Circumference of Circles

Circumference of Circles feature image.

At some point in the study of mathematics, students will need to learn how to calculate the circumference of circles, particularly pupils studying KS3 Maths (ages 11-14) or equivalent.

In order to do this, they will need to understand the basics, including which formula to use and how to apply each snippet of knowledge they are given. This post should provide well-rounded guidance on each important element.

What is Circumference?

Circumference is a type of perimeter. Circumference is the distance around the edge of a circle.

To calculate the circumference of a circle, learn this formula by heart.

Circumference of a circle = Ο€ x diameter or Ο€d

You might also see it written as 2 Γ— Ο€ Γ— radius.

Circle diagram highlighting the diameter.

Some points to remember:

β€’ The diameter is the distance from one point on a circle, through the centre, to another point on the circle.
β€’ The radius is half of the circle’s diameter.
β€’ You can use the Ο€ button on your calculator when finding the circumference of a circle,
which is approximately 3.141592654…

Example 1:

Calculate the circumference of the circle, giving your answer correct to 1 decimal place.

Circle diagram with a diameter of 8cm.

Write the formula: Circumference = Ο€d
β€’ Substitute the letter d for the measurement you have been given: Ο€ Γ— 8 = 25.13274123…
β€’ Round to the correct degree of accuracy and include the units.

Circumference = 25.1cm

Example 2:

Calculate the circumference of the circle, giving your answer correct to 1 decimal place.

Circle diagram with a radius of 5cm

This time, the radius measurement has been given so the first step is to double it to find the diameter.

5 Γ— 2 = 10cm
β€’ Write the formula: Circumference = Ο€d
β€’ Substitute the letter d for the diameter measurement you have just calculated.

Ο€ Γ— 10 = 31.41592654…
β€’ Round to the correct degree of accuracy and include the units.

Circumference = 31.4cm


For expanded insights into the circumference of circles, you can check out our Walkthrough Worksheet just below. If offers the step-by-step guidance shown above and combines it with a series of questions that are designed to help develop learning and confidence in the topic.

Circumference of Circles KS3 Walkthrough Worksheet

Circumference of Circles Walkthrough Worksheet link.

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