Circular segment

In geometry, a circular segment (symbol: ) is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc (of less than 180°) of a circle and by the chord connecting the endpoints of the arc.

Formula

Let R be the radius of the circle, θ is the central angle in radians, α is the central angle in degrees, c the chord length, s the arc length, h the sagitta (height) of the segment, and d the height of the triangular portion.

Area

The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portionthat is,

A =  \frac{R^2}{2} \left(\theta - \sin \theta \right)

with the central angle in radians, or

A =  \frac{R^2}{2} \left(\frac{\alpha\pi}{180} - \sin \alpha \right)

with the central angle in degrees.

See also

References

External links

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