calciz

Regular Polygon Calculator

Everything about a regular polygon from its side count and side length.

The key formulas

Interior angle = (n-2) × 180° / n. The apothem (center to edge midpoint) is s / (2 tan(180°/n)), and area = perimeter × apothem / 2, the same base-times-height idea as a triangle, applied n times.

Toward the circle

As n grows, the polygon closes in on the circle through its vertices: a regular 100-gon already fills 99.9% of its circumscribed circle. That squeeze is exactly how Archimedes pinned down π two millennia before calculus.