# What is the circumference of a circle?

Finds the circumference of a circle from its radius or diameter (C = 2πr = πd), or the radius and diameter from the circumference.

- Page: https://www.acalculator.org/math/circumference-calculator
- JSON spec: https://www.acalculator.org/math/circumference-calculator.json
- Version: d60411ca81cb

## Default answer

Example with the default inputs (Radius 5 in): A circle of radius 5 in (diameter 10 in) has a circumference of 31.42 in.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| r | Radius | The distance from the centre of the circle to its edge. |
| d | Diameter | The distance across the circle through its centre: twice the radius. |
| c | Circumference | The distance around the circle. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| r | Radius | The distance from the centre of the circle to its edge. |
| d | Diameter | The distance across the circle through its centre: twice the radius. |
| c | Circumference | The distance around the circle. |

## Method

C = 2πr = πd, where r is the radius and d = 2r is the diameter.

## Assumptions

- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Every length is in the unit shown next to it.
- Each value must be greater than 0.

## Worked examples

1. r = 5 gives c = 31.415927, d = 10. Source: hand calculation in content.mdx: C = 2 × π × 5 = 10π = 31.4159.
2. d = 8 gives c = 25.132741, r = 4. Source: hand calculation in content.mdx: C = π × 8 = 25.1327.
3. c = 44 gives d = 14.005635, r = 7.002817. Source: hand calculation in content.mdx: d = 44 ÷ π = 14.0056 (with π ≈ 22/7 it would be exactly 14).

## FAQ

### What is the formula for circumference?

C = 2πr, where r is the radius. Because the diameter is twice the radius, the same formula is C = πd. A 10 in pizza (diameter 10 in) has a crust 31.42 in long.

### How do I get the diameter from the circumference?

Divide by π: d = C ÷ π. A tree trunk that measures 44 in around is 44 ÷ 3.14159 = 14.01 in across.

### How do I get the radius from the circumference?

Divide by 2π: r = C ÷ 2π. A circumference of 44 in gives a radius of 7.00 in.

### Is circumference the same as perimeter?

Yes. Circumference is the word for the perimeter of a circle: the length of its edge. It is a length, so it is in inches or centimetres, not square units.

### Why do some books say the circumference of a 14 cm circle is exactly 44 cm?

They use 22/7 for π. 22/7 = 3.142857…, which is a little more than π = 3.141592…, so π × 14 is 43.98 cm, not 44 cm. This calculator uses the full value of π.

### How do I measure the circumference of a round object?

Wrap a flexible tape or a string once around it, then measure the string. To check, measure the width across the middle and multiply by π.

## Sources

- NIST Digital Library of Mathematical Functions, §3.12 Mathematical Constants, equation 3.12.1 (π = 3.14159 26535 89793…). https://dlmf.nist.gov/3.12
- OpenStax, Prealgebra 2e, §9.5 Solve Geometry Applications: Circles and Irregular Figures (C = 2πr and C = πd). https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures
- NIST Special Publication 811 (2008), Appendix B: 1 in = 0.0254 m exactly, for unit conversions.