Polygon Angle Calculator
Calculate the interior angle, exterior angle, and angle sum of any regular polygon. Optionally enter the side length to compute the area. Works for any polygon from a triangle (3 sides) to a 1000-gon.
A regular polygon has all sides equal and all interior angles equal. The formulas for angles depend only on the number of sides (n):
Polygon Angle Formulas:
- Sum of Interior Angles: (n - 2) x 180 degrees
- Each Interior Angle: (n - 2) x 180 / n degrees
- Each Exterior Angle: 360 / n degrees
- Area (with side s): (n x s^2) / (4 x tan(pi/n))
The exterior angles of any convex polygon always sum to exactly 360 degrees, regardless of the number of sides. As the number of sides increases, the polygon approaches a circle, and each interior angle approaches 180 degrees.
Common regular polygons include the equilateral triangle (3 sides, 60 degrees interior), square (4 sides, 90 degrees), pentagon (5 sides, 108 degrees), hexagon (6 sides, 120 degrees), octagon (8 sides, 135 degrees), and dodecagon (12 sides, 150 degrees).