SI derived unit

The International System of Units (SI) specifies a set of seven base units from which all other SI units of measurement are derived. Each of these other units (SI derived units) is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units.

For example, the SI derived unit of area is the square metre (m²), and the SI derived unit of density is the kilogram per cubic metre (kg/m³ or kg m⁻³). The degree Celsius (see the table below) has a somewhat unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase. The symbols for units named after persons, however, are always written with an uppercase initial letter (e.g. the symbol for the hertz is "Hz"; but the symbol for the meter is "m").^[1]

Derived units with special names

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^[2]

Name	Symbol	Quantity	Equivalents	SI base unit Equivalents
hertz	Hz	frequency	1/s	s^−1
radian	rad	angle	m/m	dimensionless
steradian	sr	solid angle	m^2/m^2	dimensionless
newton	N	force, weight	kg⋅m/s^2	kg⋅m⋅s^−2
pascal	Pa	pressure, stress	N/m^2	kg⋅m^−1⋅s^−2
joule	J	energy, work, heat	N⋅m C⋅V W⋅s	kg⋅m^2⋅s^−2
watt	W	power, radiant flux	J/s V⋅A	kg⋅m^2⋅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⋅m^2⋅s^−3⋅A^−1
farad	F	electrical capacitance	C/V s/Ω	kg^−1⋅m^−2⋅s^4⋅A^2
ohm	Ω	electrical resistance, impedance, reactance	1/S V/A	kg⋅m^2⋅s^−3⋅A^−2
siemens	S	electrical conductance	1/Ω A/V	kg^−1⋅m^−2⋅s^3⋅A^2
weber	Wb	magnetic flux	J/A T⋅m^2	kg⋅m^2⋅s^−2⋅A^−1
tesla	T	magnetic field strength, magnetic flux density	V⋅s/m^2 Wb/m^2 N/(A⋅m)	kg⋅s^−2⋅A^−1
henry	H	electrical inductance	V⋅s/A Ω⋅s Wb/A	kg⋅m^2⋅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/m^2	m^−2⋅cd
becquerel	Bq	radioactivity (decays per unit time)	1/s	s^−1
gray	Gy	absorbed dose (of ionizing radiation)	J/kg	m^2⋅s^−2
sievert	Sv	equivalent dose (of ionizing radiation)	J/kg	m^2⋅s^−2
katal	kat	catalytic activity	mol/s	s^−1⋅mol

