Hexagon Area Calculator (regular)

A regular hexagon has six equal sides and six 120° angles. It can be split into six identical equilateral triangles, each with side equal to the hexagon’s side.

Area formula:

A = (3√3 / 2) × s² ≈ 2.598 × s²

A 10 cm regular hexagon has area 259.81 cm². The factor 2.598 is roughly 6 × the equilateral-triangle factor 0.4330, which makes sense: six equilateral triangles, each (√3/4) × s², totals 6 × (√3/4) × s² = (3√3/2) × s².

Why hexagons appear everywhere in nature:

The hexagon is the most efficient way to tile a plane with equal-area cells while minimizing total edge length. Honeybees build hexagonal honeycomb because it uses the least wax for the most storage. Cooling lava forms hexagonal columns (the Giant’s Causeway in Northern Ireland). Snowflakes have six-fold symmetry from water’s hydrogen-bond geometry.

In manufacturing and construction:

• Hex bolts and nuts. The hexagonal head gives 6 wrench positions vs 4 for a square head — twice the tightening flexibility. Standard sizes are stamped as “across flats” (twice the apothem).
• Hex floor tile. Popular in bathrooms and entryways. A 6-in side tile covers 93.5 sq in.
• Asphalt pavers. Many decorative paver patterns use hexagons because they tessellate cleanly.
• Chicken wire and hardware cloth. Hexagonal openings give strength with minimum material.
• Soccer ball panels. Truncated icosahedron pattern: 20 hexagons, 12 pentagons.
• Carbon graphene sheets. A 2D layer of hexagonally-arranged carbon atoms — basis of one of the strongest known materials.

Worked example — hex floor tile:

You’re tiling a 100 sq ft bathroom with 6-inch hex tile. Area per tile = 2.598 × 6² = 93.5 sq in = 0.65 sq ft. Tiles needed: 100 / 0.65 = 154 tiles. Add 10% waste for cuts: 170 tiles.

Other measurements from the same side s:

• Apothem (inradius — center to mid-side): r = (√3 / 2) × s ≈ 0.866 × s
• Long diagonal (vertex to opposite vertex, through center): d_long = 2s
• Short diagonal (vertex to non-adjacent vertex, edge-to-edge of bolt): d_short = s × √3 ≈ 1.732 × s
• Perimeter: P = 6s

Bolt-head convention. A bolt sized “M10 hex” usually refers to thread diameter. The wrench size needed (across the flats of the hex) is a different number — the hex is sized for wrench compatibility, typically slightly bigger than the bolt nominal. An M10 bolt commonly takes a 17 mm wrench, where 17 mm = the “short diagonal” of the hex head.

Sanity-check. The hexagon fits inside its circumscribed circle of radius R = s. That circle has area πs² ≈ 3.14s². Our hexagon area 2.598s² uses about 83% of the circle — higher than the 76% for a pentagon. More sides means closer to circular.