# Changing the subject of a formula

Sometimes you need to rearrange the formula to find the value you're looking for.

## Example - circles

The area of a circle ( ) is .

This is useful if we know the radius of the circle and want to know the area. But what if we want to find the radius?

We need a formula that has (some expression in ). We get this by rearranging the formula like this:

Start by dividing both sides by :

Then find the positive square root of both sides:

Swap the sides to make it easier to read:

The formula has been rearranged. We say that now is the subject.

Question

Q1. The formula to find the circumference of a circle:

Rearrange the formula to make the subject.

Q2. The formula to convert the temperature in to the temperature in is:

Rearrange this formula so that it will convert the temperature in to the temperature in (so that is the subject).

A1. , so divide both sides by :

or,

A2.

multiply by :

divide by :