Circular sector and arc calculator
Enter a radius and a central angle in degrees and this tool returns the arc length, sector area, chord length and the perimeter of the sector — the slice of a circle bounded by two radii and the arc between them. It is handy for geometry homework, drafting and any layout involving curved segments.
How it works
The angle in degrees is first converted to radians with θ = degrees × π ÷ 180,
then each property follows a standard formula:
| Property | Formula |
|---|---|
| Arc length | r × θ |
| Sector area | ½ × r² × θ |
| Chord length | 2 × r × sin(θ ÷ 2) |
| Perimeter | arc length + 2 × r |
At θ = 2π (a full 360°) the sector area reduces to the whole-circle area πr².
Example
A radius of 10 and a 90° angle (θ = π/2 ≈ 1.5708):
| Property | Value |
|---|---|
| Arc length | ≈ 15.708 |
| Sector area | ≈ 78.540 |
| Chord length | ≈ 14.142 |
| Perimeter | ≈ 35.708 |
The conversion from degrees happens automatically, all in your browser with nothing uploaded.