A circular sector or circle sector also known as a pie piece is the portion of a circle enclosed by two radii and an arc. Its area can be calculated as described below.

Let θ be the central angle, in radians, and R the radius. The total area of a circle is π R². The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and 2π (because the area of the sector is proportional to the angle, and 2π is the angle for the whole circle)

{| $Area=\backslash pi\; R^2\backslash cdot\backslash frac\{\backslash theta\}\{2\backslash pi\}\; =\; R^2\backslash left(\backslash frac\{\backslash theta\}\{2\}\backslash right)=\; \backslash frac\{1\}\{2\}\; R^2\backslash theta$.

Also, if θ refers to the central angle in degrees, a similar formula can be derived.

{| $Area=\backslash pi\; R^2\backslash cdot\backslash frac\{\backslash theta\}\{360\}$

Circles

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