# Arc Length and Sector Area Calculator

URL: https://speedycalculator.com/calculators/math/sector-arc-length/
Last updated: 2026-10-25

> This calculator finds the arc length, sector area and chord length of a circle sector from the radius and central angle, in degrees or radians.

## Inputs

- Radius (m, cm, mm, km, in, ft, yd, mi)
- Central angle (°, rad)

## Results

- Arc length
- Sector area
- Chord length

## Formula

```
Arc = r × θ (radians)
Sector area = ½ r² θ
Chord = 2r sin(θ ÷ 2)
```

## Explanation

A sector is a slice of a circle, like a slice of pizza. The arc is its curved edge.

### How to use the Arc Length and Sector Area Calculator

- **Radius**
- **Central angle**
- Want to work backwards? Type a value into **Arc length** and **Central angle** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Convert the angle to radians, then multiply by the radius for arc length and by half the radius squared for area.

### Inputs explained

FieldWhat to enterRadiusUnits: m, cm, mm, km, in, ft …Central angleUnits: °, rad

### What each result means

- **Arc length** = [Radius] × rad([Central angle])
- **Sector area** = [Radius]^2 × rad([Central angle]) ÷ 2
- **Chord length** = 2×[Radius]×sin(rad([Central angle])÷2)

### Example values

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

Central angle (°)Arc length (m)37.53.9356.255.89757.8593.759.82112.511.7815015.71

## Worked example

Inputs — Radius: 6 m; Central angle: 75 °.

Results — **Arc length = 7.85 m**; Sector area = 23.56 m²; Chord length = 7.31 m.

## FAQ

**Why use radians?**
Arc length is simply radius × angle when the angle is in radians.

**What is a segment?**
The region between the chord and the arc.

**What formula does the Arc Length and Sector Area Calculator use?**
Arc = r × θ (radians).

**Can I work backwards from the result?**
Yes. Type the result you want into Arc length and the calculator finds the matching central angle.