Examples of derived quantities and units

Some SI derived units

Name	Symbol	Quantity	Expression in terms of SI base units
square metre	m^2	area	m^2
cubic metre	m^3	volume	m^3
metre per second	m/s	speed, velocity	m⋅s^−1
cubic metre per second	m^3/s	volumetric flow	m^3⋅s^−1
metre per second squared	m/s^2	acceleration	m⋅s^−2
metre per second cubed	m/s^3	jerk, jolt	m⋅s^−3
metre per quartic second	m/s^4	snap, jounce	m⋅s^−4
radian per second	rad/s	angular velocity	s^−1
radian per second squared	rad/s^2	angular acceleration	s^−2
newton second	N⋅s	momentum, impulse	m⋅kg⋅s^−1
newton metre second	N⋅m⋅s	angular momentum	m^2⋅kg⋅s^−1
newton metre	N⋅m = J/rad	torque, moment of force	m^2⋅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/m^2	area density	m^−2⋅kg
kilogram per cubic metre	kg/m^3	density, mass density	m^−3⋅kg
cubic metre per kilogram	m^3/kg	specific volume	m^3⋅kg^−1
mole per cubic metre	mol/m^3	molarity, amount of substance concentration	m^−3⋅mol
cubic metre per mole	m^3/mol	molar volume	m^3⋅mol^−1
joule second	J⋅s	action	m^2⋅kg⋅s^−1
joule per kelvin	J/K	heat capacity, entropy	m^2⋅kg⋅s^−2⋅K^−1
joule per kelvin mole	J/(K⋅mol)	molar heat capacity, molar entropy	m^2⋅kg⋅s^−2⋅K^−1⋅mol^−1
joule per kilogram kelvin	J/(K⋅kg)	specific heat capacity, specific entropy	m^2⋅s^−2⋅K^−1
joule per mole	J/mol	molar energy	m^2⋅kg⋅s^−2⋅mol^−1
joule per kilogram	J/kg	specific energy	m^2⋅s^−2
joule per cubic metre	J/m^3	energy density	m^−1⋅kg⋅s^−2
newton per metre	N/m = J/m^2	surface tension, stiffness	kg⋅s^−2
watt per square metre	W/m^2	heat flux density, irradiance	kg⋅s^−3
watt per metre kelvin	W/(m⋅K)	thermal conductivity	m⋅kg⋅s^−3⋅K^−1
square metre per second	m^2/s	kinematic viscosity, thermal diffusivity, diffusion coefficient	m^2⋅s^−1
pascal second	Pa⋅s = N⋅s/m^2	dynamic viscosity	m^−1⋅kg⋅s^−1
coulomb per square metre	C/m^2	electric displacement field, polarization density	m^−2⋅s⋅A
coulomb per cubic metre	C/m^3	electric charge density	m^−3⋅s⋅A
ampere per square metre	A/m^2	electric current density	A⋅m^−2
siemens per metre	S/m	electrical conductivity	m^−3⋅kg^−1⋅s^3⋅A^2
siemens square metre per mole	S⋅m^2/mol	molar conductivity	kg^−1⋅s^3⋅mol^−1⋅A^2
farad per metre	F/m	permittivity	m^−3⋅kg^−1⋅s^4⋅A^2
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	A⋅m^−1
candela per square metre	cd/m^2	luminance	cd⋅m^−2
lumen second	lm⋅s	luminous energy	cd⋅sr⋅s
lux second	lx⋅s	luminous exposure	cd⋅sr⋅s⋅m^−2
coulomb per kilogram	C/kg	exposure (X and gamma rays)	kg^−1⋅s⋅A
gray per second	Gy/s	absorbed dose rate	m^2⋅s^−3
ohm metre	Ω⋅m	resistivity	m^3⋅kg⋅s^−3⋅A^−2
kilogram per metre	kg/m	linear mass density	m^−1⋅kg
coulomb per metre	C/m	linear charge density	m^−1⋅s⋅A
mole per kilogram	mol/kg	molality	kg^−1⋅mol
kilogram per mole	kg/mol	molar mass	kg⋅mol^−1
metre per cubic metre	m/m^3	fuel efficiency	m^−2
kilogram per second	kg/s	mass flow rate	kg⋅s^−1
joule per tesla	J/T	magnetic dipole moment	m^2⋅A
watt per cubic metre	W/m^3	spectral irradiance, power density	m^−1⋅kg⋅s^−3
kelvin per watt	K/W	thermal resistance	m^−2⋅kg^−1⋅s^3⋅K
reciprocal kelvin	K^−1	thermal expansion coefficient	K^−1
kelvin per metre	K/m	temperature gradient	m^−1⋅K
square metre per volt second	m^2/(V⋅s)	electron mobility	kg^−1⋅s^2⋅A
joule per square metre second	J/(m^2⋅s)	energy flux density	kg⋅s^−3
reciprocal pascal	Pa^−1	compressibility	m⋅kg^−1⋅s^2
reciprocal henry	H^−1	magnetic reluctance	m^−2⋅kg^−1s^2⋅A^2
weber per metre	Wb/m	magnetic vector potential	m⋅kg⋅s^−2⋅A^−1
weber metre	Wb⋅m	magnetic moment	m^3⋅kg⋅s^−2⋅A^−1
tesla metre	T⋅m	magnetic rigidity	m⋅kg⋅s^−2⋅A^−1
joule per square metre	J/m^2	radiant exposure	kg⋅s^−2
cubic metre per mole second	m^3/(mol⋅s)	catalytic efficiency	m^3⋅s^−1⋅mol^−1
kilogram square metre	kg⋅m^2	moment of inertia	m^2⋅kg
newton metre second per kilogram	N⋅m⋅s/kg	specific angular momentum	m^2⋅s^−1
hertz per second	Hz/s	frequency drift	s^−2
lumen per watt	lm/W	luminous efficacy	m^−2⋅kg^−1⋅s^3⋅lm
ampere radian	A⋅rad	magnetomotive force	A
metre per henry	m/H	magnetic susceptibility	m^−1⋅kg^−1⋅s^2⋅A^2
watt per steradian	W/sr	radiant intensity	m^2⋅kg⋅s^−3
watt per steradian metre	W/(sr⋅m)	spectral intensity	m⋅kg⋅s^−3
watt per steradian square metre	W/(sr⋅m^2)	radiance	kg⋅s^−3
watt per steradian cubic metre	W/(sr⋅m^3)	spectral radiance	m^−1⋅kg⋅s^−3
watt per metre	W/m	spectral power	m⋅kg⋅s^−3

Other units used with SI

Some other units such as the hour, litre, tonne, bar and electron volt 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]

See also

• International System of Quantities (ISQ)
• International System of Units (SI)
• International Vocabulary of Metrology
• Metric prefix
• Metric system
• Non-SI units mentioned in the SI
• Planck units
• SI base unit

References

1. http://physics.nist.gov/Pubs/SP811/sec06.html
2. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6
3. "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. Retrieved 2014-09-23.

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.