Hexagon Perimeter Calculator (regular)

P = 6 × s

Six equal sides. A regular hexagon with 5 cm sides has a 30 cm perimeter.

Where hexagons show up in real measurements:

• Hex bolts and nuts. The hexagonal head is sized for wrenches across the flats (twice the apothem). When measuring across the corners (long diagonal), you get the bolt’s outer hex dimension.
• Hex floor tile. A 6-inch hex tile (side length 6 in) has 36 in of perimeter. Hex tile floors look great in bathrooms and entryways but require careful grout joints at every corner.
• Honeycomb cells. Each cell of a honeycomb is hexagonal, the most efficient tiling shape for equal-area cells.
• Hex gazebo or pavilion floors. A 4-ft side hex gazebo has 24 ft of perimeter rail.
• Hex nuts and washers in mechanical engineering.
• Chicken wire openings. Standard chicken wire has 1-inch hexagonal openings.
• Soccer ball panels. The classic truncated-icosahedron ball has 32 panels: 20 hexagons and 12 pentagons. The pentagons are what let a flat tiling curve into a ball, since hexagons alone stay flat forever.

Worked example: hex floor tile

You’re tiling a 100 sq ft bathroom with 4-in hex tile (side length 4 in). Each tile perimeter = 24 in. Area per tile = 2.598 × 16 = 41.6 sq in = 0.289 sq ft. Tiles needed = 100 / 0.289 ≈ 346 tiles. Add 10% waste: 381 tiles.

If you grout each tile edge with 1/16-in joints, the total grout length per tile is its 24-inch perimeter, but each edge is shared between two adjacent tiles, so the actual grout perimeter for the floor is half: 12 in per tile × 346 = 4,152 in (346 ft) of grout joint. Multiply by joint depth × width for grout volume.

Worked example: hex gazebo handrail

A 6-ft side hex gazebo gives 36 ft of handrail perimeter (around the outside). If the gazebo has an opening (skipping one side as a doorway), the handrail is 30 ft.

Other measurements from the same side s:

• Perimeter: P = 6s
• Apothem (half the across-flats distance): r = s × √3 / 2 ≈ 0.866 × s
• Long diagonal, across the corners: d_long = 2s
• Short diagonal, vertex to non-adjacent vertex: d_short = s × √3 ≈ 1.732 × s

That last one is worth a second look. The short diagonal and the across-flats distance come out to the same s√3, because across-flats is twice the apothem and 2 × (√3/2) = √3. So a hexagon has only two distinct widths, 2s across the corners and 1.732s across the flats, and every wrench in the drawer is sized to the second one.

• Area: A ≈ 2.598 × s²

Hex bolts and wrench sizes (the “across-flats” trap):

A bolt labeled “M10” has a 10 mm thread, but the head measures 17 mm across the flats under the older DIN standard, so you reach for a 17 mm wrench or an 11/16 in. ISO 4014 shaved that to 16 mm, which is why a mixed toolbox needs both.

Going the other way, if your wrench is 13 mm, the hex side length is 13 / √3 ≈ 7.5 mm and the bolt is typically M8.

Why hexagons tile so efficiently. Equilateral triangles, squares, and hexagons are the only regular shapes that tile a plane without gaps. Of the three, the hexagon has the largest area for a given perimeter, which on a tile floor means the least grout per square foot.

Sanity check. The hexagon’s perimeter, 6s, sits within 5% of the circumference of the circle through its corners, 2πs ≈ 6.28s. That closeness is why a hexagon reads as “nearly round” where a triangle or square never does.