Circumference and Area of a Circle

The number π

Measure all the way around any circle (its circumference) and divide by the diameter straight across it, and you always get the same number — about 3.14159. We call it π ("pi").

So the circumference is \pi times the diameter. Since the diameter is twice the radius (d = 2r), we can write it with the radius too:

C = 2\pi r

(the same thing as C = \pi d, because d = 2r).

The area inside

The area is the amount of space inside the circle. It depends on the radius squared:

A = \pi r^2

For example, a circle of radius 5 has area \pi \times 5^2 = 25\pi \approx 78.5.

circumference C = 2\pi r = \pi d;
area A = \pi r^2;
the constant \pi \approx 3.142.

See both on one circle

Step through the figure: mark the radius, trace the circumference, then shade the interior.