Calculate polygon angles from the side count
Enter the number of sides of a convex regular polygon. The calculator shows each interior angle, each exterior turning angle, each central angle, the interior angle sum, and the number of diagonals. A regular hexagon has interior angles of 120 degrees and exterior and central angles of 60 degrees.
Formulas
For n sides, the interior angle sum is (n − 2) × 180 degrees. Divide this by n for each interior angle. Each exterior angle and central angle equals 360 / n degrees. The diagonal count is n(n − 3) / 2.
Regular polygons and precision
Equal individual angles assume a convex regular polygon. The sum formula also applies to simple irregular polygons, but does not determine their individual angles. Enter a whole side count from 3 to 1,000,000. Results include exact reduced fractions and decimal approximations to six places. All calculations stay in your browser.