Polygon Interior Angle Sum Calculator

About this calculator

For any simple polygon with n sides, the sum of all interior angles is (n − 2) × 180° — a result that comes from splitting the polygon into (n − 2) triangles from a single vertex, each contributing 180°. For a regular polygon, where every angle is equal, dividing that sum by n gives the measure of each individual interior angle: a hexagon's angles sum to 720° and each one measures 120°, for instance.

Geometry students use this to check answers on angle-sum proofs, while designers and fabricators — laying out hexagonal tiles, octagonal gazebos, or CNC-cut polygonal parts — use the per-angle value to set the correct miter or cut angle at each joint so the pieces close up into a clean shape.