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
hertz Hz frequency 1/s s1
radian rad angle m/m dimensionless
steradian sr solid angle m2/m2 dimensionless
newton N force, weight kg⋅m/s2 kg⋅m⋅s2
pascal Pa pressure, stress N/m2 kg⋅m1⋅s2
joule J energy, work, heat N⋅m
watt W power, radiant flux J/s
coulomb C electric charge or quantity of electricity s⋅A
volt V voltage, electrical potential difference, electromotive force W/A
farad F electrical capacitance C/V
ohm Ω electrical resistance, impedance, reactance 1/S
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 electrical 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 m2⋅cd
becquerel Bq radioactivity (decays per unit time) 1/s s1
gray Gy absorbed dose (of ionizing radiation) J/kg m2⋅s2
sievert Sv equivalent dose (of ionizing radiation) J/kg m2⋅s2
katal kat catalytic activity mol/s s1⋅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 ms1
cubic metre per second m3/s volumetric flow m3s1
metre per second squared m/s2 acceleration ms2
metre per second cubed m/s3 jerk, jolt ms3
metre per quartic second m/s4 snap, jounce ms4
radian per second rad/s angular velocity s1
radian per second squared rad/s2 angular acceleration s2
newton second Ns momentum, impulse mkgs1
newton metre second Nms angular momentum m2kgs1
newton metre Nm = J/rad torque, moment of force m2kgs2
newton per second N/s yank mkgs3
reciprocal metre m1 wavenumber, optical power, curvature, spatial frequency m1
kilogram per square metre kg/m2 area density m2kg
kilogram per cubic metre kg/m3 density, mass density m3kg
cubic metre per kilogram m3/kg specific volume m3kg1
mole per cubic metre mol/m3 molarity, amount of substance concentration m3mol
cubic metre per mole m3/mol molar volume m3mol1
joule second Js action m2kgs1
joule per kelvin J/K heat capacity, entropy m2kgs2K1
joule per kelvin mole J/(Kmol) molar heat capacity, molar entropy m2kgs2K1mol1
joule per kilogram kelvin J/(Kkg) specific heat capacity, specific entropy m2s2K1
joule per mole J/mol molar energy m2kgs2mol1
joule per kilogram J/kg specific energy m2s2
joule per cubic metre J/m3 energy density m1kgs2
newton per metre N/m = J/m2 surface tension, stiffness kgs2
watt per square metre W/m2 heat flux density, irradiance kgs3
watt per metre kelvin W/(mK) thermal conductivity mkgs3K1
square metre per second m2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2s1
pascal second Pas = Ns/m2 dynamic viscosity m1kgs1
coulomb per square metre C/m2 electric displacement field, polarization density m2sA
coulomb per cubic metre C/m3 electric charge density m3sA
ampere per square metre A/m2 electric current density Am2
siemens per metre S/m electrical conductivity m3kg1s3A2
siemens square metre per mole Sm2/mol molar conductivity kg−1s3mol1A2
farad per metre F/m permittivity m3kg1s4A2
henry per metre H/m magnetic permeability mkgs2A2
volt per metre V/m electric field strength mkgs3A1
ampere per metre A/m magnetization, magnetic field strength Am1
candela per square metre cd/m2 luminance cdm2
lumen second lms luminous energy cdsrs
lux second lxs luminous exposure cdsrsm2
coulomb per kilogram C/kg exposure (X and gamma rays) kg1sA
gray per second Gy/s absorbed dose rate m2s3
ohm metre Ωm resistivity m3kgs3A2
kilogram per metre kg/m linear mass density m1kg
coulomb per metre C/m linear charge density m1sA
mole per kilogram mol/kg molality kg1mol
kilogram per mole kg/mol molar mass kgmol1
metre per cubic metre m/m3 fuel efficiency m2
kilogram per second kg/s mass flow rate kgs1
joule per tesla J/T magnetic dipole moment m2A
watt per cubic metre W/m3 spectral irradiance, power density m1kgs3
kelvin per watt K/W thermal resistance m2kg1s3K
reciprocal kelvin K1 thermal expansion coefficient K1
kelvin per metre K/m temperature gradient m1K
square metre per volt second m2/(Vs) electron mobility kg1s2A
joule per square metre second J/(m2s) energy flux density kgs3
reciprocal pascal Pa1 compressibility mkg1s2
reciprocal henry H1 magnetic reluctance m2kg1s2A2
weber per metre Wb/m magnetic vector potential mkgs2A1
weber metre Wbm magnetic moment m3kgs2A1
tesla metre Tm magnetic rigidity mkgs2A1
joule per square metre J/m2 radiant exposure kgs2
cubic metre per mole second m3/(mols) catalytic efficiency m3s1mol1
kilogram square metre kgm2 moment of inertia m2kg
newton metre second per kilogram Nms/kg specific angular momentum m2s1
hertz per second Hz/s frequency drift s2
lumen per watt lm/W luminous efficacy m2kg1s3lm
ampere radian Arad magnetomotive force A
metre per henry m/H magnetic susceptibility m1kg1s2A2
watt per steradian W/sr radiant intensity m2kgs3
watt per steradian metre W/(srm) spectral intensity mkgs3
watt per steradian square metre W/(srm2) radiance kgs3
watt per steradian cubic metre W/(srm3) spectral radiance m1kgs3
watt per metre W/m spectral power mkgs3

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



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