Circles and π

A circle has no straight sides, but one number ties it all together: π.

π: the circle's constant

Take any circle's distance around — its circumference — and compare it to the distance straight across — its diameter. You always get the same ratio: about 3.14159…, which we call π. So the circumference is always

C = π × diameter = 2 π r, where r is the radius.

That's true for every circle, from a coin to a planet — π never changes.

Area: π r²

To find the area, cut the circle into thin wedges and fan them out, alternating tip-up and tip-down. They line up into a rectangle: its height is the radius r, and its base is half the way around the circle, π r. The thinner the wedges, the closer it gets to a perfect rectangle.

A rectangle's area is base × height, so the circle's area is

π r × r = π r².

Every circle answer comes from one measurement, the radius r: the circumference is 2 π r, and the area is π r².