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.
What is the radius of the circle, with circumference 50 cm, below?
Start with the formula:
Radius = C⁄2π
/ means ÷ and
π is pi
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
The radius of the circle is 8 cm.
The slider below shows another real example of how to find the radius of a circle from the circumference.
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
- can be expressed in terms of the radius or diameter.
Most students remember the cirumference of a circle with a diameter d
But what if you are told the radius r
instead? Multiply it by 2 to find the diameter.
If you substitute 2r
, 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