dimension  The  basic quantities of physics are mass, length, time,  electric current, temperature, luminous intensity, and the amount  of substance. Other related quantities such as velocity, acceleration,   force,   energy,   etc.   can   be derived  from combination  of  these  basic  quantities  and are called derived quantities.

The  way a derived quantity is related to the basic quantity can  be  shown by the dimensions of that quantity. As an example consider velocity which is length divided by time. The dimension of  velocity  is  written  as  [L]  [T]^-1.  The  square brackets enclosing  the  letter  L and T indicate that we are dealing with dimension of  length  and  time. In appendix II, in the table ‘derived SI unit of various physical quantities’, you can find the dimension of the physical quantities by replacing [M] for kg, [T] for s, [L] for m.  

Use of dimensions -

i)  To  check equation : The dimensions of physical quantities is  each  side  of an equation must match. Consider for example the equation

t = 2 p [l/g]^1/2

the time period of simple pendulum. Dimension in the L.H.S. of the equation is [T].

In  the R.H.S. 2p is a dimensionless constant and the other factor has the dimension [T] Therefore  the dimension in each side of the equation is the same. This  simple  method  helps  us  to  recall  an  equation correctly.

(ii)  Dimension  can  also be used to derive an equation between physical quantities. (see Stokes law)