A regular polygon is any shape with equal sides and equal angles — squares, regular pentagons, hexagons, and octagons are the everyday examples. Once you know the number of sides and the length of one side, every other measurement (area, perimeter, angles, apothem) follows from a small set of trigonometric formulas.
How the Regular Polygon Calculator works
The calculator takes the number of sides (n) and the side length (s) and derives everything else. Perimeter is simply n × s. The interior angle, (n − 2) × 180 / n, comes from the fact that any simple polygon's interior angles always sum to (n − 2) × 180°, split evenly across n equal angles in a regular polygon. The apothem — the distance from the center to the midpoint of a side — is s / (2 × tan(π/n)), derived by splitting the polygon into n congruent isosceles triangles from the center. Multiplying half the perimeter by the apothem gives the area, the same logic used to find a triangle's area from its base and height.
Inputs and what they mean
Only two numbers matter: the number of sides (n, a whole number of 3 or more) and the side length (any positive number). The unit dropdown is a display label only — it doesn't convert your numbers, so make sure the side length you enter is already in the unit you selected. Small n values (3, 4, 5, 6) cover the shapes people usually mean by "polygon"; larger values approximate a circle more and more closely, since the interior angle approaches 180° as n grows.
Limits and edge cases
This calculator only handles regular polygons — every side and angle equal. For a polygon with unequal sides or a shape whose vertices you know as (x, y) coordinates, use the Polygon Area Calculator's coordinate-based Shoelace formula instead. n must be a whole number of 3 or greater; there's no such thing as a 2-sided or fractional-sided polygon. Extremely large n values are mathematically valid but visually indistinguishable from a circle.