Arc Length Calculator
Enter the radius and the central angle to get the arc length, sector area, chord length and segment area.
- θ = 1.0472 rad
- Arc s = r × θ = 10 × 1.0472 = 10.472 cm
- Sector = ½ r² θ = 52.3599 cm²
- Chord = 2r sin(θ/2) = 10 cm
Arc length
10.472cm
- Sector area
- 52.3599 cm²
- Chord
- 10 cm
- Segment area
- 9.0586 cm²
Arc length formula
An arc is a fraction of the full circumference. If the angle is θ degrees, the arc is θ/360 of 2πr, so s = 2πr × θ/360. In radians it collapses to s = rθ — which is exactly why radians exist: one radian is the angle whose arc equals the radius.
The sector (pizza slice) area is the same fraction of πr²: A = θ/360 × πr², or ½r²θ in radians. The segment is the sliver between the chord and the arc: sector minus the triangle, ½r²(θ − sin θ).
Questions people ask
How do I find the arc length without the angle?
If you know the chord c and radius r, the angle is θ = 2 × arcsin(c / 2r). Then s = rθ.
How do I convert degrees to radians?
Multiply by π/180. 90° = π/2 ≈ 1.5708 rad.
What is the arc length of a semicircle?
Half the circumference: πr. For r = 10 that is about 31.42.