Circumference Calculator

How this circumference calculator works

The circumference is the distance around a circle. This circumference calculator needs just one measurement: enter the radius, the diameter, the area or a known circumference and it works out the other three. It uses C = 2πr, which is the same as C = πd, with π = 3.14159265. The units are yours to choose: whatever unit you enter comes back out, and the area is in that unit squared.

The formulas

• Circumference: C = 2 × π × r = π × d
• Diameter: d = 2 × r
• Area: A = π × r²
• From the circumference: r = C ÷ (2π)
• From the area: r = √(A ÷ π)

Worked examples

A 14-inch pizza has a radius of 7 in, so its circumference is 2 × π × 7 = 43.98 in and its area is π × 49 = 153.94 in². A bicycle wheel with a 26 in diameter rolls forward 26 × π = 81.68 in per turn. Going the other way, a tree trunk measured at 94.2 in around has a diameter of 94.2 ÷ π = 30 in. A ring size works the same way: a finger that is 17 mm across needs a circumference of 17 × π = 53.4 mm.

Common mistakes

Mixing up radius and diameter is the usual one: the radius is half the diameter, and doubling the radius doubles the circumference but quadruples the area. Another is using 3.14 for large circles. For a 100 m diameter circle, 3.14 gives 314 m while π gives 314.16 m, a 16 cm difference. This calculator uses the full precision of π and rounds only the displayed result.

Measuring a real circle

For a physical object, wrap a flexible tape or a piece of string around it, mark the overlap, and measure the string; that is the circumference, and dividing by π gives the diameter. Measuring across a pipe or tree often misses the true center, so the string method is more accurate. For flat shapes beyond circles, such as ellipses and sectors, use the area calculator, and for round solids like cylinders and spheres use the volume calculator.