How do you find the area of a regular hexagon?

Area = (3 x square root of 3 / 2) x side squared, which is about 2.598 x side squared. A regular hexagon is made of six equilateral triangles, which is where this formula comes from.

What is the difference between the long and short diagonal?

The long diagonal runs vertex to vertex and equals twice the side length. The short diagonal runs across the flats and equals the side length times the square root of 3 (about 1.732 x side).

What is the apothem of a hexagon?

The apothem is the distance from the centre to the middle of a side (the inradius). For a regular hexagon it equals (square root of 3 / 2) x side, about 0.866 x side. It is half the short diagonal.

Can I work backwards from the area or a diagonal?

Yes. Choose what you know — side, long diagonal, short diagonal, or area — and the tool first solves for the side, then derives every other property from it.

What is the "width across flats" of a hexagon?

That is the short diagonal: the distance between two opposite flat sides, equal to side x square root of 3. It is the measurement that matters for fitting a hex nut or bolt to a spanner.

Does this tool upload anything?

No — all maths happens in your browser and no data is sent anywhere.

Hexagon Calculator — Gera Tools

Regular hexagon calculator

Tell the tool what you know — the side length, the long or short diagonal, or the area — and it derives every other property of a regular hexagon: area, perimeter, both diagonals and the apothem. It is useful for tiling, nut-and-bolt sizing, board-game grids, and geometry homework.

How it works

The calculator first solves for the side length from whatever you entered, then computes the rest. A regular hexagon is six equilateral triangles meeting at the centre, which gives these exact relationships (where s is the side):

Area = (3√3 / 2) · s² ≈ 2.598 · s²
Perimeter = 6 · s
Long diagonal (vertex to vertex) = 2 · s
Short diagonal (flat to flat, the width across flats) = s · √3 ≈ 1.732 · s
Apothem (centre to side midpoint) = (√3 / 2) · s ≈ 0.866 · s

If you start from the area, it reverses the area formula: s = √(2·area / (3√3)).

Example

For a hexagon with side = 10:

Property	Formula	Value
Area	2.598 × 10²	259.81
Perimeter	6 × 10	60
Long diagonal	2 × 10	20
Short diagonal	10 × √3	17.32
Apothem	0.866 × 10	8.66

All calculations stay in your browser; nothing is uploaded.