SI derived unit

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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 metre 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
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
watt W power, radiant flux J/s
coulomb C electric charge or quantity of electricity s⋅A s⋅A
volt V voltage, electrical potential difference, electromotive force W/A
farad F electrical capacitance C/V
ohm Ω electrical resistance, impedance, reactance V/A kg⋅m2⋅s−3⋅A−2
siemens S electrical conductance 1/Ω
weber Wb magnetic flux J/A
tesla T magnetic field strength, magnetic flux density V⋅s/m2
henry H inductance V⋅s/A
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

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
radian per second squared rad/s2 angular acceleration s−2
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
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 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, stiffness 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, thermal diffusivity, 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 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 A⋅m−2
siemens per metre S/m electrical 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 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/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
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/m3 fuel efficiency m−2
kilogram per second kg/s mass flow rate kg⋅s−1
joule per tesla J/T magnetic dipole moment m2⋅A
watt per cubic metre W/m3 spectral irradiance, power density m−1⋅kg⋅s−3
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
square metre per volt second m2/(V⋅s) electron mobility kg−1⋅s2⋅A
joule per square metre second J/(m2⋅s) energy flux density kg⋅s−3
reciprocal pascal Pa−1 compressibility m⋅kg−1⋅s2
reciprocal henry H−1 magnetic reluctance m−2⋅kg−1s2⋅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
joule per square metre J/m2 radiant exposure kg⋅s−2
cubic metre per mole second m3/(mol⋅s) catalytic efficiency m3⋅s−1⋅mol−1
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
hertz per second Hz/s frequency drift s−2
lumen per watt lm/W luminous efficacy m−2⋅kg−1⋅s3⋅lm
ampere radian A⋅rad magnetomotive force A
metre per henry m/H magnetic susceptibility m−1⋅kg−1⋅s2⋅A2
watt per steradian W/sr radiant intensity m2⋅kg⋅s−3
watt per steradian metre W/(sr⋅m) spectral intensity m⋅kg⋅s−3
watt per steradian square metre W/(sr⋅m2) radiance kg⋅s−3
watt per steradian cubic metre W/(sr⋅m3) 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, 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


  2. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  3. "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. Retrieved 23 September 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>


  • 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.CS1 maint: multiple names: authors list (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

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