Four different ways to find the radius of a circle

Recommended Lessons

Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.

The four different ways to find the radius of a circle are shown below:

  • Using the diameter
  • Using the circumference
  • Using the area
  • Using the central angle of a sector and the area of the sector

How to find the radius of a circle using the diameter


In a circle, the radius is always half the length of its diameter.

r = d / 2

Example #1:

Find the radius if the diameter is 20 inches

r = d / 2 = 20 / 2 = 10

The radius is 10 inches.

How to find the radius of a circle using the circumference


The example below illustrates clearly how to find the radius of a circle when the circumference is known.

Example #2:

Suppose the circumference of a circle is 50.24 inches. Find the radius, r.

find the radius of a circle given circumference

The radius is 8 inches when the circumference is 50.24 inches

How to find the radius of a circle using the area


The formula to find the area of a circle is A = πr2

Example #3:

Find the radius if the area of the circle is equal to 50 cm2

A = πr2

Substitute 50 for A 

50 = πr2

Substitute 3.14 for π

50 = 3.14r2

Divide both sides of the equation by 3.14

50 ÷ 3.14 = (3.14 ÷ 3.14)r2

15.92 = (1)r2

15.92 = r2

r = √(15.92)

r = 3.98

The radius is 3.98 cm

How to find the radius of a circle using the central angle of a sector and the area of the sector

The formula to find the area of a sector is A = (n0 / 3600)πr2

n0 is the measure of the central angle 

Example #4:

Find the radius if the central angle is 90 degrees and the area of the sector is equal to 19.63 cm2

A = (n0 / 3600)πr2

Substitute 19.63 for A 

19.63 = (n0 / 3600)πr2

Substitute 90 degrees for n0 

19.63 = (900 / 3600)πr2

19.63 = (0.25)πr2

19.63 = 0.785r2

Divide both sides by 0.785

19.63 ÷ 0.785 = (0.785 ÷ 0.785)r2

25.0063 = (1)r2

25.0063 = r2

r = √(25.0063)

r = 5

Find the area of a circle