SI derived unit

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, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre (m2), and of density is kilograms per cubic metre (kg/m3). The number of derived units is unlimited.

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


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
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 dimensionless
steradian sr solid angle m2/m2 dimensionless
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 N⋅m = 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 s⋅A
volt V voltage, electrical potential difference, electromotive force W/A = J/C kg⋅m2⋅s−3⋅A−1
farad F electric capacitance C/V kg−1⋅m−2⋅s4⋅A2
ohm Ω electric resistance, impedance, reactance 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 kg⋅m2⋅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 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 m−2⋅cd
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

Examples of derived quantities and units

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Some SI derived 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 m⋅s−1
cubic metre per second m3/s volumetric flow m3⋅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 quartic second m/s4 snap, jounce m⋅s−4
radian per second rad/s angular velocity s−1
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 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
mole per cubic metre mol/m3 amount of substance concentration m−3⋅mol
cubic metre per mole m3/mol molar volume m3⋅mol−1
joule second J⋅s action m2⋅kg⋅s−1
joule per kelvin J/K heat capacity, entropy m2⋅kg⋅s−2⋅K−1
joule per kelvin mole J/(K⋅mol) molar heat capacity, molar entropy m2⋅kg⋅s−2⋅K−1⋅mol−1
joule per kilogram kelvin J/(K⋅kg) specific heat capacity, specific entropy m2⋅s−2⋅K−1
joule per mole J/mol molar energy m2⋅kg⋅s−2⋅mol−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 kg⋅s−2
watt per square metre W/m2 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 m2/s kinematic viscosity, diffusion coefficient m2⋅s−1
pascal second Pa⋅s = N⋅s/m2 dynamic viscosity m−1⋅kg⋅s−1
coulomb per square metre C/m2 electric displacement field, polarization vector 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 A⋅m−2
siemens per metre S/m conductivity m−3⋅kg−1⋅s3⋅A2
siemens square metre per mole S⋅m2/mol molar conductivity kg-1⋅s3⋅mol−1⋅A2
farad per metre F/m permittivity m−3⋅kg−1⋅s4⋅A2
henry per metre H/m 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 magnetic field strength A⋅m−1
candela per square metre cd/m2 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 m2⋅s−3
ohm metre Ω⋅m resistivity m3⋅kg⋅s−3⋅A−2

Some other metric units, such as the litre, are not SI units, but are accepted for use with the SI.

See also


  • 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)

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