# Circle Calculator — Radius, Diameter, Circumference, Area

> Find a circle’s radius, diameter, circumference and area from any one value, plus arc length and sector area. Works in mm, cm, m, inches and feet. Free.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/circle-calculator/
- **Price:** Free, no sign-up required

## Overview

A circle is fully described by a single measurement: give it the radius, the diameter, the circumference (the distance around) or the area, and the other three are fixed. This calculator takes whichever one you know and solves the rest at once, in millimetres, centimetres, metres, inches or feet. Switch to sector mode to slice the circle by a central angle and get the arc length, the area of the slice and the straight-line chord across it.

## How to read your result

The large figure is the area; beside it sit the radius, diameter and circumference, all in the unit you chose. The “same circle in other units” panel restates the area and circumference in every other length unit, so a radius typed in inches can be read off in centimetres without retyping. In sector mode, arc length is the curved edge of the slice, sector area is the pie-piece area, and the chord is the straight line joining the two ends of the arc.

## Method

From the radius r: diameter = 2r, circumference C = 2πr (= πd), area A = πr². Working backwards, a known circumference gives r = C ÷ (2π) and a known area gives r = √(A ÷ π). For a sector with central angle θ measured in radians, arc length = rθ, sector area = ½r²θ, and the chord = 2r·sin(θ ÷ 2); an angle entered in degrees is converted with θ = degrees × π ÷ 180.

## Example

- **Setup:** A radius of 5 cm.
- **Result:** The diameter is 10 cm, the circumference is about 31.42 cm (2 × π × 5), and the area is about 78.54 cm² (π × 5²). A 90° sector of that circle has an arc 7.85 cm long and an area of 19.63 cm².

## Frequently asked questions

### How do I find circumference from the radius or diameter?

Circumference is 2 × π × radius, which is the same as π × diameter. With a radius of 5 cm that is 2 × 3.14159 × 5 ≈ 31.42 cm. Enter the radius (or diameter) and the calculator returns the circumference instantly.

### Can I work backwards from the circumference or area?

Yes. Choose “Circumference” or “Area” as the value you know. The calculator inverts the formulas — radius = circumference ÷ (2π), or radius = √(area ÷ π) — and then fills in every other property of the circle.

### What is the arc length and area of a sector?

A sector is a pie-slice bounded by two radii and an arc. For a central angle θ in radians, the arc length is r × θ and the sector area is ½ × r² × θ. A full turn (360° or 2π) gives back the whole circumference and area; a 90° sector is exactly one quarter of each.

### Which units can I use?

Millimetres, centimetres, metres, inches and feet. Lengths convert through the exact international definitions (1 inch = 2.54 cm, 1 foot = 0.3048 m), and areas convert by the square of the length factor, so 1 ft² = 0.0929 m².

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## Sources

- https://mathworld.wolfram.com/Circle.html
- https://en.wikipedia.org/wiki/Circular_sector

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Interactive version: https://youcalc.com/en/math/circle-calculator/ · From YouCalc — https://youcalc.com