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SI Base Units & Derived Units

The data presented here is derived from publications of NIST, so it is in the public domain. However, this HTML implementation is not in the public domain. It is provided to make for easier access.

SI Base Units
The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.


Table 1.  SI base units
SI base unit
Base quantityNameSymbol
lengthmeterm
masskilogram      kg
timeseconds
electric currentampereA
thermodynamic temperature      kelvinK
amount of substancemolemol
luminous intensitycandelacd


For detailed information on the SI base units, see Definitions of the SI base units and their Historical context.

SI Derived Units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.


Table 2.  Examples of SI derived units
SI derived unit
Derived quantityNameSymbol
areasquare meterm2
volumecubic meterm3
speed, velocitymeter per secondm/s
accelerationmeter per second squared  m/s2
wave numberreciprocal meterm-1
mass densitykilogram per cubic meterkg/m3
specific volumecubic meter per kilogramm3/kg
current densityampere per square meterA/m2
magnetic field strength  ampere per meterA/m
amount-of-substance concentrationmole per cubic metermol/m3
luminancecandela per square metercd/m2
mass fractionkilogram per kilogram, which may be represented by the number 1kg/kg = 1



For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in Table 3.

Table 3.  SI derived units with special names and symbols
SI derived unit
Derived quantityNameSymbol  Expression 
in terms of 
other SI units
Expression
in terms of
SI base units
plane angleradian (a)rad  -m·m-1 = 1 (b)
solid anglesteradian (a)sr (c)  -m2·m-2 = 1 (b)
frequencyhertzHz  -s-1
forcenewtonN  -m·kg·s-2
pressure, stresspascalPaN/m2m-1·kg·s-2
energy, work, quantity of heat  jouleJN·mm2·kg·s-2
power, radiant fluxwattWJ/sm2·kg·s-3
electric charge, quantity of electricitycoulombC  -s·A
electric potential difference,
electromotive force
voltVW/Am2·kg·s-3·A-1
capacitancefaradFC/Vm-2·kg-1·s4·A2
electric resistanceohmOmegaV/Am2·kg·s-3·A-2
electric conductancesiemensSA/Vm-2·kg-1·s3·A2
magnetic fluxweberWbV·sm2·kg·s-2·A-1
magnetic flux densityteslaTWb/m2kg·s-2·A-1
inductancehenryHWb/Am2·kg·s-2·A-2
Celsius temperaturedegree Celsius°C  -K
luminous fluxlumenlmcd·sr (c)m2·m-2·cd = cd
illuminanceluxlxlm/m2m2·m-4·cd = m-2·cd
activity (of a radionuclide)becquerelBq  -s-1
absorbed dose, specific energy (imparted), kermagrayGyJ/kgm2·s-2
dose equivalent (d)sievertSvJ/kgm2·s-2
catalytic activitykatalkats-1·mol
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.



For a graphical illustration of how the 22 derived units with special names and symbols given in Table 3 are related to the seven SI base units, see relationships among SI units.

Note on degree Celsius.
The derived unit in Table 3 with the special name degree Celsius and special symbol °C deserves comment. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation

t= T- T0.

The unit of Celsius temperature is the degree Celsius, symbol °C. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by

t/°C = T/K - 273.15.

It follows from the definition of t that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numerical value of a given temperature difference or temperature interval whose value is expressed in the unit degree Celsius (°C) is equal to the numerical value of the same difference or interval when its value is expressed in the unit kelvin (K). Thus, temperature differences or temperature intervals may be expressed in either the degree Celsius or the kelvin using the same numerical value. For example, the Celsius temperature difference Deltat and the thermodynamic temperature difference DeltaT between the melting point of gallium and the triple point of water may be written as Deltat = 29.7546 °C = DeltaT = 29.7546 K.

The special names and symbols of the 22 SI derived units with special names and symbols given in Table 3 may themselves be included in the names and symbols of other SI derived units, as shown in Table 4.


Table 4.  Examples of SI derived units whose names and symbols include SI derived units with special names and symbols
SI derived unit
Derived quantityNameSymbol
dynamic viscositypascal secondPa·s
moment of forcenewton meterN·m
surface tensionnewton per meterN/m
angular velocityradian per secondrad/s
angular accelerationradian per second squaredrad/s2
heat flux density, irradiancewatt per square meterW/m2
heat capacity, entropyjoule per kelvinJ/K
specific heat capacity, specific entropyjoule per kilogram kelvinJ/(kg·K)
specific energyjoule per kilogramJ/kg
thermal conductivitywatt per meter kelvinW/(m·K)
energy densityjoule per cubic meterJ/m3
electric field strengthvolt per meterV/m
electric charge densitycoulomb per cubic meterC/m3
electric flux densitycoulomb per square meterC/m2
permittivityfarad per meterF/m
permeabilityhenry per meterH/m
molar energyjoule per moleJ/mol
molar entropy, molar heat capacityjoule per mole kelvinJ/(mol·K)
exposure (x and gamma rays)coulomb per kilogramC/kg
absorbed dose rategray per secondGy/s
radiant intensitywatt per steradianW/sr
radiancewatt per square meter steradianW/(m2·sr)
catalytic (activity) concentrationkatal per cubic meterkat/m3
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