Circle Segment Area
Calculator
Results
- Area
- 16.35011
- Central angle (degrees)
- 73.739795
- Arc length
- 12.870022
- Segment height (sagitta)
- 2
Results
| Area | 16.35011 |
| Central angle (degrees) | 73.739795 |
| Arc length | 12.870022 |
| Segment height (sagitta) | 2 |
formula-map diagram
- Area
- 16.35011
- Central angle (degrees)
- 73.739795
- Arc length
- 12.870022
- Segment height (sagitta)
- 2
Formula map
Formula
A = (r²/2) × (θ − sin θ), θ = 2·asin(c ÷ 2r)= 16.350110879328
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
More in Advanced geometry
See all →Frequently asked questions
What is a circular segment, as distinct from a circular sector?+
A circular segment is the region between a chord and the arc it cuts off, like a 'slice' with the triangular part removed, whereas a sector is the full pie-slice shape from the center out to the arc. The segment area equals the sector area minus the triangular area formed by the two radii and the chord.
What is the formula for the area of a circular segment?+
Area = (r²/2)(θ − sinθ), where r is the circle's radius and θ is the central angle in radians subtended by the chord. The r²θ/2 term is the sector's area, and the r²sin(θ)/2 term subtracts the triangular portion.
Why must the angle be in radians for this formula, not degrees?+
The r²θ/2 sector-area term is derived directly from the radian definition of angle (arc length divided by radius), so plugging in a degree value instead of radians would give a badly incorrect result. If you only have the angle in degrees, convert it first by multiplying by π/180.
How can I find the segment area if I only know the chord length, not the central angle?+
First find the central angle using the chord length formula, θ = 2·arcsin(chord/(2r)), then plug that angle into the segment area formula. This two-step process is common since chord length is often easier to measure directly than the central angle.
What is the maximum possible segment area for a given circle?+
The segment area is maximized when θ = π radians (180°), which is simply the semicircle, splitting the circle exactly in half through its center. Beyond 180°, the 'segment' becomes the major (larger) segment, which is better calculated as the full circle area minus the minor segment's area.