Finding the Radius from the Diameter
(KS3, Year 7)

The radius of a circle is half of the diameter. radius_from_diameter

How to Find the Radius from the Diameter

Finding the radius from the diameter is easy.

Question

What is the radius of the circle, with diameter 10 cm, below?

Step-by-Step:

1

Divide the diameter, 10 cm, by 2.

10 ÷ 2 = 5 cm

Answer:

The radius of the circle is 5 cm.

Lesson Slides

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

Interactive Widget

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

Why Is Knowing the Radius in Terms of the Diameter 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 area of a circle with a radius r as: area_of_a_circle_mini

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