How to Find the Radius from the Circumference

Finding the Radius from the Circumference

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

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.

Slider

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

See Also

What is the radius? What is a circle? What is the circumference? Find the radius from the circumference of a circle ( interactive widget)