Area of a circle

The area of a circle is the plane region bounded by the circle's circumference.

The region shaded in gray inside of circle A above is its area.

The area of a circle can be found using the following formula:

A = πr2

where A is area, r is radius, and π is the mathematical constant approximately equal to 3.14159.

Alternatively, if using the circle's diameter, D, the area is:

Or, if using the circle's circumference, C, the area is:


Find the area of circle O below.

Using A = πr2,

A = π·82 = 64π ≈ 201.06

Area formula proof

The formula for the area of a circle can be proven in a number of ways. One such way involves breaking the circle into equal sectors and rearranging them to construct a parallelogram.