Essentials of the SI: Base & derived units (2024)

Essentials of the SI: Base & derived units (1) For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in Table3.
Table 3. SI derived units with special names and symbols
SI derived unit
Derived quantity Name Symbol Expression
in terms of
other SI units
in terms of
SI base units
plane angle radian (a) rad - m·m-1 = 1 (b)
solid angle steradian (a) sr (c) - m2·m-2 = 1 (b)
frequency hertz Hz - s-1
force newton N - m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C - s·A
electric potential difference,
electromotive force
volt V W/A m2·kg·s-3·A-1
capacitance farad F C/V m-2·kg-1·s4·A2
electric resistance ohm Essentials of the SI: Base & derived units (2) V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2·kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2·kg·s-2·A-2
Celsius temperature degree Celsius °C - K
luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
activity (of a radionuclide) becquerel Bq - s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2
dose equivalent (d) sievert Sv J/kg m2·s-2
catalytic activity katal kat s-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 Essentials of the SI: Base & derived units (3)t and the thermodynamic temperature difference Essentials of the SI: Base & derived units (4)T between the melting point of gallium and the triple point of water may be written as Essentials of the SI: Base & derived units (5)t = 29.7546 °C = Essentials of the SI: Base & derived units (6)T = 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 quantity Name Symbol
dynamic viscosity pascal second Pa·s
moment of force newton meter N·m
surface tension newton per meter N/m
angular velocity radian per second rad/s
angular acceleration radian per second squared rad/s2
heat flux density, irradiance watt per square meter W/m2
heat capacity, entropy joule per kelvin J/K
specific heat capacity, specific entropy joule per kilogram kelvin J/(kg·K)
specific energy joule per kilogram J/kg
thermal conductivity watt per meter kelvin W/(m·K)
energy density joule per cubic meter J/m3
electric field strength volt per meter V/m
electric charge density coulomb per cubic meter C/m3
electric flux density coulomb per square meter C/m2
permittivity farad per meter F/m
permeability henry per meter H/m
molar energy joule per mole J/mol
molar entropy, molar heat capacity joule per mole kelvin J/(mol·K)
exposure (x and Essentials of the SI: Base & derived units (7) rays) coulomb per kilogram C/kg
absorbed dose rate gray per second Gy/s
radiant intensity watt per steradian W/sr
radiance watt per square meter steradian W/(m2·sr)
catalytic (activity) concentration katal per cubic meter kat/m3

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Essentials of the SI: Base & derived units (2024)
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