Circumference Calculator

Circumference uses the two equivalent forms C = 2 x pi x r when you know the radius, or C = pi x d when you know the diameter. Because d = 2r, both expressions give the same answer. The calculator picks the form that matches your input and shows it under "How this was solved".

Pi is the ratio of a circle's circumference to its diameter, the same value for every circle in flat Euclidean space. It is irrational (cannot be written as a fraction) and transcendental (not a root of any polynomial with rational coefficients), so its decimal never terminates and never repeats. The calculator uses JavaScript's Math.PI, which carries about 15 significant digits, and rounds the displayed pi to 2 decimals for readability.

Yes. Pick "Circumference (C)" as the given value and enter the circumference. The calculator inverts the formula with r = C / (2 x pi), then derives d = 2r and A = pi x r^2. You can also start from area: it solves r = sqrt(A / pi) and then computes diameter and circumference. Any one of the four properties is enough to find the other three.

The exact circumference of a circle with radius 5 is 10 x pi, which has no finite decimal expansion. The decimal you see (about 31.4159) is a rounded approximation. For schoolwork that asks for "exact form", write the answer as a multiple of pi (for example 10 pi). For engineering, the rounded decimal is what you measure and build with.

Anywhere a circle rolls, fits, or wraps: tire and wheel sizing (one rotation covers a distance equal to the circumference), running tracks (a 400 m lane is set by inner-edge circumference), bicycle gearing and odometers, pipe and pulley sizing, cake and pizza pans, hat and ring fitting, and even Earth's equator (about 24,901 miles, derived from the planet's radius).