# What are my circle's measurements?

Finds the radius, diameter, circumference, and area of a circle from any one of them, with C = 2πr and A = πr².

- Page: https://www.acalculator.org/math/circle-calculator
- JSON spec: https://www.acalculator.org/math/circle-calculator.json
- Version: 702986190c7e

## Default answer

Example with the default inputs (Radius 5 in): A circle of radius 5 in has a diameter of 10 in, a circumference of 31.42 in, and an area of 78.54 in².

## 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: its perimeter. |
| a | Area | The space inside 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: its perimeter. |
| a | Area | The space inside the circle. |

## Method

d = 2r, C = 2πr = πd, and A = πr², where r is the radius.

## 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, and the area is in the square unit shown next to it.
- Each value must be greater than 0.

## Worked examples

1. r = 5 gives d = 10, c = 31.415927, a = 78.539816. Source: hand calculation in content.mdx: d = 2 × 5 = 10, C = 2π × 5 = 31.4159, A = π × 5² = 78.5398.
2. d = 12 gives r = 6, c = 37.699112, a = 113.097336. Source: hand calculation in content.mdx: r = 12 ÷ 2 = 6, C = π × 12 = 37.6991, A = π × 6² = 113.0973.
3. c = 100 gives r = 15.915494, d = 31.830989, a = 795.774715. Source: hand calculation in content.mdx: r = 100 ÷ 2π = 15.9155, A = C² ÷ 4π = 795.7747.
4. a = 50 gives r = 3.989423, d = 7.978846, c = 25.066283. Source: hand calculation in content.mdx: r = √(50 ÷ π) = 3.9894, C = 2√(πA) = 25.0663.

## FAQ

### How do I find the area of a circle from its circumference?

First find the radius, r = C ÷ 2π, then the area, A = πr². In one step, A = C² ÷ 4π. A circumference of 100 cm gives a radius of 15.92 cm and an area of 795.77 cm².

### How do I find the radius from the area?

Divide the area by π and take the square root: r = √(A ÷ π). An area of 50 in² gives a radius of √(50 ÷ 3.14159…) = 3.99 in.

### What is the difference between circumference and area?

The circumference is a length: the distance around the circle, in inches, centimetres, or feet. The area is the space inside, in square units such as in² or cm². Doubling the radius doubles the circumference but makes the area four times as large.

### Why is the diameter twice the radius?

The radius runs from the centre to the edge. The diameter runs from edge to edge through the centre, so it is one radius out and one radius back: d = 2r.

### What value of π does the calculator use?

It uses π to about 16 significant figures, 3.141592653589793. Using 3.14 instead gives answers that are about 0.05% too small, which is enough to change the second decimal place of a larger circle.

### Can I mix units, such as a radius in feet and an area in square inches?

Yes. Each box has its own unit switch, and the calculator converts between them. The answer changes unit, not size.

## 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, C = πd, A = πr²). 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.