## The Lesson

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

## 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?

# 1

Start with the formula:
Radius = C
Don't forget: / means ÷ and π is pi (≈ 3.14)

# 2

Substitute the circumference into the formula. In our example, C = 50.
Radius = 50 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. Open the slider in a new tab

## 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: 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: Read more about how to find the circumference of a circle using the radius