Circle Segment Calculator
Find the area, chord, arc length and sagitta height of a circular segment from its radius and central angle.
units
degrees
28.54
Segment areaSegment area
9.1%
Rest of circle
90.9%
- 1
Angle to radians
90 × π ÷ 180 = 1.570796 - 2
Sector area
½ × 10² × 1.570796 = 78.5398 - 3
Triangle area
½ × 10² × sin(1.570796) = 50Area of the triangle formed by the two radii — subtracted from the sector. - 4
Segment area
78.5398 − 50 = 28.54
How does this calculator work?
A circular segment is the area between a chord and its arc. From radius r and central angle θ, the segment area is ½·r²·(θ − sin θ), the chord is 2r·sin(θ/2), the arc is r·θ, and the sagitta height is r(1 − cos(θ/2)), with θ in radians.
Formula
How this is calculated
A circular segment is the region of a circle cut off by a chord. Enter the circle radius r and the central angle θ that subtends the chord, measured in degrees. The angle is first converted to radians with θ_rad = θ·π/180 because all trigonometric formulas operate in radians.
The segment area equals ½·r²·(θ_rad − sin θ_rad): the area of the circular sector minus the area of the triangle formed by the two radii and the chord. The chord length is 2r·sin(θ_rad/2), the arc length along the curve is r·θ_rad, and the sagitta (the maximum height of the segment, the distance from the chord to the arc) is r(1 − cos(θ_rad/2)).
Inputs must be positive, with θ between 0 and 360 degrees; values outside this range or a non-positive radius return no result. All lengths share the same unit as the radius, and areas are in that unit squared. The donut compares the segment area against the full circle area πr², so a 360° angle fills the whole circle.
Frequently asked questions
A sector is bounded by two radii and the arc (a pie slice), while a segment is bounded by a chord and the arc. The segment area is the sector area minus the triangular area between the two radii.
The sagitta is the height of the segment: the perpendicular distance from the midpoint of the chord to the arc, computed as h = r(1 − cos(θ/2)).
Yes. Angles above 180° describe a major segment (more than half the circle). The same formulas apply for any θ from 0 up to 360 degrees.
Also known as
TG we-Calculate Editorial Team. (2026). Circle Segment Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/circle-segment-calculator
TG we-Calculate Editorial Team. "Circle Segment Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/circle-segment-calculator.
TG we-Calculate Editorial Team, "Circle Segment Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/circle-segment-calculator
@misc{wecalculate_circle_segment_calculator, title = {Circle Segment Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/circle-segment-calculator}}, year = {2026}, note = {TG we-Calculate} }
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