HesapHanem

Exterior Angle Calculator

Enter the number of sides of the polygon.

How it is calculated

The tool is for a regular polygon, one with equal sides and equal angles. With n sides, exterior = 360° ÷ n and interior = 180° − exterior. The sum of the exterior angles is always shown as 360°. Angles are printed in degrees to three decimals. The number of sides is rounded to the nearest whole number, so 6.6 is treated as 7, and any value below 3 returns nothing because a polygon needs at least three sides. For an irregular polygon the individual angles differ, so these values apply only to the average, not to each corner.

Worked example

For a regular heptagon, n = 7. The exterior angle is 360 ÷ 7 = 51.429°. The interior angle is 180 − 51.429 = 128.571°. Check: seven exterior angles of 51.429° add up to 360°, and the interior angles add to 7 × 128.571 = 900°, which equals (7 − 2) × 180°.

Try this example →

Common mistakes

  • Using the tool for an irregular polygon. The formula assumes all angles are equal, so a rectangle-like shape with unequal sides will not match these values.
  • Confusing exterior and interior angles. The exterior angle is the turn you make at each corner; the interior angle is what is left of the 180° on the straight line.
  • Entering a fractional number of sides. The tool rounds it, so 6.6 gives the same answer as 7.
  • Entering a known angle instead of a side count. If you know the exterior angle and want the sides, divide 360 by it, then enter that whole number.

About this calculator

For any convex regular polygon, the exterior angle at each vertex — the angle between one side and the extension of the adjacent side — is simply 360° divided by the number of sides (n), and the sum of all exterior angles always adds up to exactly 360° no matter how many sides the polygon has. The interior angle is just its supplement: 180° minus the exterior angle.

This relationship is one of the cleanest results in polygon geometry and a building block for more complex angle-chasing problems. Students and teachers use it to check work on interior/exterior angle problems, while drafters and CAD designers rely on it when laying out regular polygonal shapes, bolt-hole patterns, or architectural elements with equal-angle turns.

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Comments (1)

  • Editorial team

    Exterior angles are the turning angles in a path. If you are programming a turtle-graphics drawing, a CNC outline or a robot that walks a polygon, you go forward one side length and then turn by the exterior angle: 72.000° for a regular five-sided shape, 30.000° for twelve sides. At 360 sides the turn shrinks to 1.000°, which is why many sides look like a circle. What are you drawing or building with it?

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