Circumference Calculator

Circumference

On this page, we will explain an important property of circles called the circumference. The topics we will cover are:



  • What is the circumference of a circle?
  • How can you calculate the circumference of a circle?
  • An example of calculating the circumference of the Earth

What is the circumference of a circle?

The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares, but for shapes made up of straight lines, we use the word perimeter and for circles we use the word circumference.

This diagram shows the circumference of a circle.

There are also some other important distances on a circle, called the radius (r) and diameter (d) We will need these to calculate the circumference. The diameter is the distance from one side of the circle, to the other, passing through the center (middle of the circle). The radius is half of this distance.

This diagram shows the circumference, diameter, center and radius on a circle.

How can you calculate the circumference of a circle?

If you know the diameter or radius of a circle, you can work out the circumference. To begin with, remember that pi is a number, written down with the symbol π.  π is roughly equal to 3.14. Then, the formula for working out the circumference of the circle is:

Circumference of circle = π x Diameter of circle

which we usually write in the shortened form C = πd. This tells us that the circumference of the circle is three “and a bit” times as long as the diameter. We can see this on the graphic below:

You can also work out the circumference if you know the radius. Remember that the diameter is double the length of the radius. We already know that C = πd. If r is the radius of the circle, then d = 2r. So, C = 2πr.

Example 1

A circle has a diameter of 10cm, what is its circumference?

Answer

We know that C = πd. Since the diameter is 10cm, we have that C = π x 10cm = 31.42cm (to 2 decimal places).

Example 2

A circle has a radius of 3m, what is its circumference?

Answer

We know that C = 2πr. Since the radius is 3m, we have that C = π x 6m  = C= 18.84 (to 2 decimal places).

Example 3

Find the missing length (marked with a ?) on the diagram below:

Answer

The missing length is the circumference, and the diameter is marked as being 4.3m on the diagram. So, we have that C = πd, so C = π x 4.3m = 13.51m (to 2 decimal places). So, the missing length is 13.51m.

Working out the circumference of the Earth

Using these calculations, it’s possible to work out the circumference of the Earth! Scientists have worked out the diameter of the Earth to be 12,742km (in fact, even the Ancient Greeks had pretty good estimates for this diameter). Given this information, what is the circumference of the Earth?

 

Again, we know that C = πd, and that here d = 12,742km. So, we can calculate the circumference of the Earth as C = π x 12,742km = 40,030km.