# Derived Units

The base or fundamental SI units like length, mass, time are independent of each other. The SI units for all other physical quantities such as area, density, velocity can be derived in terms of the base SI units and are called derived units.

In order to find the derived unit for a physical quantity you have to find out the relationship between the physical quantity and the base physical quantities. Then, substitute the units of the base physical quantities to find the desired derived unit.

**Example 1: Derive the SI unit for area of a surface**

In order to derive the unit, you need to find out the relationship between area and the base physical quantities. The area of a surface is the product of its length and breadth. So,

Area = length × breadth

Since breadth is also a kind of length, you can write,

Area = length × length

Then to find the derived unit for area, substitute the units of the base physical quantities as

Unit of area = metre × metre = (metre)^{2} = m^{2}

Thus, the SI unit of area is m^{2} and is pronounced as squared metre. Similarly, **volume** would have the SI unit as m^{3} or cubic metre.

**Example 2: Find the derived unit for force**

Force is defined as

Force = mass × acceleration = mass × (change in velocity/time)

Since, change in velocity = Length/time

So, Force = mass × (length/time) × (1/time) = mass × (length/time^{2})

The SI unit of force can be found by substituting the SI units of the base physical quantities on the right side of the expression. Thus,

SI unit of force = kg m/s^{2} = kg ms^{-2}