Area of a Segment of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

area of a Segment of a Circlecircle segment

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