Circle sector - perimeter and area

A circular sector is the pie-slice-shaped region of a circle bounded by two radii and the arc that connects their endpoints. You can picture it as a wedge cut from a round cake: the two straight edges run from the centre to the rim, and the curved edge follows the circle itself. The central angle between the radii determines how much of the disk the sector covers, from a thin sliver up to the whole circle. When that angle is less than a straight angle the piece is called the minor sector, and the larger remaining piece is the major sector; together the two make up the entire disk.

A sector is defined entirely by just two quantities, the radius and the central angle, which makes its area and its curved arc length easy to describe once those are known. Because it captures a fair, proportional share of a circle, the sector is the natural tool for anything divided into angular parts. It appears in pie and doughnut charts, in the design of gears, fans, and radar sweeps, and in tasks such as measuring a field of view or the coverage of a rotating sprinkler. Whenever a problem involves a fraction of a circle rather than the whole thing, the sector is the shape that makes the calculation clean.