Circular Segment Area (Chord and Height)

Enter the chord length and height (sagitta) to instantly find a circular segment area, plus its radius, central angle, and arc length.

Input

Enter the chord length c and the segment height h (sagitta) to compute the segment area, radius, central angle, and arc length.

Chord length c

Height h (sagitta)

Segment area

11.18238

Radius r

Central angle θ

106.260205°

Arc length

9.272952

Enter the chord and height in the same unit. The area is in that unit squared, lengths in that unit, and the angle is in degrees.

The radius is found from r = (c² / 4 + h²) / (2h), where c is the chord length and h is the segment height (sagitta).
The central angle θ comes from cos(θ/2) = (r − h) / r, so θ = 2·acos((r − h) / r). This stays correct even when the height exceeds the radius (a segment larger than a semicircle).
The arc length is r·θ and the segment area is (r² / 2)·(θ − sin θ), with θ in radians.
Enter the chord and height in the same unit. The area is in that unit squared, lengths in that unit, and the angle is shown in degrees.

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