Segment Area Calculator
Calculate the area of a circular segment (sector minus triangle) from radius and angle.
Inputs
units
°
Segment Area
28.5398sq units
Step by step
Convert angle to radians
θ = 90° = 1.570796 rad
Segment area = sector − triangle
A = ½ × 10² × (1.570796 − sin(1.570796))
= 28.5398
How it works
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
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.