Segment Area Calculator

Enter a radius and central angle to calculate the area of a circular segment.

How to Use the Segment Area Calculator

Enter a radius and the central angle in degrees. The calculator returns the segment area, alongside the full sector area for comparison.

A segment is the sliver left over after cutting the triangular part out of a sector — take the pie-slice (sector) area and subtract the triangle formed by the two radii and the chord connecting their endpoints:

segment area = sector area − triangle area
             = ½ × radius² × (angle in radians − sin(angle))

At small angles, the chord and the arc are nearly the same length, so the segment is razor-thin — the triangle eats almost the entire sector. Push the angle toward 180° and the triangle collapses to zero area (its "height" vanishes), so the segment and the sector become identical: a full half-circle.