What Is the Area of a Hexagon Calculator?
This calculator finds the area of a regular hexagon — a six-sided polygon where all sides and angles are equal — using only its side length. A regular hexagon is one of the most efficient shapes in nature, appearing in honeycombs, snowflakes, and nut and bolt heads. Knowing its area is useful in geometry, tiling, engineering, and crafts.
How to Use It
Enter the length of one side of the hexagon and click calculate. The tool instantly returns the area in square units and the perimeter. The units are whatever you used for the side length: enter centimetres and the area comes back in square centimetres.
The Formula Explained
The area of a regular hexagon with side length s is:
$$A = \frac{3\sqrt{3}}{2} \times s^{2}$$
A regular hexagon can be divided into six identical equilateral triangles, each with area \(\frac{\sqrt{3}}{4}s^{2}\). Multiplying by six gives \(\frac{6\sqrt{3}}{4}s^{2} = \frac{3\sqrt{3}}{2}s^{2} \approx 2.598 \times s^{2}\). The perimeter is simply six times the side length, \(P = 6s\).
Worked Example
Suppose a hexagon has a side length of 10 units. Then $$A = \frac{3\sqrt{3}}{2} \times 10^{2} = 2.5980762 \times 100 \approx 259.81 \text{ square units},$$ and the perimeter is \(6 \times 10 = 60\) units.
Area Across Common Hexagon Sizes
The apothem (distance from the center to the midpoint of a side) is \(a = \frac{\sqrt{3}}{2}s \approx 0.8660\,s\). Below are realistic regular-hexagon examples with side length, perimeter \(6s\), apothem, and area \(2.598\,s^2\).
| Scenario | Side \(s\) | Perimeter | Apothem | Area |
|---|---|---|---|---|
| Bolt head | 0.5 cm | 3.00 cm | 0.43 cm | 0.65 cm² |
| Floor tile | 10 cm | 60.00 cm | 8.66 cm | 259.81 cm² |
| Garden paver | 20 cm | 120.00 cm | 17.32 cm | 1039.23 cm² |
| Gazebo footprint | 1.5 m | 9.00 m | 1.30 m | 5.85 m² |
For the gazebo: \(A = 2.598076 \times 1.5^2 = 2.598076 \times 2.25 = 5.85\ \text{m}^2\), and apothem \(= 0.8660 \times 1.5 = 1.30\ \text{m}\).
Square Unit Conversions
Once you have a hexagon area, use these exact factors to convert between common units of area. Multiply by the factor shown to convert from the left unit to the right unit.
| From | To | Multiply by |
|---|---|---|
| mm² | cm² | 0.01 (÷100) |
| cm² | m² | 0.0001 (÷10,000) |
| m² | ft² | 10.763910417 |
| ft² | in² | 144 (exact) |
| in² | cm² | 6.4516 (exact) |
These are reciprocal pairs: to reverse a conversion, divide by the same factor (e.g. cm² → in² means dividing by 6.4516). The factors 144 in²/ft² and 6.4516 cm²/in² are exact by definition (1 in = 2.54 cm exactly, so \(2.54^2 = 6.4516\)).
FAQ
Does this work for irregular hexagons? No. This formula only applies to regular hexagons where all six sides are equal. Irregular hexagons must be split into triangles and summed individually.
What is the apothem? The apothem (distance from centre to the midpoint of a side) is \(a = \frac{\sqrt{3}}{2}s\). The area also equals \(\frac{1}{2} \times \text{perimeter} \times \text{apothem}\).
Can I use any unit? Yes — the area is returned in the square of whatever unit you input, so be consistent.
