SIUnitsAndDerivations

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SI units and derivations

(Topic)

The seven SI base units are given in the table below. These units are assumed to be independent of each other.

base quantity	SI base unit	symbol
length, position	meter	$\mathrm{m}$
mass	kilogram	$\mathrm{kg}$
time	second	$\mathrm{s}$
current	ampere	$\mathrm{A}$
temperature	Kelvin	$\mathrm{K}$
amount of substance	mole	$\mathrm{mol}$
intensity	candela	$\mathrm{cd}$

There are many quantities that can be measured using units that are derived from the base units. Some of these are written in terms of the base units. Some examples are given in the table below.

quantity	SI derived unit	symbol
area	square meter	$\mathrm{m^2}$
volume	cubic meter	$\mathrm{m^3}$
speed, velocity	meter per second	$\mathrm{m/s}$
acceleration	meter per second squared	$\mathrm{m/s^2}$
density	kilogram per cubic meter	$\mathrm{kg/m^3}$
specific volume	cubic meter per kilogram	$\mathrm{m^3/kg}$
concentration	mole per cubic meter	$\mathrm{mol/m^3}$
wave number	reciprocal meter	$\mathrm{m^{-1}}$
current density	ampere per square meter	$\mathrm{A/m^2}$
magnetic field strength	ampere per cubic meter	$\mathrm{A/m^3}$
luminance	candela per square meter	$\mathrm{cd/m^2}$

Other derived units have their own names. Some examples are given in the table below.

quantity	SI unit	symbol	derivation from other SI units
volume	liter	$\mathrm{L}$ or $\mathrm{\ell}$	$\mathrm{10^{-3}m^3}$
plane angle	radian	$\mathrm{rad}$
solid angle	steradian	$\mathrm{sr}$
frequency	hertz	$\mathrm{Hz}$	$\mathrm{s^{-1}}$
force	newton	$\mathrm{N}$	$\mathrm{kg \cdot m/s^2}$
pressure, stress	Pascal	$\mathrm{Pa}$	$\mathrm{N/m^2}$
energy, work	joule	$\mathrm{J}$	$\mathrm{N \cdot m}$
power	watt	$\mathrm{W}$	$\mathrm{J/s}$
charge	coulomb	$\mathrm{C}$	$\mathrm{A \cdot s}$
potential difference	volt	$\mathrm{V}$	$\mathrm{W/A}$
resistance	ohm	$\mathrm{\Omega}$	$\mathrm{V/A}$
temperature	degree Celsius	$\mathrm{{}^{\circ}C}$	$\mathrm{K}+273.15$