# Hexagon Calculator

URL: https://speedycalculator.com/calculators/math/hexagon/
Last updated: 2026-10-30

> The hexagon calculator finds the area, perimeter, long and short diagonals, circumradius and inradius of a regular hexagon from its side – or from any of those values.

## Inputs

- Side a (cm, m, mm, in, ft, yd, km, mi)

## Results

- Area
- Perimeter
- Long diagonal
- Short diagonal
- Circumradius
- Inradius (apothem)

## Formula

```
A = (3√3/2)·a²,  P = 6a,  D = 2a,  d = √3·a,  R = a,  r = (√3/2)·a
```

## Explanation

Regular hexagons tile the plane with the shortest total edge length for a given area, which is why bees build hexagonal honeycombs. They appear in nuts and bolts, floor tiles, board games and carbon molecules.

### How to use the Hexagon Calculator

- **Side a**
- Every result field is editable: type into **Area** or any other result and **Side a** plus every other field update to match.

Results update as you type, and everything is calculated in your browser.

### How it works

A regular hexagon splits into six equilateral triangles of side a, which gives all the formulas. Type into any result to find the side that produces it.

### What each result means

- **Area** = 3×sqrt(3)÷2×[Side a]^2
- **Perimeter** = 6×[Side a]
- **Long diagonal** = 2×[Side a]
- **Short diagonal** = sqrt(3)×[Side a]
- **Inradius (apothem)** = sqrt(3)÷2×[Side a]

### Example values

How the main result changes when **Side a** changes and everything else stays at the example values above:

Side a (cm)Area (cm²)2.516.2383.7536.5354564.95196.25101.48747.5146.141810259.8076

## Worked example

Inputs — Side a: 5 cm.

Results — **Area = 64.951905 cm²**; Perimeter = 30 cm; Long diagonal = 10 cm; Short diagonal = 8.660254 cm; Circumradius = 5 cm; Inradius (apothem) = 4.330127 cm.

## Key terms

- **Regular hexagon**: A six-sided polygon with equal sides and angles.

## FAQ

**What is each interior angle of a hexagon?**
120°.

**Why do bees use hexagons?**
They tile without gaps and use the least wax per stored volume.

**How do I measure a hex nut?**
Across flats is the short diagonal-direction width = √3·a; across corners = 2a.

**How many diagonals does a hexagon have?**
Nine: three long and six short.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [Wolfram MathWorld – Hexagon](https://mathworld.wolfram.com/Hexagon.html)