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Polygon Angle Calculator

Find the interior angles of a polygon.

Result

135.00 °
1,080.00 °

How it is calculated

For a regular polygon with n sides the interior angles add up to (n − 2) × 180°, because the polygon can be split into n − 2 triangles from one corner. All angles are equal, so each is (n − 2) × 180° / n. The tool shows both the sum and the single interior angle in degrees with two decimals. n must be a whole number of at least 3; decimals or smaller values give no result. The formula holds only for regular polygons, where all sides and angles are equal. Irregular shapes share the same angle sum, but their individual angles differ.

Worked example

A regular octagon has n = 8 sides. Angle sum: (8 − 2) × 180 = 6 × 180 = 1,080.00 °. Each interior angle: 1,080 / 8 = 135.00 °. So the tool shows 135.00 ° per corner and a total of 1,080.00 °. As a check, two adjacent walls meeting at such a corner leave an exterior angle of 45 °, and 8 × 45 = 360.

Try this example →

Common mistakes

  • Using n × 180° instead of (n − 2) × 180°, which overestimates the sum.
  • Applying the single-angle result to an irregular polygon whose angles differ.
  • Entering the number of corners as a decimal or fewer than 3; a polygon needs a whole number from 3 up.
  • Mixing up interior and exterior angles: they add up to 180° at a corner.

About this calculator

This calculator finds a regular polygon's interior angle using (n−2)×180°/n and its total angle sum using (n−2)×180°, where n is the number of sides — so a hexagon's angles sum to 720° with each interior angle at 120°.

It's used in geometry classes, and by anyone designing tiling patterns, cutting angled pieces for a woodworking or metalworking project, or laying out a polygon-shaped structure where the exact corner angles need to be known in advance.

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  • Editorial team

    Each-angle values apply to a regular polygon with all sides and angles equal. The angle sum, (n minus 2) times 180, holds for any simple polygon, so it works as a check on a measured shape: a pentagon should total 540, and if your measured angles are off by several degrees, recheck the measuring. The side count must be a whole number of 3 or more. Are you laying out tiles, building a frame or solving homework?

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