Hexagon Calculator

A hexagon has exactly six sides. This is the defining feature of all hexagons, whether regular or irregular. In a regular hexagon, all six sides are equal in length and all interior angles are 120°.

A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles are equal (each measuring 120°). The sum of all interior angles is 720°. This calculator applies specifically to regular hexagons.

The apothem, also called the inradius (r), is the perpendicular distance from the center of the hexagon to the midpoint of any side. For a regular hexagon with side length a, the apothem is r = (√3 / 2) × a.

A regular hexagon has two types of diagonals. The long diagonal (d) connects two opposite vertices and equals 2a (twice the side length). The short diagonal (s) connects two vertices with one vertex between them and equals √3 × a.

The area of a regular hexagon with side length a is A = (3√3 / 2) × a². If you know the perimeter instead, first divide by 6 to get the side length, then apply the formula. This calculator accepts any known dimension and computes the area automatically.

The circumradius (R) is the radius of the circle that passes through all six vertices of the hexagon. For a regular hexagon, R equals the side length a — making it straightforward to work between side length and circumradius.

Divide the perimeter by 6 to get the side length, then use A = (3√3 / 2) × a². For example, if the perimeter is 24, the side is 4 and the area is approximately 41.57 square units. Select 'Perimeter (P)' in this calculator to solve it directly.

Hexagons appear frequently in nature — most famously in honeycomb structures — because they are the most efficient shape for tiling a flat surface with no gaps while maximizing enclosed area for a given perimeter. This efficiency makes them ideal for structures like beehives, basalt columns, and bubble formations.