Free Hexagon Calculator

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A regular hexagon has six equal sides and six equal interior angles (each 120°). It's one of only three regular polygons that can tile a flat plane with no gaps (along with the triangle and square), which is exactly why hexagons show up in honeycomb structures, bathroom and floor tiling, and modern engineering nut/bolt-head designs. Its area, apothem, and both diagonal lengths all follow directly from the side length via closed-form formulas.

How it works

Enter the side length s. A regular hexagon splits neatly into six equilateral triangles from its center, which is why its area formula, Area=(3√3/2)s², carries a factor of 3√3 from combining those six triangles' areas. The apothem (the perpendicular distance from center to a side's midpoint) is Apothem=s√3/2. The long diagonal, connecting two opposite vertices through the center, equals 2s (twice the side length) — notably, this also means the circumradius of a regular hexagon equals its side length exactly. The short diagonal, skipping just one vertex, equals s√3.

Enter side length.
Click Calculate to see your results.

Examples

Side length 5

Area = (3√3/2)(25) ≈ 64.95. Apothem = 5√3/2 ≈ 4.33. Long diagonal = 2(5) = 10. Short diagonal = 5√3 ≈ 8.66.

Side length 12 (e.g. a hex bolt head, in mm)

Area = (3√3/2)(144) ≈ 374.12 mm². Apothem = 12√3/2 ≈ 10.39 mm — this is the "wrench flat-to-flat" half-distance used when sizing hex fasteners.

Common mistakes to avoid

Confusing the apothem (center to edge midpoint) with the circumradius (center to vertex, which equals the side length in a regular hexagon).
Mixing up the long diagonal (2s, through the center) with the short diagonal (s√3, skipping one vertex).
Applying these formulas to an irregular hexagon — they only hold for a regular hexagon with all sides and angles equal.

Frequently asked questions

The long diagonal connects opposite vertices, passing straight through the center (length 2s); the short diagonal skips just one vertex and doesn't pass through the center (length s√3 ≈ 1.732s).

Because a regular hexagon is made of six equilateral triangles meeting at the center — each triangle's three sides (two of which are radii, one of which is a hexagon side) are all equal by definition of "equilateral," which forces the radius to equal the side length.

A regular hexagon's interior angle is exactly 120°, and three hexagons meeting at a point contribute 3×120°=360° — filling the space around that point perfectly, with no gaps or overlaps.

The general regular-polygon area formula is (1/2) × perimeter × apothem. For a hexagon, perimeter=6s and apothem=s√3/2, and multiplying those together (times 1/2) simplifies to the (3√3/2)s² formula.

720°, from the general polygon formula (n-2)×180° with n=6; a regular hexagon splits that evenly into six 120° angles.

Six equilateral triangles, one for each side — this decomposition is exactly how the area formula (3√3/2)s² is derived, by finding one triangle's area and multiplying by six.