Circumference: a circle's perimeter

A circle has no corners and no straight sides — so there's nothing to add up. Instead, the distance around a circle has its own name: circumference.

One number does it all: π

Measure the distance around any circle (the circumference C) and divide by the distance straight across (the diameter d). You always get the same number:

C ÷ d = π ≈ 3.14159…

This ratio is the same whether the circle is a coin or a planet. Rearranging:

C = π × d = 2πr (since diameter = 2 × radius)

Unrolling the circumference

The easiest way to see it: imagine rolling the circle along a flat surface for exactly one full rotation. The point where it started meets the ground again after it has traveled exactly C = 2πr.

The unrolled edge is about 6.28 radii long (2π ≈ 6.283). Every circle, regardless of size, unrolls to exactly 6.28 radii.

Circumference vs. diameter

Both give the same answer — diameter is just r × 2, so pick whichever you know.

Why π shows up again

Earlier you saw π in the area formula (A = πr²). That's not a coincidence: π describes the relationship between a circle's linear dimensions and its curved ones. Circumference is the linear version (multiply r once by 2π); area is the square version (multiply r² by π).