Hexagon Calculator
Solve a regular hexagon from any one measurement — side, long diagonal, short diagonal, perimeter, or area. Enter the number in any unit (inches, feet, cm, meters) and every result comes back in that same unit, with area in square units.
Example: with What do you know? Side length (a) · Value 10 → Area: 259.808 square units.
- Side (a)10 units
- Perimeter (6a)60 units
- Long diagonal (2a)20 units
Computed by the calculator below using its default values. Change any input to see your own numbers.
Regular hexagon: A = (3√3/2)a² ≈ 2.598076a². The long diagonal is exactly twice the side — a hexagon is six equilateral triangles around a center.
Why the hexagon formula works
A regular hexagon is six equilateral triangles arranged around a center point. Each triangle has area (√3/4)a², so six of them give A = 6 × (√3/4)a² = (3√3/2)a² ≈ 2.598a². That construction also explains the diagonals: the long diagonal passes through the center and spans two triangle sides, so it is exactly 2a, while the short diagonal cuts across two triangles and works out to √3·a ≈ 1.732a.
The apothem — the perpendicular distance from center to the middle of a side — is (√3/2)a ≈ 0.866a. It matters for real projects: hexagonal pavers, tiles, and gazebo bases are usually specified by width across the flats, which is twice the apothem. That flat-to-flat width works out to √3·a, numerically the same as the short diagonal, so if a spec sheet gives you across-the-flats, enter it under short diagonal and everything else follows.
How it’s calculated
A = (3√3/2)a² with 3√3/2 ≈ 2.598076; perimeter P = 6a; long diagonal d = 2a; short diagonal s = √3·a with √3 ≈ 1.732051; apothem = (√3/2)a ≈ 0.866025a. Reverse solving: a = d/2, a = s/√3, a = P/6, a = √(A/2.598076). Results keep your input unit; area is in that unit squared.
Regular hexagons only — all six sides and angles equal. Irregular hexagons need to be split into triangles and summed.
Regular hexagon dimensions by side length
| Side a | Area (3√3/2)a² | Perimeter | Long diagonal | Short diagonal / across flats |
|---|---|---|---|---|
| 1 | 2.60 | 6 | 2 | 1.73 |
| 2 | 10.39 | 12 | 4 | 3.46 |
| 5 | 64.95 | 30 | 10 | 8.66 |
| 10 | 259.81 | 60 | 20 | 17.32 |
| 12 | 374.12 | 72 | 24 | 20.78 |
Computed with A = (3√3/2)a², d = 2a, s = √3a; rounded to 2 decimals.
Common mistakes
- Entering the long diagonal as the side — a hexagon measured 12 in corner-to-corner has 6 in sides, and area 4× smaller than side = 12 would give.
- Confusing the two diagonals: corner-to-opposite-corner is 2a, but corner-to-corner skipping one vertex (equal to width across the flats) is √3·a.
- Expecting area to double when the side doubles — it quadruples, because the side is squared.
- Using the hexagon formula on a shape that is not regular; stretched honeycomb sketches need triangulation instead.
Frequently asked questions
What is the area formula for a hexagon?
For a regular hexagon with side a, area A = (3√3/2)a², which is about 2.598 × a². It comes from splitting the hexagon into six equilateral triangles of area (√3/4)a² each.
How do I find hexagon area from the diagonal?
The long (corner-to-corner) diagonal is exactly twice the side, so divide it by 2 to get a, then apply A = (3√3/2)a². A 12-unit diagonal means a 6-unit side and area of about 93.53 square units.
What is the apothem of a hexagon?
It is the perpendicular distance from the center to the midpoint of a side: (√3/2)a, about 0.866a. Area can also be written as ½ × perimeter × apothem — the same number either way.
Is the width across the flats the same as a diagonal?
Numerically yes: flat-to-flat width equals √3·a, the same value as the short corner-to-corner diagonal. Paver and bolt sizes are usually quoted across the flats, so enter that as the short diagonal here.
Why are hexagons so common in nature?
Among shapes that tile a plane with no gaps, the hexagon encloses the most area for the least perimeter. Bees minimize wax per unit of honey storage; basalt columns crack toward the same geometry.