Math

Segment Area Calculator

Find the area of a circular segment from radius and central angle.

Calculated Output

Segment area 7.135

Formula: area = ½ r²(θ − sin θ), θ in radians

Step-by-Step Breakdown

1. Values used:

2. Radius = 5

3. Central angle = 90 °

5. Segment area = 7.135

Did this calculator solve your problem today?

The math behind it

area = ½ r²(θ − sin θ), where θ is the central angle in radians. It equals the sector area minus the triangle area.

Radius 5, angle 90° → ½·25·(π/2 − 1) ≈ 7.13.

Segment vs sector?

A sector is the pie slice; a segment removes the triangle, leaving just the cap beyond the chord.