Circular Segment Area Calculator

About this calculator

A circular segment is the region between a chord and the arc it cuts off from a circle. Its area is given by A = ½·r²·(θ − sinθ), where r is the circle's radius and θ is the central angle in radians subtended by the chord; the θ term accounts for the full pie-slice (sector) area, while subtracting sinθ removes the triangular portion between the two radii and the chord, leaving just the curved sliver.

Engineers use this formula to calculate the cross-sectional area of liquid in a partially filled horizontal cylindrical tank or pipe (a common problem in fluid storage and flow-rate calculations), architects use it to size arched windows, doors, and vaulted openings, and machinists use it when computing material removed by a curved cut. Geometry students also encounter it as a standard application of integrating circular sector and triangle areas.