Polygon Interior Angle Calculator
Find the sum of interior angles, each interior and exterior angle, the number of diagonals and area of a regular polygon.
Your inputs
Results
Sum of interior angles
720 °
- Each interior angle (regular polygon)
- 120 °
- Each exterior angle (regular polygon)
- 60 °
- Number of diagonals
- 9
- Area of the regular polygon
- 10.392305
✓Exact calculation — rounded only for display
What this calculator does
Any polygon’s interior angles add up to a fixed total that depends only on its number of sides.
Formula and method
Worked example
Calculated by this tool with its default inputs:
Inputs
- Number of sides: 6
- Side length (optional, for a regular polygon): 2
Results
- Sum of interior angles: 720 °
- Each interior angle (regular polygon): 120 °
- Each exterior angle (regular polygon): 60 °
- Number of diagonals: 9
- Area of the regular polygon: 10.392305
How to read the results
Exterior angles of any convex polygon add up to 360°.
Assumptions and limitations
- Use one length unit consistently; areas are in square units and volumes in cubic units of that length.
Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.
Questions
What is the interior angle of a hexagon?
120° for a regular hexagon.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy