Calculate the area of a circular segment from radius and central angle with chord length and segment height.
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28.54
Segment area
78.54
Sector area
50
Triangle area
14.14
Chord length
15.71
Arc length
2.93
Segment height
Also in Circles
Geometry
The segment area calculator finds the area of a circular segment — the region between a chord and its arc — from radius and central angle.
Segment area = sector area minus triangle area. Sector area = (1/2)*r^2*theta. Triangle area = (1/2)*r^2*sin(theta). So segment = (1/2)*r^2*(theta - sin(theta)).
The chord length is 2r*sin(theta/2) and the segment height is r - r*cos(theta/2).
For angles over 180 degrees, the segment is a major segment (more than half the circle). The formula still applies.
Frequently asked questions
A sector is a pie-slice shape bounded by two radii and an arc. A segment is bounded by a chord and the arc above it.
For a 180-degree angle, the triangle area is zero (the "triangle" is a line), so the segment area equals the sector area = pi*r^2/2.
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