ConverterHub

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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