## 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?## Step-by-Step:

# 1

# 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.## 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