What this calculator finds
Every polygon’s interior angles add up to a fixed total based only on its number of sides. This calculator finds that sum, plus the size of each individual interior and exterior angle assuming the polygon is regular (all sides and angles equal).
The formulas
- Sum of interior angles = (n − 2) × 180°, where n is the number of sides.
- Each interior angle (regular polygon) = Sum ÷ n
- Each exterior angle (regular polygon) = 360° ÷ n
The sum-of-interior-angles formula comes from the fact that any polygon can be split into (n − 2) triangles, each contributing 180°. Exterior angles of any convex polygon always add up to exactly 360°, regardless of the number of sides. This tool is for general math and educational purposes.
Last reviewed August 2026