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Instant Calculation
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Every polygon's interior angles add up to a predictable total based only on its number of sides — no measuring required.
This calculator finds the sum of interior angles, and each interior and exterior angle (for a regular polygon), from the number of sides alone.
How it works
Enter the number of sides. The calculator applies the formula (n-2) × 180° to find the sum of interior angles, then divides by n for the interior angle of a regular polygon, and separately computes 360°/n for the exterior angle.
- Enter number of sides.
- Click Calculate to see your results.
Examples
Hexagon (6 sides)
A hexagon's interior angles sum to 720°, meaning each interior angle of a regular hexagon is 120°, with a 60° exterior angle.
Who should use it
- Checking geometry coursework involving polygon interior and exterior angles.
- Designing a regular polygon shape and needing to know its exact vertex angles.
Industry applications
- Geometry education
- Design, architecture, and CAD (regular polygon layouts)
Advantages
- Calculates sum, interior, and exterior angles all from a single input.
- Works for any polygon from a triangle (3 sides) upward.
Limitations
- The per-angle results (interior/exterior) assume a regular polygon — irregular polygons only get the angle sum.
Common mistakes to avoid
- Applying the "each interior angle" result to an irregular polygon, where individual angles can vary widely even though the sum is fixed.
- Confusing interior and exterior angles — they're supplementary (add up to 180°) at each vertex.
Best practices
- Remember the sum of interior angles formula applies to every polygon (regular or not) with that many sides — only the "each angle" values assume regularity.
Tips
- A quick way to check a floor plan or design is regular: the sum of any polygon's exterior angles is always 360°, regardless of how many sides it has.