Segment Area Calculator
Calculate the area of a circular segment (sector minus triangle) from radius and angle.
About Segment Area Calculator
A circular segment is the region between a chord and the arc it subtends. Its area equals the sector area minus the triangular area formed by the two radii and the chord.
Formula
Segment Area
A = ½ × r² × (θ − sin θ)
- r
- Radius
- θ
- Central angle in radians
Worked example
With the default values below, Segment Area Calculator returns Segment Area of 28.5398. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Radiusminimum 0 units
- 10 units
- Central Angleaccepts 0–360 °
- 90 °
Results
- Segment Area
- 28.5398 sq units
Step by step
- 1Convert angle to radians
- 2Segment area = sector − triangle= 28.5398
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When is the segment area largest?
For a semicircle (180°), the segment is the upper half of the circle. The formula still applies.
Does this work for major segments?
For angles > 180° the formula gives the major segment area directly.