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Area and Circumference of Circles

circle 1

If you divide the circumference of any circle by its diameter you will always get the same number 3.14...

This number is called pi. Pi is usually represented by the symbol π

Pi is an irrational number, that means it goes on forever, the first 50 digits of pi are: 3.14159265358979323846264338327950288419716939937510

To calculate the circumference of a circle we use the formula:
Circumference = π × diameter

This can be simplified to: Circumference = πd

Because 2 radiuses are equal to a diameter we can also use the formula:
Circumference = 2 × π × radius

This can be simplified to: Circumference = 2πr

It doesn't matter which formula you use, they are the same and will give the same answer.

Example 1: A circle has a diameter of 8 cm. Work out the circumference of the circle.

We can use the formula:
Circumference = π × diameter

We can substitute 8 in for the diameter:
Circumference = π × 8
π × 8 can be written as 8π

The diameter was given in cm, so the answer is 8π cm

We can leave the answer in terms of pi unless we are asked to give the answer as a decimal.

To convert our answer in to a decimal we can use a calculator, there should be a pi button on your calculator.

On the classwiz it is above the Ans button:

classwiz

For the pi button we press shift then Ans:

Calculator buttons pi = Calculator buttons shiftCalculator buttons ans

To work out the circumference in the calculator we press:

Calculator buttons shiftCalculator buttons ansCalculator buttons timesCalculator buttons 8Calculator buttons equals

This gives an answer of 8π, to convert the answer to a decimal we press the SD button:

Calculator buttons SD

This gives us 25.13274123, or 25.1 to 1 decimal place.

We can say the circumference is 25.1 cm to 1 decimal place.

Example 2: A circle has a radius of 9 metres. Work out the circumference of the circle.

This time we have been given the radius of a circle. We can either use the formula:
Circumference = 2 × π × radius

Or we could multiply the radius by 2 to get the diameter and use the formula:
Circumference = π × diameter

If we use:
Circumference = 2 × π × radius

We need to substitute 9 in for the radius:
Circumference = 2 × π × 9

If we are leaving our answer in terms of pi we can simplify our answer by multiplying 2 and 9
2 × 9 = 18
So now we have 18 × π which we can write as 18π

The radius was measured in metres so the answer is 18π metres

If we use a calculator to convert 18π to a decimal we get 56.5 metres to one decimal place.

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Labelled circle showing centre, radius, diameter, circumference, tangent, arc, and sector

Circles have special parts that appear in questions and diagrams. The centre is the middle point, a radius goes from the centre to the edge, and a diameter goes all the way across through the centre.

A tangent touches the circle at exactly one point, an arc is part of the circumference, and a sector is a slice made by two radii and an arc. These words help you read the diagram before you choose a formula.

The diameter is twice the radius, so d=2rd = 2rd=2r and r=d2r = \frac{d}{2}r=2d​. Circumference is the distance around the edge, while area is the space inside. Circumference uses length units such as cm or m, while area uses square units such as cm2cm^2cm2 or m2m^2m2. The key formulas are shown below.

C=πd=2πr C = \pi d = 2\pi r C=πd=2πr A=πr2 A = \pi r^2 A=πr2

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Practice questions

Question 1

2 marks

On the diagram below, draw a radius of the circle.

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Name the line segment that goes from the centre of a circle to its edge.

Area and Circumference of Circles Revision Guide

  1. GCSE
  2. /Maths
  3. /Area and Circumference of Circles

Revision notes for Edexcel GCSE Maths Area and Circumference of Circles. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Practise questions

1 of 2

A circle has a diameter of 14 cm14\text{ cm}14 cm. What is its circumference in terms of π\piπ?

Practise questions

1 of 3

A circle has a radius of 6 m6\text{ m}6 m. What is its circumference in terms of π\piπ?

Practise questions

1 of 3

A circle has a radius of 5 cm5 \text{ cm}5 cm. What is its circumference?