Math
Arc Length and Sector Area Calculator
Find the arc length, sector area, chord length and segment area of a circle from its radius and the angle at the centre.
°
Arc length
10.472
- Sector area
- 52.3599
- Chord length
- 10
- Segment area
- 9.0586
A 60° slice of a circle with radius 10 has an arc 10.472 long and an area of 52.36.
How it's worked out
- Angle in radians
60° × π ÷ 1801.047198 - Arc length
r × θ = 10 × 1.04719810.472 - Sector area
½ r² θ52.3599
The formulas
Arc = rθ · Sector = ½r²θ · Chord = 2r sin(θ ÷ 2) · Segment = ½r²(θ − sin θ)
Worked example
Radius 10 and 60° (π/3 radians): the arc is 10.47, the sector area 52.36 and the chord exactly 10.
Questions people ask
How do I find arc length?
Radius × angle in radians, or 2πr × angle ÷ 360. A 60° arc of radius 10 is 10.47.
How do I find the area of a sector?
½ × r² × angle in radians, or πr² × angle ÷ 360.
What is a chord?
The straight line joining the two ends of the arc: 2r × sin(angle ÷ 2).
About this calculator
Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem