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
| Field | What to enter |
|---|---|
| Radius | Units: m, cm, mm, km, in, ft … |
| Central angle | Units: °, 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) |
|---|---|
| 37.5 | 3.93 |
| 56.25 | 5.89 |
| 75 | 7.85 |
| 93.75 | 9.82 |
| 112.5 | 11.78 |
| 150 | 15.71 |
Formula
Arc = r × θ (radians)Sector area = ½ r² θChord = 2r sin(θ ÷ 2)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.
Frequently asked questions
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.