Circumferences
(KS3, Year 7)

The Lesson

The circumference is the distance measured around a circle. The circumference is often denoted by C. The image below shows what we mean by the circumference:

circumference

Dictionary Definition

The Oxford English Dictionary defines the circumference as "the curved line which forms the boundary of a circle."

Examples of the Circumference

The circle below has a circumference of 20 cm. This is the distance around the circle.

circumference of 20 cm The circle below has a circumference of 12 inches.

circumference of 12 inches

How to Find the Circumference

The circumference of a circle is related to its radius and diameter.

How to Find the Circumference from the Radius

The circumference is the radius multiplied by 2π. If the circumference is C and the radius is r (as shown in the image below), then we can find the circumference using the formula:

circumference equals 2 times pi times radius
Read more about how to find the circumference using the radius

How to Find the Circumference from the Diameter

The circumference is the diameter multiplied by π. If the circumference is C and the diameter is d (as shown in the image below), then we can find the circumference using the formula:

circumference equals pi times diameter
Read more about how to find the circumference using the diameter

Interactive Widget

Here is an interactive widget to help you learn about the circumference.

What Is a Circle?

A circle is a shape containing a set of points that are the same radius from the center of the circle.

Circumference and the Circle

In everyday language, the circumference is used to refer to the boundary of the circle (that is the curved blue line).

circle Technically, the circle is defined as the boundary (the curved blue line). The circumference is the distance around the boundary.
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See Also

What is a circle? What is the radius? What is the diameter? Finding the circumference of a circle using the radius Finding the circumference of a circle using the diameter Learn about the circumference ( interactive widget)