Dimensional Formulae and Dimensional Equations

The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity.

For example, the dimensional formula of the volume is [M° L3 T°], and that of speed or velocity is [M° L T-1]. Similarly, [M° L T–2] is the dimensional formula of acceleration and [M L–3 T°] that of mass density.

An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity.

Thus, the dimensional equations are the equations, which represent the dimensions of a physical quantity in terms of the base quantities
Example:
Volume [V] = [M0 L3 T0]
Speed [υ ] = [M0 L T–1]
Force [F] = [M L T–2]
Density [ρ ] = [M L–3 T0]

The dimensional equation can be obtained from the equation representing the relations between the physical quantities.

The dimensional formulae of a large number and wide variety of physical quantities, derived from the equations representing the relationships
among other physical quantities and expressed in terms of base quantities.