Circumference of a Circle Calculator

How to calculate the circumference of a circle

The circumference is the distance around a circle. Which formula you use depends on the measurement you already have:

• Radius: C = 2πr
• Diameter: C = πd
• Area: C = 2√(πA)

In the calculator, C is the circumference, r the radius, d the diameter and A the area. The diameter is always twice the radius (d = 2r), so the first two formulas give the same answer. The calculator uses π to 15 decimal places (3.141592653589793).

From area to circumference

If you only know the area, go through the radius. The area is A = πr², so the radius is r = √(A/π). Put that into C = 2πr and you get C = 2√(πA). Choose Area in the calculator and enter the area in square units, such as in² or ft².

For the opposite calculation, from radius, diameter or circumference to area, use the circle area calculator.

Examples

• Round table top with a radius of 18 in: C = 2 × π × 18 ≈ 113.10 in.
• 12-inch pizza (diameter 12 in): C = π × 12 ≈ 37.70 in.
• Circular patio of 50 ft²: C = 2 × √(π × 50) ≈ 25.07 ft, and the radius is about 3.99 ft.

Common mistakes

• Mixing up radius and diameter. If you put the diameter into 2πr, the answer doubles. A circle with a diameter of 10 in has a circumference of π × 10 ≈ 31.42 in, not 2 × π × 10 ≈ 62.83 in.
• Rounding π to 3.14. 3.14 is about 0.05% less than π. For a diameter of 100 in, 3.14 × 100 = 314 in, while π × 100 ≈ 314.16 in. That is close enough for an estimate, but the gap grows with the size of the circle.

Frequently asked questions