🔷Polygon Angle Calculator
Find interior and exterior angles from sides, or sides from a known angle.
Free Polygon Angle Calculator
Find the interior and exterior angles of any regular polygon with our free polygon angle calculator. Enter the number of sides and instantly get the sum of interior angles, each individual interior angle, and each exterior angle — with the formula shown and a diagram of the shape.
Working the other way? Enter a known interior or exterior angle and the calculator solves for the number of sides, flagging clearly if the angle doesn't correspond to any whole-sided regular polygon rather than showing a fractional, meaningless answer.
Common polygons are named automatically — triangle, pentagon, hexagon, and beyond. No sign-up, no downloads — just enter a value and calculate.
About the Polygon Angle Calculator
Features
Forward mode
Sides to interior and exterior angles, sum and per-angle.
Reverse mode
Angle to number of sides, with validation for non-matching angles.
Polygon naming
Automatic naming from triangle through decagon, then "n-gon".
Diagram
A scaled regular polygon drawn for the current number of sides.
Frequently Asked Questions
How do I find the sum of interior angles?
Use (n−2)×180°, where n is the number of sides — this calculator does it instantly.
How do I find one interior angle of a regular polygon?
Divide the sum by n: (n−2)×180°/n.
What's the sum of exterior angles?
Always 360°, regardless of the number of sides, for any convex polygon.
Can I work backwards from an angle to find the number of sides?
Yes, enter a known interior or exterior angle and it solves for n.
What if the angle doesn't match a whole-sided polygon?
The calculator flags this clearly rather than showing a fractional, meaningless number of sides.
Does it name the polygon?
Yes, common polygons (triangle through decagon) are named automatically based on n.
Does this work for irregular polygons?
The angle sum formulas apply to any polygon, but the per-angle values assume a regular (equal-angle) polygon.
Does it show a diagram?
Yes, a scaled polygon with n sides is drawn.
Is it free?
Completely free, no sign-up or limits.
Does it work on mobile?
Yes, fully responsive.