Circumference of a Circle Calculator

What is the circumference of a circle?

The circumference is the length of the boundary of a circle, the distance you would walk by going once around it. It is the circle's version of a perimeter, and it is measured in ordinary length units such as centimetres or feet, not in square units.

Two lengths describe the size of a circle. The radius r runs from the centre to the edge. The diameter d crosses the circle through the centre and is exactly twice the radius. Whatever the size of the circle, dividing its circumference by its diameter always gives the same number, called pi (π) and approximately 3.14159265.

Circumference formula

C = 2 × π × r = π × dC is the circumference, r the radius and d the diameter.

The definition of pi gives the second form directly, and the first follows because d = 2r. Rearranged, the same relationship answers the opposite question:

• Radius from circumference: r = C ÷ (2π)
• Diameter from circumference: d = C ÷ π
• Circumference from the area A: C = 2 × √(π × A), because A = π × r²

If you need the area instead, the area of a circle calculator uses the radius you already have.

How to use the calculator

1. Type the radius into Circle radius. It starts at 3 so there is an example to look at.
2. Choose the unit beside it: mm, cm, dm, m, km, in, ft, yd or mile.
3. Press Calculate. The circumference appears in the same unit, for instance 18.849556 cm.

If you know the diameter, halve it before entering it, because the field expects the radius. Results are rounded to at most six decimal places, and a whole-number result is shown without a decimal point. A negative or empty radius is rejected.

Worked examples

Example 1: a small disc. For r = 3 cm, C = 2 × π × 3 ≈ 18.8496 cm.

Example 2: from the diameter. A round table is 20 in across. Its circumference is π × 20 ≈ 62.8319 in; entering the radius 10 in into the calculator gives the same figure.

Example 3: from the area. A circle covers 50 m². Then C = 2 × √(π × 50) = 2 × √157.0796 ≈ 25.0663 m.

Example 4: wheel travel. A bicycle wheel with a 33 cm radius has a circumference of 2π × 33 ≈ 207.3451 cm, so the bicycle rolls about 2.07 m per revolution. A kilometre is 100,000 cm, which takes 100,000 ÷ 207.3451 ≈ 482.3 revolutions.

Which value of pi is used?

Pi is irrational, so its decimal expansion never ends or repeats. The calculator uses the full double-precision value of π that the computer provides, about 15 to 16 significant digits, and then rounds only the displayed answer.

Hand calculations often substitute an approximation. The fraction 22/7 is about 0.04% too large and 3.14 is about 0.05% too small. For a 10 m radius circle that is a difference of roughly 2.5 cm and 3.2 cm, which is fine for a garden but not for a machined part. If you copy a result from here into another calculation, keep as many digits as you can.

Practical applications

• Wheels and rollers: the circumference is the distance covered in one turn, which links wheel size to speed and distance.
• Belts, ropes and bands: the length of material wrapped once around a pipe, drum or tree trunk is the circumference of its cross-section.
• Running tracks and circular paths: the lap length of a circular route follows from its radius.
• Geography: with a mean Earth radius of about 6,371 km, the formula gives roughly 40,030 km, close to the equatorial length of about 40,075 km.
• Fencing and edging: curved borders for ponds, flower beds or round tables.

Common mistakes

• Entering the diameter as the radius. The result will be twice as large as it should be.
• Confusing circumference with area. Circumference is a length (2πr); area is a surface (πr²) and is measured in square units.
• Rounding pi too early. Round at the end of the calculation, not at the beginning.
• Mixing units. Keep the radius unit consistent; to change the answer to another unit afterwards use the length converter.

For the edge length of straight-sided shapes see the perimeter calculator, the perimeter of a rectangle calculator and the perimeter of a triangle calculator.