Circular sector

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A circular sector is shaded in green

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 $π r 2$ . 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):

$A = \pi r^2 \cdot \frac{\theta}{2 \pi} = r^2 \left( \frac{\theta}{2} \right) = \frac{1}{2} r^2 \theta.$

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

$A = \pi r^2 \cdot \frac{\theta}{360}$

Sectors can have special relationships, which include halves, quadrants, and octants.

The length, $L$ , of the perimeter of a sector is given by the following formula:

$L = \left( \pi \cdot r \cdot \frac{\theta}{180}\right)$

where θ is in degrees.

[edit] See also

Circular segment - the part of the sector which remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary.
conic section