A circular segment is the region between a chord (a straight line connecting two points on a circle) and the arc it cuts off — like the shape of a lens or the top of a stop sign's rounded cut.
A circular segment is the region between a chord (a straight line connecting two points on a circle) and the arc it cuts off — like the shape of a lens or the top of a stop sign's rounded cut. This calculator finds the segment's area, chord length, and arc length from the circle's radius and the central angle between the two points.
A circular window has a radius of 20 cm, and the segment cut off spans a 60° central angle. In radians, θ ≈ 1.047. Segment Area = 0.5 × 20² × (1.047 − sin(1.047)) ≈ 22.6 cm². Chord Length = 2 × 20 × sin(30°) = 20 cm. Arc Length = 20 × 1.047 ≈ 20.94 cm.
It's the region between a chord and the arc it cuts off — like the smaller piece left over when you slice a circle with a straight line that isn't through the center.
Segment area = sector area − triangle area, or using the direct formula: 0.5 × r² × (θ − sin θ), where θ is the central angle in radians.
A sector is the "pie slice" bounded by two radii and an arc; a segment is bounded by a chord and an arc, cutting off a smaller piece that doesn't include the circle's center.