# Area of a Segment of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

## area of a Segment of a Circle

A segment is the area of a sector of a circle minus a piece of that sector.

### area of a Segment of a Circle formula

$$A = \frac { 1 } { 2 } r^2 \left( \; \theta \;-\; sin \; \theta \; \right) \;\;$$  (when $$\; \theta \;$$ is in radians)

$$A = \frac { 1 } { 2 } r^2 \left( \; \frac {\pi} {180} \theta \;-\; sin \; \theta \; \right) \;\;$$  (when $$\; \theta \;$$ is in degrees)

$$A = \frac { \theta \;-\; sin \; \theta } { 2 } r^2 \;\;$$  (when $$\; \theta \;$$ is in radians)

$$A = \left( \frac { \theta \; \pi } { 360 } - \frac { sin \; \theta } { 2 } \right) r^2 \;\;$$  (when $$\; \theta \;$$ is in degrees)

Where:

$$A$$ = area

$$\pi$$ = Pi

$$r$$ = radius

$$\theta$$ = angle

Tags: Equations for Area