⋅kg⋅s⁻¹
newton metre second	N⋅m⋅s	angular momentum	m²⋅kg⋅s⁻¹
newton-metre	N⋅m = J/rad	torque, moment of force	m²⋅kg⋅s⁻²
newton per second	N/s	yank	m⋅kg⋅s⁻³
reciprocal metre	m⁻¹	wavenumber, optical power, curvature, spatial frequency	m⁻¹
kilogram per square metre	kg/m²	area density	m⁻²⋅kg
kilogram per cubic metre	kg/m³	density, mass density	m⁻³⋅kg
cubic metre per kilogram	m³/kg	specific volume	m³⋅kg⁻¹
joule-second	J⋅s	action	m²⋅kg⋅s⁻¹
joule per kilogram	J/kg	specific energy	m²⋅s⁻²
joule per cubic metre	J/m³	energy density	m⁻¹⋅kg⋅s⁻²
newton per metre	N/m = J/m²	surface tension, stiffness	kg⋅s⁻²
watt per square metre	W/m²	heat flux density, irradiance	kg⋅s⁻³
square metre per second	m²/s	kinematic viscosity, thermal diffusivity, diffusion coefficient	m²⋅s⁻¹
pascal-second	Pa⋅s = N⋅s/m²	dynamic viscosity	m⁻¹⋅kg⋅s⁻¹
kilogram per metre	kg/m	linear mass density	m⁻¹⋅kg
kilogram per second	kg/s	mass flow rate	kg⋅s⁻¹
watt per steradian square metre	W/(sr⋅m²)	radiance	kg⋅s⁻³
watt per steradian cubic metre	W/(sr⋅m³)	radiance	m⁻¹⋅kg⋅s⁻³
watt per metre	W/m	spectral power	m⋅kg⋅s⁻³
gray per second	Gy/s	absorbed dose rate	m²⋅s⁻³
metre per cubic metre	m/m³	fuel efficiency	m⁻²
watt per cubic metre	W/m³	spectral irradiance, power density	m⁻¹⋅kg⋅s⁻³
joule per square metre second	J/(m²⋅s)	energy flux density	kg⋅s⁻³
reciprocal pascal	Pa⁻¹	compressibility	m⋅kg⁻¹⋅s²
joule per square metre	J/m²	radiant exposure	kg⋅s⁻²
kilogram square metre	kg⋅m²	moment of inertia	m²⋅kg
newton metre second per kilogram	N⋅m⋅s/kg	specific angular momentum	m²⋅s⁻¹
watt per steradian	W/sr	radiant intensity	m²⋅kg⋅s⁻³
watt per steradian metre	W/(sr⋅m)	spectral intensity	m⋅kg⋅s⁻³

Chemistry

Name	Symbol	Quantity	Expression in terms of SI base units
mole per cubic metre	mol/m³	molarity, amount of substance concentration	m⁻³⋅mol
cubic metre per mole	m³/mol	molar volume	m³⋅mol⁻¹
joule per kelvin mole	J/(K⋅mol)	molar heat capacity, molar entropy	m²⋅kg⋅s⁻²⋅K⁻¹⋅mol⁻¹
joule per mole	J/mol	molar energy	m²⋅kg⋅s⁻²⋅mol⁻¹
siemens square metre per mole	S⋅m²/mol	molar conductivity	kg⁻¹⋅s³⋅A²⋅mol⁻¹
mole per kilogram	mol/kg	molality	kg⁻¹⋅mol
kilogram per mole	kg/mol	molar mass	kg⋅mol⁻¹
cubic metre per mole second	m³/(mol⋅s)	catalytic efficiency	m³⋅s⁻¹⋅mol⁻¹

Electromagnetics

Name	Symbol	Quantity	Expression in terms of SI base units
coulomb per square metre	C/m²	electric displacement field, polarization density	m⁻²⋅s⋅A
coulomb per cubic metre	C/m³	electric charge density	m⁻³⋅s⋅A
ampere per square metre	A/m²	electric current density	m⁻²⋅A
siemens per metre	S/m	electrical conductivity	m⁻³⋅kg⁻¹⋅s³⋅A²
farad per metre	F/m	permittivity	m⁻³⋅kg⁻¹⋅s⁴⋅A²
henry per metre	H/m	magnetic permeability	m⋅kg⋅s⁻²⋅A⁻²
volt per metre	V/m	electric field strength	m⋅kg⋅s⁻³⋅A⁻¹
ampere per metre	A/m	magnetization, magnetic field strength	m⁻¹⋅A
coulomb per kilogram	C/kg	exposure (X and gamma rays)	kg⁻¹⋅s⋅A
ohm metre	Ω⋅m	resistivity	m³⋅kg⋅s⁻³⋅A⁻²
coulomb per metre	C/m	linear charge density	m⁻¹⋅s⋅A
joule per tesla	J/T	magnetic dipole moment	m²⋅A
square metre per volt second	m²/(V⋅s)	electron mobility	kg⁻¹⋅s²⋅A
reciprocal henry	H⁻¹	magnetic reluctance	m⁻²⋅kg⁻¹⋅s²⋅A²
weber per metre	Wb/m	magnetic vector potential	m⋅kg⋅s⁻²⋅A⁻¹
weber metre	Wb⋅m	magnetic moment	m³⋅kg⋅s⁻²⋅A⁻¹
tesla metre	T⋅m	magnetic rigidity	m⋅kg⋅s⁻²⋅A⁻¹
ampere radian	A⋅rad	magnetomotive force	A
metre per henry	m/H	magnetic susceptibility	m⁻¹⋅kg⁻¹⋅s²⋅A²

Photometry

Name	Symbol	Quantity	Expression in terms of SI base units
lumen second	lm⋅s	luminous energy	s⋅cd
lux second	lx⋅s	luminous exposure	m⁻²⋅s⋅cd
candela per square metre	cd/m²	luminance	m⁻²⋅cd
lumen per watt	lm/W	luminous efficacy	m⁻²⋅kg⁻¹⋅s³⋅cd

Thermodynamics

Name	Symbol	Quantity	Expression in terms of SI base units
joule per kelvin	J/K	heat capacity, entropy	m²⋅kg⋅s⁻²⋅K⁻¹
joule per kilogram kelvin	J/(K⋅kg)	specific heat capacity, specific entropy	m²⋅s⁻²⋅K⁻¹
watt per metre kelvin	W/(m⋅K)	thermal conductivity	m⋅kg⋅s⁻³⋅K⁻¹
kelvin per watt	K/W	thermal resistance	m⁻²⋅kg⁻¹⋅s³⋅K
reciprocal kelvin	K⁻¹	thermal expansion coefficient	K⁻¹
kelvin per metre	K/m	temperature gradient	m⁻¹⋅K

Other units used with SI

Some other units such as the hour, litre, tonne, bar, and electronvolt are not SI units, but are widely used in conjunction with SI units.

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.^[3]

References

^ Suplee, Curt (2 July 2009). "Special Publication 811". Nist.
^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
^ "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. Retrieved 23 September 2014.

Bibliography

I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Blackwell Science Inc. p. 72.{{cite book}}: CS1 maint: multiple names: authors list (link)

External links

Media related to SI derived units at Wikimedia Commons

v t e SI units
Base units	ampere candela kelvin kilogram metre mole second
Derived units with special names	becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber
Other accepted units	astronomical unit dalton day decibel degree of arc electronvolt hectare hour litre minute minute and second of arc neper tonne
See also	Conversion of units Metric prefixes Historical definitions of the SI base units 2019 redefinition System of units of measurement
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