Area Calculator guide
How to Find the Area of a Regular Hexagon
The area of a regular hexagon with side s is A = (3√3 ÷ 2) × s², which works out to about 2.598 × s². For a hexagon with sides of 6, the area is 2.598 × 36 ≈ 93.53. The perimeter is simply 6 × s.
The formula
A = (3√3 ÷ 2) × s²
The awkward-looking constant 3√3 ÷ 2 is approximately 2.598076. If you would rather not carry a surd around, multiplying the side squared by 2.598 is accurate enough for almost any practical purpose.
For a hexagon with sides of 6: A = 2.598 × 6² = 2.598 × 36 ≈ 93.53 square units.
Where the formula comes from
A regular hexagon is six equilateral triangles arranged around a centre point. Draw lines from the middle to each corner and you can see them.
That is not a coincidence of the hexagon — it is the reason the hexagon works at all. Each triangle has a 60° angle at the centre, and six lots of 60° is exactly 360°, so they close up perfectly with no gap.
The area of one equilateral triangle with side s is (√3 ÷ 4) × s². Six of them gives 6 × (√3 ÷ 4) × s², which simplifies to (3√3 ÷ 2) × s². That is the formula, and it is worth deriving once so that it stops being an arbitrary number to memorise.
Perimeter
Six equal sides, so the perimeter is 6 × s. For our example that is 6 × 6 = 36.
This is one place where the hexagon is genuinely easier than the shapes around it. There is no square root and nothing to look up.
If you know the width instead of the side
Hexagons are often measured across rather than along an edge, particularly in engineering, and there are two different "widths" — which is a common source of confusion.
Across the corners (also called the long diagonal) is exactly 2s. So if a hexagon measures 12 across its widest points, the side is 6.
Across the flats — the distance between two opposite edges — is s√3, about 1.732s. A hexagon with sides of 6 measures about 10.39 across the flats.
Spanner and bolt sizes use across-the-flats, which is why a "10mm" bolt head is not 10mm along any of its edges.
Why hexagons show up everywhere
Honeycomb, floor tiles, carbon molecules, bolt heads, chicken wire, the pattern on a football — hexagons appear so often that it is worth knowing why.
Of the three regular shapes that tile a flat surface with no gaps — triangles, squares and hexagons — the hexagon encloses the most area for the least perimeter. For bees, that means the most honey stored for the least wax used.
That property has a name, the honeycomb conjecture, and it was only proved rigorously in 1999, despite having been suspected for around two thousand years.
