What is Sector of a Circle? A sector is a segment of a circle that includes an arc and the two radii that connect the arc's endpoints to the circle's centre. It represents a fraction of the circle, defined by the arc—part of the circle's perimeter—and the radii at the arc's ends. The perimeter of a circle sector is the combined length of two radii and the arc that forms the sector. The formula to calculate the perimeter of a sector is derived below. A sector of a circle is a portion or part of a circle that is composed of an arc and its two radii. Learn more about its types, formula, facts, and example. Perimeter of a sector The perimeter is the distance all around the outside of a shape. We can find the perimeter of a sector using what we know about finding the length of an arc.