Circumference Calculator
Find the circumference of a circle from its radius, diameter or area. Free circumference calculator that also returns the diameter and area with the C = 2πr formula shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Circumference Calculator Works
Pick whether you know the radius, diameter or circumference, enter the value, and this calculator instantly returns all four core circle measurements: radius, diameter, circumference and area. It works in any unit — the answers come back in the same unit you entered (and area in those units squared).
The Formula
Circumference: C = 2πr = πd Area: A = πr²
Pi (π ≈ 3.14159) is the fixed ratio of a circle’s circumference to its diameter. Because the diameter is exactly twice the radius, the two circumference formulas are identical.
To work backwards from a circumference to the radius:
r = C ÷ (2π)
Worked Example
For a circle with a diameter of 10:
- Radius = 10 ÷ 2 = 5
- Circumference = π × 10 = ≈ 31.4159
- Area = π × 5² = π × 25 = ≈ 78.5398 square units
Quick Conversions
| You know | To get circumference |
|---|---|
| Radius r | C = 2πr |
| Diameter d | C = πd |
| Area A | C = 2π × √(A ÷ π) |
Why Circumference Matters
The circumference shows up everywhere a round edge needs measuring: fitting a belt or O-ring, calculating how far a wheel travels in one rotation, edging a circular garden bed, or trimming fabric and trim around a round table. Because it scales linearly with the radius, doubling a circle’s radius doubles its circumference but quadruples its area — a handy relationship to keep in mind when sizing anything circular.
Frequently asked questions
How do I calculate the circumference of a circle?+
Multiply the diameter by π (about 3.14159), or multiply the radius by 2π. In symbols, C = πd = 2πr. For a circle with a 10 cm diameter, the circumference is π × 10 ≈ 31.42 cm.
What is the formula for circumference?+
The circumference of a circle is C = 2πr, where r is the radius, or equivalently C = πd, where d is the diameter. Both give the same answer because the diameter is twice the radius. Pi (π) is the constant ratio of any circle's circumference to its diameter, approximately 3.14159.
How do I find the radius from the circumference?+
Divide the circumference by 2π. So r = C ÷ (2π). For example, a circle with a 31.42 cm circumference has a radius of 31.42 ÷ (2 × 3.14159) ≈ 5 cm. This calculator does the reverse calculation automatically when you enter a circumference.
What is the difference between circumference and area?+
Circumference is the distance around the edge of a circle, measured in linear units like cm or inches. Area is the space enclosed inside the circle, measured in square units. They use different formulas: C = 2πr for circumference and A = πr² for area. The calculator shows both.
What value of pi should I use?+
For most work, π ≈ 3.14159 is more than accurate enough, and many classrooms use 3.14 for quick estimates. This calculator uses the full-precision value of pi built into JavaScript (about 15 significant digits), so your results are as exact as the inputs you provide.