Math
Regular polygon area
Calculate area and perimeter of a regular polygon.
Calculators / Math / Polygon interior angles
Polygon interior angles calculator
Find a simple polygon’s angle sum and the individual angles of a regular polygon.
On this page
Sum of interior angles720°
One regular interior angle120°
One regular exterior angle60°
Calculator controls
How to calculate
Find a simple polygon’s angle sum and the individual angles of a regular polygon.
Sum of interior angles =
(n-2)*180 °One regular interior angle =
(n-2)*180/n °One regular exterior angle =
360/n °Worked example
- Number of sides: 6
- Sum of interior angles: 720 °
- One regular interior angle: 120 °
- One regular exterior angle: 60 °
Assumptions and limits
The polygon must be simple and planar. Equal individual angles are assumed only for the regular-polygon outputs; self-intersecting paths are excluded.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find a simple polygon’s angle sum and the individual angles of a regular polygon. A concave simple polygon has the same total angle sum, but its individual angles need not match the regular values.
When this tool is useful
A concave simple polygon has the same total angle sum, but its individual angles need not match the regular values.
Understanding your inputs
| Input | Example |
|---|---|
Number of sides n | 6 |
Frequently asked questions
What does this model leave out?
The polygon must be simple and planar. Equal individual angles are assumed only for the regular-polygon outputs; self-intersecting paths are excluded.
How do I reproduce the example?
Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.