Circumference of a Circle Using the Radius
(KS3, Year 7)
The circumference of a circle is found using the formula:

circumference circle radius formula
In the formula, r is the radius of the circle. The image below shows what we mean by radius: circumference_circle_r

How to Find the Circumference of a Circle Using the Radius

Question

What is the circumference of a circle with a radius of 5 cm, as shown below?
circumference circle 5

Step-by-Step:

1

Start with the formula:
Circumference = 2πr
Don't forget: π is pi (≈ 3.14) and 2πr = 2 × π × r.

2

Substitute the radius into the formula. In our example, r = 5.
Circumference = 2 × π × 5 = 31.4 cm

Answer:

The circumference of the circle with a radius of 5 cm is 31.4 cm

Lesson Slides

The slider below shows another real example of how to find the circumference of a circle.

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

What Is Pi?

π is the symbol for pi. π is how many times longer a circle's circumference is than its diameter. It is the circumference divided by the diameter:

pi2 π is the same for all circles, and is approximately equal to 3.14.

A Note on Units

The circumference of a circle is a length. Whatever the units of the radius is, that is the units of the circumference. If the radius is in cm, the circumference is in cm. If it is inches, the circumference is in inches.
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This page was written by Stephen Clarke.