Circle sector calculator

Find arc length, chord, sector area and circular-segment area from radius and central angle.

Your input

Outputs are cleared when the input changes.

Result

Enter your data or use the example, then run the tool.

Worked example

r=2 and 90° give arc π, sector π, chord 2√2 and segment π−2.

360° gives a full-circle area, circumference as arc length and zero chord.

Method

Convert the angle to radians θ; arc=rθ, sector=r²θ/2 and chord=2r sin(θ/2).

Segment area is r²(θ−sinθ)/2. A small-angle expansion reduces cancellation for tiny angles.

Limits

Radius must be positive, angle between zero and one full turn. All lengths use one consistent input unit, areas its square.

Floating-point geometry only; no material strength, cutting allowance or fabrication certification.

Sources

OpenStax: angles, radians and sector area

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