Circular Segment Area Calculator

How it is calculated

The tool uses A = ½ · r² · (θ − sin θ), where r is the circle's radius and θ the central angle in radians. You enter the angle in degrees, and the tool converts it with θ = degrees × π / 180. The term ½·r²·θ is the whole pie slice (sector), and ½·r²·sin θ is the triangle formed by the two radii and the chord. Subtracting leaves the curved segment. The radius must be above zero and the angle above 0 and at most 360 degrees. The area is returned in square units of whatever length unit you used for the radius, labelled generically as units². At 180 degrees the segment is exactly a half circle, and at 360 degrees it is the whole circle.

Common mistakes

• Entering the angle in radians. The field takes degrees, so 1.57 would be read as a tiny 1.57 degree angle, not a right angle.
• Using the inscribed angle or the angle at the circumference instead of the central angle at the centre. The inscribed angle is half as large for the same arc.
• Entering the chord length or the height of the segment as the radius. The first field is the circle's own radius, so convert from chord and height first if that is all you know.
• Expecting a result for an angle above 360 degrees. It is rejected, and an angle of exactly 0 also gives no result.
• Reading the answer as the sector area. The segment is smaller than the pie slice because the triangle to the centre has been removed (except at 360 degrees, where nothing is cut away).