Case 1
- Number of sides
- 6
120.00°
Open with these valuesPolygon Interior Angle Calculator
120.00°
Result: 120.00 °Any n-sided polygon splits into n − 2 triangles, so its interior angles add to (n − 2) × 180°. Shared equally among the corners of a regular polygon, each angle is (n − 2) × 180° ÷ n: 108° in a pentagon, 120° in a hexagon. The exterior angle is what is left of 180°.
Worked examples
Case 2
- Number of sides
- 5
108.00°
Open with these valuesCase 3
- Number of sides
- 12
150.00°
Open with these valuesHow it's calculated
α = (n − 2) × 180° ÷ n
- StepEnter the number of sides — a whole number of 3 or more.
- StepRead each interior angle of the regular polygon, in degrees.
- ResultMultiply by n for the sum, or subtract from 180° for the exterior angle.
Reference table
| Sides n | Shape · sum of interior angles | Each angle |
|---|---|---|
| 3 | Triangle · 180° | 60.00 |
| 4 | Square · 360° | 90.00 |
| 5 | Pentagon · 540° | 108.00 |
| 6 | Hexagon · 720° | 120.00 |
| 12 | Dodecagon · 1800° | 150.00 |
| 100 | Hectogon · 17640° | 176.40 |
Questions
How do I calculate the interior angle of a polygon?
Use (n − 2) × 180° ÷ n, where n is the number of sides. First take the sum of the interior angles, (n − 2) × 180°, then divide by the number of corners. For a hexagon that is (6 − 2) × 180° ÷ 6 = 120° per angle.
What is the sum of the interior angles?
For any simple polygon it is (n − 2) × 180°. A triangle sums to 180°, a quadrilateral to 360°, a pentagon to 540° and a hexagon to 720°. Each extra side adds another 180°.
Why is the formula (n − 2) × 180°?
Because a polygon with n sides can be cut into n − 2 triangles by drawing diagonals from a single corner. Each triangle contributes 180°, so the interior angles add to (n − 2) × 180°. The 2 stands for the two sides that meet at that shared corner.
Does this work for irregular polygons?
The sum of (n − 2) × 180° holds for any simple polygon, regular or not. The per-angle figure only applies to a regular polygon, where every side and every angle is equal. In an irregular polygon the individual angles differ but still add to the same total.
What is the difference between interior and exterior angles?
An interior angle sits inside the polygon at a corner; the exterior angle is its supplement, the turn you make while walking the perimeter. Together they make 180° at each corner. The exterior angles of any polygon add to 360°, so in a regular polygon each one is 360° ÷ n.
Sources and last check
Information, not professional advice.