Regular Pentagon Area Calculator

About this calculator

This calculator finds the area and perimeter of a regular pentagon (five equal sides and angles) from its side length s: Area = ¼·√(5(5+2√5))·s², a formula derived from splitting the pentagon into five congruent isosceles triangles from its center and using the apothem (the distance from center to the midpoint of a side). Perimeter is simply 5·s.

Regular pentagons and their defining ratio are closely tied to the golden ratio φ ≈ 1.618 — the ratio of a pentagon's diagonal to its side is exactly φ — which is why pentagonal geometry appears in art, architecture, and design (like the Pentagon building, home plate in baseball being a modified pentagon, and pentagonal floor tiles).

Geometry students computing regular polygon areas, architects and designers working with pentagonal layouts, and hobbyists building pentagon-based crafts or models all use this calculator, entering just the side length.