Dimension (measurement)

The dimension of a measurement describes what things that it is measuring. Dimension is separate from the amount or size: for example, feet, miles, metres, and kilometres all have the same dimension, length, but one of each unit measures a different amount of length.

Kind

Measurements with the same dimension can, mathematically, be added or subtracted, but this does not always give a number that means something. For example, the dimension of molar energy is used to represent both the heat of fusion of a chemical compound and the molar Gibbs free energy of a thermodynamic system, but even though these dimensions match, the quantities describe different objects, so they are not of the same kind, and adding them together does not give a useful quantity.

Examples of dimensions

Many common dimensions are made from multiplication or division of length, time, and mass. Most systems of units define a group of fundamental units, then use these relationships between dimensions to define other derived units.

Dimension	Formula	SI unit	CGS unit	American customary unit
Length	$L$	metre	centimetre	foot (unit)
Area	$L^{2}$	square metre	square centimetre	square foot
Volume	$L^{3}$	litre	cubic centimetre	gallon or dry gallon
Time	$T$	second	second	second
Speed or velocity	${\frac {L}{T}}$	metre per second	centimetre per second	foot per second
Acceleration	${\frac {L}{T^{2}}}$	metre per second squared	centimetre per second squared	foot per second squared
Mass	$M$	kilogram	gram	pound (mass)
Force or weight	${\frac {LM}{T^{2}}}$	newton	dyne	pound (force)
Pressure	${\frac {M}{LT^{2}}}$	pascal	barye	pounds per square inch
Energy	${\frac {L^{2}M}{T^{2}}}$	joule	erg	British thermal unit
Power	${\frac {L^{2}M}{T^{3}}}$	watt	erg per second	horsepower