Circle Radius Calculator

A circle is the set of all points in a plane at a fixed distance from a center point. The radius R is that fixed distance — the most fundamental measurement of any circle.

The diameter is twice the radius: d = 2R. It passes through the center and connects two opposite points on the circle.

The circumference of a circle is the distance around its edge:

C = 2πR

where:

• C — circumference,

• R — radius,

• π — approximately 3.14159.

The area enclosed by a circle:

S = πR²

where:

• S — area,

• R — radius,

• π — approximately 3.14159.

Working backward — finding the radius when you know the circumference or area — requires solving these formulas for R. The calculator does that algebra automatically.

Solving for Radius from Circumference:

R = C / 2π

where C is circumference, R is radius, π ≈ 3.14159.

Solving for Radius from Area:

R = √(S / π)

where S is area, R is radius, π ≈ 3.14159.