# Hexagon Calculator

Calculate regular hexagon area, perimeter, apothem, and diagonals from side length. Free online hexagon calculator with instant results and formulas.

## What this calculates

Calculate all properties of a regular hexagon from its side length. This tool instantly computes the area, perimeter, apothem, long diagonal, and short diagonal of any regular hexagon.

## Inputs

- **Side Length** — min 0 — The length of one side of the regular hexagon.

## Outputs

- **Area** — The area of the regular hexagon.
- **Perimeter** — The total length of all six sides.
- **Apothem** — The distance from the center to the midpoint of a side.
- **Long Diagonal** — The diagonal passing through the center (vertex to opposite vertex).
- **Short Diagonal** — The diagonal connecting two vertices separated by one vertex.

## Details

A regular hexagon has six equal sides and six equal interior angles of 120 degrees each. It is one of only three regular polygons that can tile a plane without gaps (along with the equilateral triangle and square), making it extremely common in nature and engineering.

Regular Hexagon Formulas (side length = s):

- Area: A = (3 x sqrt(3) / 2) x s^2

- Perimeter: P = 6s

- Apothem: a = s x sqrt(3) / 2

- Long Diagonal: d = 2s (passes through center)

- Short Diagonal: d = s x sqrt(3) (connects vertices one apart)

The hexagon can be divided into six equilateral triangles, which is why its area equals six times the area of an equilateral triangle with the same side length. The apothem is the height of each of these triangles.

Hexagons appear in honeycomb structures, bolt heads, floor tiles, graphene molecular structure, basalt columns (like Giant's Causeway), and board games. Their efficient packing makes them optimal for many engineering and natural applications.

## Frequently Asked Questions

**Q: What is a regular hexagon?**

A: A regular hexagon is a polygon with six equal sides and six equal interior angles of 120 degrees each. It has six lines of symmetry and rotational symmetry of order 6. A regular hexagon can be divided into six congruent equilateral triangles.

**Q: How do I calculate the area of a hexagon?**

A: For a regular hexagon with side length s, the area is A = (3 x sqrt(3) / 2) x s^2, which is approximately 2.598 x s^2. You can also calculate it as A = (3/2) x s x a, where a is the apothem (distance from center to the midpoint of a side).

**Q: What is an apothem?**

A: The apothem is the distance from the center of a regular polygon to the midpoint of any side. For a regular hexagon with side s, the apothem equals s x sqrt(3) / 2. It is perpendicular to the side it reaches and represents the height of the equilateral triangles that make up the hexagon.

**Q: Why are hexagons so common in nature?**

A: Hexagons are common because they provide optimal packing efficiency. In a honeycomb, hexagonal cells use the least wax to enclose the most honey. Hexagonal tiling covers a plane with no gaps and the shortest total perimeter for a given area, making it the most material-efficient shape for regular tessellation.

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Source: https://vastcalc.com/calculators/math/hexagon
Category: Math
Last updated: 2026-04-21