What Is a Hexagon Calculator?
A hexagon calculator computes the key measurements of a regular hexagon — area, perimeter, and diagonals — from a single side length. A regular hexagon has six equal sides and six equal angles, and it appears throughout nature and design, from honeycombs to nuts and bolts to floor tiles. Enter the side length and the calculator returns all the hexagon's properties.
How to Use the Calculator
- Enter the side length of the regular hexagon.
- Calculate — see the area, perimeter, and diagonals.
Regular Hexagon Formulas
| Property | Formula (side = s) |
|---|---|
| Area | (3√3 ÷ 2) × s² |
| Perimeter | 6s |
| Long diagonal | 2s |
| Short diagonal | s√3 |
Worked Example
For a regular hexagon with side 4: the area is (3√3 ÷ 2) × 16 ≈ 41.57, the perimeter is 6 × 4 = 24, the long diagonal is 8, and the short diagonal is 4√3 ≈ 6.93.
Why the Area Formula Works
A regular hexagon can be divided into six identical equilateral triangles, each with side s. The area of one equilateral triangle is (√3 ÷ 4) × s², and six of them give (3√3 ÷ 2) × s² — the hexagon area formula.
Where Hexagons Appear
- Nature: honeycomb cells, which use the least material to tile a plane.
- Engineering: nuts, bolts, and tiling patterns.
- Design: floor tiles, graphics, and game boards.
Frequently Asked Questions
What is the area of a regular hexagon?
The area is (3√3 ÷ 2) × side², which is about 2.598 times the side length squared. For a side of 4, that is roughly 41.57 square units.
What is the perimeter of a hexagon?
For a regular hexagon, the perimeter is six times the side length, since all six sides are equal.
How many diagonals does a hexagon have?
A hexagon has nine diagonals in total. The longest span across the center equals twice the side length, and the shorter diagonals equal the side times √3.
Why are honeycombs hexagonal?
Hexagons tile a plane with no gaps using the least perimeter for a given area, so bees use the least wax to store the most honey — an efficient natural design.
Is this hexagon calculator free?
Yes — it is completely free, requires no signup, and computes all hexagon properties.