Bitesize has changed! We're updating subjects as fast as we can. Visit our new site to find Bitesize guides and clips - and tell us what you think!
Print

Maths

Circles

Circumference of a circle

image: circumference of the circle

The circumference is the length of the edge around a circle.

For any circle, the circumference is:

3.141592... × the diameter.

Or in symbols: C = (3.141592...)d

This is true for all circles and so 3.141592... is therefore a special, unique number, and we represent it with the Greek letter π.(The symbol π is called 'pi' in English and is pronounced 'pie').

So we can write the formula for the circumference of a circle as: C = πd

However, the diameter is equal to 2 × radius, (2r), so we can also write this formula as:

C = 2πr

It does not matter which of these formulae you use. But you must be careful to use the correct length for the formula (the radius or diameter).

Look at the following example:

Question
image: circle split into 8, diameter: 50cm

Find the circumference of a wheel with a diameter of 50 cm. Use π = 3.14.

toggle answer

Answer

Solution 1: Using C = πd

We know that the diameter is 50 cm, so we simply calculate:

πd = 3.14 × 50 = 157 cm

Solution 2: Using C = 2πr

We have been given the diameter (50 cm), so we must start by finding the radius. The radius is half the diameter, so the radius is 25 cm.

2πr = 2 × 3.14 × 25 = 157 cm

Question

A plate has a radius of 15 cm. Find the circumference by using the π button on your calculator, and give your answer correct to 1 decimal place (dp).

image: circle, radius:15cm

toggle answer

Answer

The answer is 94.2 cm.

Solution 1 : Using C = πd

We must first calculate the diameter:

d = 2r, so d = 2 × 15 = 30 cm

C = π × 30 = 94.2477...

C = 94.2 cm (1 d.p.)

Solution 2 : Using C = 2πr

C = 2 × π × 15 = 94.2477...

C = 94.2 cm (1 dp)

Back to Geometry and measures index

BBC navigation

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.