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Finding the Radius from the Circumference

(KS3, Year 7)

The radius of a circle is found from the circumference of a circle using the formula: radius equals circumference divided by 2 pi

In this formula, C is the circumference of the circle. The image below shows what we mean by finding the radius from the circumference: circumference and radius on a circle

How to Find the Radius from the Circumference

Finding the radius from the circumference is easy.

Question

What is the radius of the circle, with circumference 50 cm, below? circle with a circumference of 50 cm

Step-by-Step:

1

Start with the formula:

Radius = ^C⁄_2π

Don't forget: / means ÷ and π is pi (≈ 3.14)

2

Substitute the circumference into the formula. In our example, C = 50.

Radius = ⁵⁰⁄_2π

Radius = 50 ÷ 2 ÷ π

Radius = 25 ÷ π

Radius = 25 ÷ 3.14

Radius = 8 cm

Answer:

The radius of the circle is 8 cm.

Lesson Slides

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

Interactive Widget

Here is an interactive widget to help you learn about finding the radius of a circle from its circumference.

Why Is Knowing the Radius in Terms of the Circumference Useful?

Most of the properties of a circle - such as its circumference and area - can be expressed in terms of the radius or diameter. Most students remember the cirumference of a circle with a diameter d as: circumference_from_diameter_mini

But what if you are told the radius r instead? Multiply it by 2 to find the diameter. If you substitute 2r for d, a formula for the circumference of a circle in terms of the radius can be found: circumference_from_radius_mini