Math

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Polygon Angle Calculator.

Calculate regular polygon interior and exterior angles.

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Set your values

Results update as you type.

Interior angle: 120

Interior angle

0.000000
Exterior angle: 60

Exterior angle

0.000000
Interior-angle sum: 720

Interior-angle sum

0.000000

Results update automatically as you type.

Use Cases

Math homework and geometry studies

Quickly verify interior and exterior angle values for regular polygons when solving geometry problems or studying polygon properties.

Example: Check that a regular octagon has interior angle 135° and exterior angle 45°.

Design and construction planning

Use angle calculations for creating regular polygon shapes in woodworking, tiling, or graphic design, ensuring accurate cuts and layouts.

Example: Determine the miter angle for a regular pentagon frame: exterior angle 72°.

Frequently Asked Questions

What is a regular polygon?
A regular polygon is a polygon with all sides and all angles equal. Examples include equilateral triangles, squares, and regular pentagons. This calculator assumes a regular polygon when computing angles.
How do I find the interior angle of a regular polygon?
For a regular polygon with n sides, the sum of interior angles is (n-2)*180°. Divide that sum by n to get each interior angle. For example, a hexagon (n=6) has interior angle (6-2)*180/6 = 120°.
What is the exterior angle of a regular polygon?
The exterior angle is the angle between any side and the extension of the adjacent side. For a regular polygon, each exterior angle equals 360° divided by the number of sides. For a square, that's 90°.

Tips & Common Mistakes

Tips

  • Enter the number of sides as a positive integer greater than 2, since a polygon must have at least 3 sides.
  • Remember that interior and exterior angles are supplementary: they always add up to 180°.
  • For very large numbers of sides, the interior angle approaches 180° and the exterior angle approaches 0°, but never reaches those values.
  • Use the exterior angle to find the central angle of a regular polygon: it's the same value, useful for dividing a circle into equal parts.

Common Mistakes to Avoid

  • Using a non-integer or a value less than 3 for the number of sides, which does not represent a valid polygon.
  • Confusing interior and exterior angles: interior is inside the shape, exterior is outside when extending a side.
  • Forgetting that the sum of exterior angles of any polygon is always 360°, not 180°.

Last updated: August 13, 2026