| expression of the dependence of a quantity on the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factor
NOTE 1 – A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity.
NOTE 2 – The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity Q is denoted by dim Q.
NOTE 3 – In deriving the dimension of a quantity, no account is taken of its scalar, vector or tensor character.
NOTE 4 – In a given system of quantities,
– quantities of the same kind have the same dimension,
– quantities of different dimensions are always of different kinds, and
– quantities having the same dimension are not necessarily of the same kind. For example, in the ISQ, pressure and energy density (volumic energy) have the same dimension L–1MT–2. See also note 5.
NOTE 5 – In the International System of Quantities (ISQ), the symbols representing the dimensions of the base quantities are:
||Symbol for dimension
|amount of substance
Thus, the dimension of a quantity Q is denoted by dim Q = LαMβTγIδΘεNζJη, where the exponents, named dimensional exponents, are positive, negative, or zero. Factors with exponent 0 are usually omitted. When all exponents are zero, the symbol 1, printed in sans-serif type, is used to represent the dimension. Examples are:
- The dimension of force is dim F = LMT–2.
- Mass concentration of a given component and mass density (volumic mass) have the same dimension ML–3.
- Electric current and scalar magnetic potential have the same dimension I1 = I, although they are not quantities of the same kind.
NOTE 6 – An exponent can be fractional.
The period T of a pendulum of length l at a place with the local acceleration of free fall g is:
Hence dim C(g) = T·L−1/2.