Regular Polygon Interior Angle Calculator
For a regular polygon, all interior angles are equal and the sum depends only on the number of sides. This assumes a convex regular polygon.
How to use this calculator
- Enter a whole number of sides of at least three.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by polygon interior angle calculator
Interior angle = 180° × (n − 2) ÷ n; total interior-angle sum = 180° × (n − 2).
- Interior angle = 180° × (n − 2) ÷ n; total interior-angle sum = 180° × (n − 2).
- Irregular or concave polygons can have different individual angles; this calculation applies to regular convex polygons.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
An octagon has eight sides.
Each interior angle is 180 × 6 ÷ 8 = 135°; the sum is 1,080°.
Each interior angle is 135° for a regular octagon.
Understanding the result
For a regular polygon, all interior angles are equal and the sum depends only on the number of sides. This assumes a convex regular polygon.
Irregular or concave polygons can have different individual angles; this calculation applies to regular convex polygons.
Important notes
Irregular or concave polygons can have different individual angles; this calculation applies to regular convex polygons.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
What is the sum of a triangle’s interior angles?
The formula gives 180° for three sides.
Can it calculate an irregular polygon?
No. Individual angles are not equal for an irregular polygon.
How should I interpret this result?
Irregular or concave polygons can have different individual angles; this calculation applies to regular convex polygons.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.