Polygon Angles Calculator

Enter the number of sides to get the angles of a regular polygon, or enter an interior angle to find how many sides it has.

What Do You Want to Find?
Fractions and decimals both work.
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Each interior angle
Sum of interior angles
Each exterior angle
Central angle
Diagonals
Name
Work

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Polygon Angle Formulas

Sum of interior angles = (n − 2) × 180°
Each interior angle (regular) = (n − 2) × 180° ÷ n   Each exterior angle = 360° ÷ n
Diagonals = n(n − 3) ÷ 2   Sides from an interior angle: n = 360 ÷ (180 − angle)

Worked Example

Tips

The angle sum works for any polygon, regular or not; the "each angle" values assume all sides and angles are equal. Miter saws: for an n-sided frame, cut each end at 180° ÷ n (22.5° for an octagon).