# Segment Area Calculator

URL: https://speedycalculator.com/calculators/math/segment-area/
Last updated: 2026-10-30

> The segment area calculator finds the area of a circular segment – the region between a chord and its arc – from the radius and either the central angle or the segment height, with the arc length and chord.

## Inputs

- Radius r (cm, m, mm, in, ft, yd, km, mi)
- Also known
- Central angle α (°, rad, π rad, grad, turn)
- Segment height h (cm, m, mm, in, ft, yd, km, mi)

## Results

- Central angle
- Segment area
- Arc length
- Chord length
- Share of the circle

## Formula

```
A = r²(α − sin α)/2,  α = 2·arccos((r − h)/r)
```

## Explanation

Circular segments appear in tank volumes (a cylinder lying on its side is partly full), arched windows, bridge arches and the shape of a lens. Their area is the sector minus the triangle under the chord.

### How to use the Segment Area Calculator

- **Radius r**
- **Also known**
- **Central angle α**
- **Segment height h**

Results update as you type, and everything is calculated in your browser.

### How it works

Enter the radius and the angle or height. If h is greater than r the segment is the larger part of the circle, which the formula handles automatically.

### Inputs explained

FieldWhat to enterRadius rUnits: cm, m, mm, in, ft, yd …Also knownChoose one: Central angle α, Segment height hCentral angle αUnits: °, rad, π rad, grad, turnSegment height hUnits: cm, m, mm, in, ft, yd …

### What each result means

- **Segment area** = [Radius r]^2×(rad([Central angle]) - sin(rad([Central angle])))÷2
- **Arc length** = [Radius r]×rad([Central angle])
- **Chord length** = 2×[Radius r]×sin(rad([Central angle])÷2)
- **Share of the circle** = [Radius r]^2×(rad([Central angle]) - sin(rad([Central angle])))÷2÷(pi×[Radius r]^2)×100

### Example values

How the main result changes when **Radius r** changes and everything else stays at the example values above:

Radius r (cm)Segment area (cm²)57.1357.516.05361028.539812.544.59351564.214620114.1593

## Worked example

Inputs — Radius r: 10 cm; Also known: Central angle α; Central angle α: 90 °.

Results — Central angle = 90 °; **Segment area = 28.539816 cm²**; Arc length = 15.707963 cm; Chord length = 14.142136 cm; Share of the circle = 9.0845 %.

## Key terms

- **Circular segment**: The area between a chord and its arc.

## FAQ

**What is a circular segment?**
The region cut off by a chord.

**How is it different from a sector?**
A sector is bounded by two radii; a segment by a chord.

**How do I find the liquid in a horizontal tank?**
Segment area × tank length.

**What if h = r?**
The segment is a half-circle.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [Wolfram MathWorld – Circular segment](https://mathworld.wolfram.com/CircularSegment.html)