Circular Sector Calculator

About this calculator

A circular sector is the pie-slice-shaped region bounded by two radii and the arc between them. This calculator finds the arc length, s = r·θ, and the sector area, A = ½·r²·θ, where θ is the central angle measured in radians (the calculator handles degree input by converting internally).

These formulas come directly from the definition of a radian — the angle that produces an arc length equal to the radius — and scale down proportionally from the full circle's circumference (2πr) and area (πr²) by the fraction of the full angle (θ/2π) the sector represents.

Engineers and machinists calculating material for curved parts like gears, pipe fittings, or sheet-metal cutouts, architects designing curved features like fan windows or arches, and geometry students working through circle problems all use this calculator by entering a radius and central angle.