Sum of Interior Angles Calculator

About this calculator

The interior angles of any polygon always add up to a fixed total that depends only on the number of sides, found by splitting the shape into triangles from one corner and multiplying the triangle count by 180 degrees. A triangle's angles sum to 180, a quadrilateral's to 360, and the pattern continues predictably as sides are added.

Architects and structural designers use this when working out roof pitches and polygonal room layouts, since knowing the total angle sum lets them check that a multi-sided design will actually close up correctly. It is also a foundational result in classroom geometry that students use to verify measurements in any polygon-based problem.