basic

Circular Segment Area Calculator

A = (1/2) · r² · (θ − sin θ) for the chord-bound region.

Compute the area of a circular segment (the region between a chord and an arc) from the circle radius and the central angle θ in degrees: A = (1/2) · r² · (θ_rad − sin θ_rad). Reports chord length and arc length.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

°

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

A_segment = (1/2) · r² · (θ − sin θ); chord = 2 · r · sin(θ/2); arc = r · θ.

In depth

Compute the area of a circular segment (the region between a chord and an arc) from the circle radius and the central angle θ in degrees: A = (1/2) · r² · (θ_rad − sin θ_rad). Reports chord length and arc length.