View source for Base quantity and Dimensions

Physical '''base quantities''' have the important property that all other '''derived quantities''' are derivated algebraically from them. In the SI there are seven base quantities: length (''l''), mass (''m''), time (''t''), electric current (''I''), Thermodynamic temperature (''T''), amount of substance (''n'') and luminous intensity (''I<sub>v</sub>''). By convention, all of these physical quantities are organized in a '''dimensional system''' based on the base quantities, each of which is regarded as having its own dimension. Joseph Fourier introduced in 1822 the concept of physical dimension defining that the physical quantities that are of the same kind (commensurable) have the same dimension and can directly be compared to each other. For example, we can compare kilograms with pounds, both quantities have different units but the same dimension. If the physical quantities present different dimensions, they cannot be expressed in terms of similar units and cannot be compared in quantity (incommensurable). For example, asking if a minute is larger than a kilometer in meaningless.The derived quantities will also have dimensions derived algebraically from the seven base quantities by multiplication and division. For example:


::::*The dimension of length is written as [L] and the dimension of time as [T]. When we analyse the dimension of a derived unit such as velocity, which is distance (length) divided by time, then becomes [LT<sup>-1</sup>] in its notation.


The proper definition of the dimensional system for the physical quantities becomes relevant when we perform a dimensional analysis, which is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed. Any physically meaningful equation (and any inequality) will have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation.

{| class="wikitable"
|-
! Base quantity
! Symbol for quantity
! Symbol for dimension
|-
| length
| ''l''
| L
|-
| mass
| ''m''
| M
|-
| time
| ''t''
| T
|-
| electric current
| ''I''
| I
|-
| thermodynamic temperature
| ''T''
| Θ
|-
| amount of substance
| ''n''
| N
|-
| luminous intensity
| ''I<sub>v</sub>''
| J
|}