Hex Paper
Created for free at puzzleandprint.com
1 cm hexagons
Or take one that is already made
Ruled sheets at the standard sizes, each one a single page. The measurement is printed at the foot, so a reprint can be checked against a ruler.
1 cm hexagonal graph paper, full page10 mm sides · 17.32 mm across, about 13 mm from the sidesDownload PDF ↓
1 cm hexagonal graph paper10 mm sides · 17.32 mm acrossDownload PDF ↓
1/2 inch hexagonal graph paper12.7 mm sides · 22 mm acrossDownload PDF ↓
5 mm hexagonal graph paper5 mm sides · 8.66 mm acrossDownload PDF ↓Every sheet here is free to print as often as you like. If one saved you time, the tip jar is on Ko-fi.
Hexagons tile the plane without leaving gaps, and unlike squares every neighbor is the same distance away: there are no awkward diagonals that count as one step but measure about 1.41 times as far. That is why wargames and tabletop campaigns have drawn their maps on hexes since the sixties, and why hex paper is worth having in a drawer if you build worlds on paper.
The other half of the audience is chemistry. A benzene ring is a hexagon, and so is every six-membered ring in an organic structure, so drawing on hex paper turns a fiddly freehand sketch into something that just follows the lines. The sheets here have a vertex at the top of each hexagon, which is the orientation rings are conventionally drawn in.
Sizing is given twice, because hex paper is quoted both ways. The number in the name is the length of one side of a hexagon; the second figure is the distance straight across it, which is what you want if you are planning how many fit on a map. A 1 cm hex is 1.73 cm across.
Only whole hexagons are printed, so each grid stops where the next hexagon would be cut by the margin: the 1 cm grid comes out about 173 mm wide, the 5 mm one about 182 mm and the half inch one about 176 mm, each centered with the spare paper shared equally between the two sides. The fourth sheet, shown first, rules the 1 cm grid out toward the edges of the paper: 179 hexagons in 17 rows, about 190 mm wide and 260 mm tall, about 13 mm from each side. The one other mark on each sheet is a small line at the foot giving the size, such as 10 mm sides and 17.32 mm across, so a reprint can be checked with a ruler.
Which hex paper size suits a map with counters or drawn symbols
For a map that has to hold coin-sized counters or drawn symbols, the half inch hex paper is the roomiest: each hexagon is 22 mm across its flat sides, and 90 whole hexagons fit on the page in 12 rows. A British penny (20.3 mm) or a US one-cent coin (19.05 mm) sits inside one with a little space around it, and neither fits within the 17.32 mm of the 1 cm sheet. The standard 1 cm sheet holds 143 hexagons in 15 rows and the full page one 179 in 17, enough for a region with room to draw a tree or a tower in each, and the 5 mm sheet holds 656 in 32 rows, 8.66 mm across, for a large area at a fine scale.
The rows alternate in length, 10 and 9 on the standard 1 cm sheet, 11 and 10 on the full page one, 8 and 7 on the half inch and 21 and 20 on the 5 mm, because every second row is pushed half a hexagon to the right and loses one at the end. Before drawing anything, decide what one step from a hexagon to its neighbor stands for, a mile, a day's march or a room, because the sheet fixes how many steps the map can hold. A map planned on the standard 1 cm sheet at one mile a step is about ten miles wide, and eleven on the full page one; the same map on the 5 mm sheet can be twenty-one.
Drawing fused rings and carbon chains on hex paper
Neighboring hexagons on hex paper share a side, so fused ring systems can be traced straight off the grid: naphthalene is two hexagons sharing one side, and anthracene is three in a straight row. Because the hexagons here stand with a point at the top, two rings side by side share a vertical side, which is the way naphthalene is usually drawn. A ring added in the next row down joins at a slanted side instead, and three rings arranged that way give the bent shape of phenanthrene, so both three-ring structures come from the same sheet.
Every corner of the grid is a meeting of 120 degree angles, the angle used for the zigzag chains of skeletal formulas, so a carbon chain can follow the edges along the top of a row of hexagons with each bend on a corner. What the grid will not do is a five-membered ring, as in cyclopentane, or a six-membered ring drawn as a chair; those still need drawing by hand. For structure work the 5 mm sheet gives 656 small rings for a page of reactions, and the 1 cm sheet leaves room to write atom labels beside each ring.
Common questions
Why hexagons rather than squares for a map?
Because each hexagon has six neighbors, all the same distance away and each sharing a full side with it. A square has eight: four across a side and four that touch only at a corner, about 1.41 times as far off, so a square map has to rule on whether a corner touch counts as adjacent, and a hex map never does.
What size is a 1 cm hex?
One centimeter along each side, which makes it 1.73 cm across the flat sides and 2 cm from the top point to the bottom one. Rows sit 1.5 cm apart down the page because each row nests into the gaps of the row above, which is why the standard 1 cm sheet fits 15 rows rather than the 12 it would hold stacked point to point, and the full page one 17 rather than 13.
How do I measure distance on a hex map?
Count the steps from each hexagon to a neighbor rather than measuring with a ruler, since all six neighbors are one step away. Each step covers the width of a hexagon across its flat sides: 17.32 mm on the 1 cm sheet, 22 mm on the half inch and 8.66 mm on the 5 mm. Give one step a distance, a mile or a day of travel, and every route on the map can be counted the same way.
Want to know when new printables go up?
New printables when they go up, mostly seasonal, a few times a year.