Sector Area Calculator

About this calculator

A circular sector is the pie-slice-shaped region bounded by two radii and the arc between them, defined by a central angle θ. Its area scales proportionally to that angle's fraction of a full circle: area = (θ/360°) × πr², and the arc length follows the same logic applied to the circumference: arc length = (θ/360°) × 2πr — both formulas simply take the "whole circle" formula and scale it down by what fraction of 360° the sector actually spans.

Sector geometry appears constantly in engineering and design: gear teeth, fan blades, pie charts, pizza slices, and the sweep of a windshield wiper or a rotating sprinkler head are all sectors, and calculating their area matters for material estimates, load distribution across rotating components, and irrigation coverage planning. Architects also use sector geometry for fan-shaped structures like amphitheater seating sections and curved building facades.

This calculator takes a sector's radius and central angle and returns both its area and arc length.