# 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.

## Formulae

A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area).

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 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 portion—that is,

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

or with the central in degrees,

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