Radius of a Circle

Radius of a circle

The radius of a circle is the distance from its center to any point on its edge (or boundary). It's half the diameter and a key measurement for calculating area, circumference, and more.

How to Calculate the Radius?

You usually find the radius when you know one of these three things: the diameter, the circumference, or the area.

1. If you know the diameter (d)

Simplest case!

r = d / 2

(Radius is exactly half the diameter.)

2. If you know the circumference (C)

r = C / (2π)

(Or equivalently: r = C ÷ (2 × π))

π ≈ 3.14159 (or use 3.14 for quick estimates).

3. If you know the area (A)

r = √(A / π)

First, divide the area by π, then take the square root.

Circle radius calculations examples

Example 1 – From diameter

Diameter = 32 cm

r = 32 / 2

r = 16 cm

Example 2 – From circumference

Circumference = 25 m

r = 25 / (2 × 3.14)

r = 25 / 6.28

r ≈ 3.98 m

Example 3 – From area

Area = 78.54 cm²

r = √(78.54 / 3.14159)

r = √(25)

r = 5 cm