Circumference of a Circle
(KS3, Year 7)

The Lesson

The circumference of a circle is found using the formula:

In the formula, d is the diameter of the circle. The image below shows what we mean by diameter:

How to Find the Circumference of a Circle

Question

What is the circumference of a circle with a diameter of 10 cm, as shown below?

Step-by-Step:

1

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

2

Substitute the diameter into the formula. In our example, d = 10.
Circumference = π × 10 = 31.4 cm

Answer:

The circumference of the circle with a diameter of 10 cm is 31.4 cm.

Lesson Slides

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

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.

Radius and Diameter

The diameter of a circle is twice the length of its radius. If you are given the radius of a circle, double it to find the diameter and put this in the formula.

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:

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 diameter is, that is the units of the circumference. If the diameter is in cm, the circumference is in cm. If it is inches, the circumference is in inches.
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See Also

What is the circumference? What is a circle? What is the diameter? What is pi?