Polygon Angle Calculator
Calculate the sum of interior angles, and each interior and exterior angle of a regular polygon, from a triangle up to any number of sides.
Shape
Heptagon (7 sides)
Sum of interior angles
900°
Each interior angle (regular)
128.571°
Each exterior angle (regular)
51.429°
Sum of exterior angles
360°
Recommended Settings
Pro Tips
- •The sum of a polygon's exterior angles is always 360°, no matter how many sides it has - only the sum of interior angles depends on the number of sides
- •The interior and exterior angle at any vertex always add up to 180°, since they form a straight line together
- •Interior and exterior angle formulas here assume a regular polygon - one with all sides and angles equal - irregular polygons only share the same total sum of interior angles, not equal individual angles
- •As the number of sides increases, each interior angle gets closer to 180°, which is why a polygon with very many sides starts to look like a circle
Most Popular
Most geometry problems ask about a hexagon (6 sides) or heptagon (7 sides), both common on tests
When to Use This Tool
Find the interior or exterior angle of a polygon for a homework problem.
Verify the angle measures of a regular polygon you're working with.
Get exact angle measurements when designing or constructing a polygon shape.
See how the sum of interior angles formula scales with the number of sides.
How It Works
Calculate the sum of interior angles using the formula (n - 2) × 180°, derived from dividing the polygon into triangles
Divide that sum by the number of sides to get each interior angle, assuming a regular polygon
Calculate each exterior angle as 360° divided by the number of sides, since exterior angles always sum to a full circle
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Frequently Asked Questions
Why is the sum of interior angles (n-2) × 180°?
Any polygon can be divided into (n-2) triangles by drawing diagonals from one vertex, and since each triangle's angles sum to 180°, the whole polygon's interior angles sum to (n-2) × 180°.
Why do exterior angles always sum to 360°?
As you walk around any convex polygon's perimeter, you make one full turn (360°) by the time you return to your starting direction, and the exterior angles represent exactly those turns.
Does this work for irregular polygons?
The sum of interior angles formula and the sum of exterior angles (360°) apply to any simple polygon, but the individual 'each angle' values assume a regular polygon with equal sides and angles.
Is my data sent anywhere?
No. All calculations happen locally in your browser.