Define Dimensional Analysis with Example

While calculating, there is a need to convert units from one system to other. The method used to accomplish this is called factor label method or unit factor method or dimensional analysis. This is illustrated below.


A piece of metal is 3 inch (represented by in) long. What is its length in cm?

We know that 1 inch = 2.54 cm

From this equivalence, we can write

1 inch / 2.54 cm = 1

thus 1 inch / 2.54 cm equals 1 and 2.54 cm /1 inch; also equals 1. Both of these are called unit factors.

If some number is multiplied by these unit factors (i.e. 1), it will not be affected otherwise.

Say, the 3 is given above is multiplied by the unit factor. So,

3 in = 2.54 cm / 1 inch =3 x 2.54 cm = 7.62 cm

Now the unit factor by which multiplication 2.54 cm is to be done is that unit factor ( 1 inch in the above case) which gives the desired units i.e., the numerator should have that part which is required in the desired result. It should also be noted in the above example that units can be handled just like other numerical parts. It can be cancelled, divided, multiplied, squared etc.