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. A standard ball has 20 hexagonal panels.

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: 380 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 (across-flats / 2): r = s × √3 / 2 ≈ 0.866 × s
• Long diagonal (vertex to opposite vertex): d_long = 2s
• Short diagonal (vertex to non-adjacent vertex, vertical edge of hex bolt cross-section): d_short = s × √3 ≈ 1.732 × s
• Area: A ≈ 2.598 × s²

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

A bolt labeled “M10” has 10 mm thread diameter, but a 17 mm hex head — so you need a 17 mm wrench (or 11/16 in). The “17” is the across-flats measurement of the hex.

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

Why hexagons tile so efficiently. Compare to other regular polygons for tile floors: equilateral triangles, squares, and hexagons are the ONLY regular shapes that tile a plane without gaps. The hexagon achieves this with the largest area-to-perimeter ratio of the three — minimum grout per tile area.

Sanity check. The hexagon’s perimeter (6s) is close to the circumference of its circumscribed circle (2π × s ≈ 6.28 × s) — within 5%. This is why a hexagon looks “nearly circular” compared to a triangle or square.