The circumference or perimeter of a circle is the distance around the edge of the circle. To calculate the circumference of a circle you can use the formula:

C = Ï€ Ã— d

C represents the Circumference.

d represents the diameter of the circle (the diameter is the distance all the way across the centre of the circle)

Ï€ stands for Pi (Pi is a number equal to 3.142 rounded to 3 decimal places. You can use the Ï€ button on your scientific calculator.)

So basically all you need to do is multiply the diameter of the circle by Ï€ if you want to find the circumference of a circle.

To find the area of the circle you can use the following formula:

A = Ï€ Ã— rÂ²

A represents the area.

r represents the radius of the circle (the radius is the distance half way across the centre, so it is half the value of the diameter).

Notice that the formula for circumference uses the diameter and the formula for the area uses the diameter.

Example 1

Find the circumference and area of this circle:

Notice that you are given the diameter which is 38cm so the radius is 19cm.

First of all calculate the circumference of the circle:

C = Ï€ Ã— d

C = Ï€ Ã— 38 (make sure you substitute the diameter into your formula)

C = 119.4 cm to 1 decimal place.

Next calculate the area of the circle.

A = Ï€ Ã— rÂ²

A = Ï€ Ã— 19Â² (make sure you substitute the radius into your formula)

A = 1134 cmÂ² rounded to the nearest whole number.

Example 2

Calculate the circumference and area of this circle shown below:

This time you are given the radius of the circle which is 4.2 m so the diameter of the circle is 8.4 m.

First of all calculate the circumference of the circle:

C = Ï€ Ã— d

C = Ï€ Ã— 8.4 (make sure you substitute the diameter into your formula)

C = 26.4 m to 1 decimal place.

Next calculate the area of the circle.

A = Ï€ Ã— rÂ²

A = Ï€ Ã— 4.2Â² (make sure you substitute the radius into your formula)

A = 55.4 mÂ² rounded to the nearest whole number.

Example 3

A bicycle wheel has a diameter of 33cm.How far does the bike travel in one turn.

Here you need to work out the circumference of the circle as the distance travelled in one turn is the same as the circumference of the circle. So all you need to do is substitute the diameter (33cm) into your formula:

C = Ï€ Ã— d

C = Ï€ Ã— 33 (make sure you substitute the diameter into your formula)

C = 104 cm to the nearest centimetre.