As usual, rather than actually prep, I find it much more useful and productive to agonize and fret over how exactly I should go about prepping until the desire to prep fades away. But at least this time I think I’ve actually gotten somewhere with it: namely I’ve decided on an alternative to overland mapping with a hex map.

There are three main advantages to overland mapping with a hex map, as I see it:

- Easy to judge distance due to the built in scale
- Easy to judge density of points of interest, also due to the built in scale
- Easy to scale the map up or down and put things roughly where they need to be

BUT, in my case I don’t actually want to RUN a game on a hex map from the player’s point of view. I want more of the feel of players navigating by landmark, finding points of interest and traveling from one to another because sight navigation is easier than heading directly to the end destination, similar to Ben Robbins’ West Marches game (see comment #7 here).

No hexes, no squares – just an open terrain map … they would say “march southwest into the woods for three miles, looking for a big tree” and then we’d check Wilderness Lore to see if they went anywhere close to where they intended. If I described a ridge they saw and they would point at their map and say “hey, we must be here” I would shrug and neither confirm nor deny.

Hex maps (from the player’s perspective) badly undermine that dynamic because it’s far easier to just say “I travel a hex east, then a hex northeast, then a hex north” than to pretend you don’t have access to the convenience of hexes on your map. Yes, you can make house navigation rules to shift the effectiveness back towards landmarks (basically add a big penalty to your navigation roll if you’re not using landmarks), but that’s an extra layer of complexity.

So the next step is obvious: why not just make a hex map and not tell the players that they’re on a hex map? Well, turns out there’s a very good reason: On a hex map, southwest isn’t really southwest, or at least not without a lot of painful jiggering it isn’t. Instead it’s 30 degrees south of west, which is about 15 degrees off (or 60 degrees south, which is off 15 degrees the other way). Who cares, right? Well, your players will care if they travel a week north, a week east, and then travel home southwest because they’re not actually going to get home. You could correct that by actually having them travel southwest when they say they do, the fact that it doesn’t line up with any of the lines on your map be damned, (you can find the distance at 30 degrees south of west and 60 degrees south of west and then draw an arc between them.Â The center is roughly SW if your arc was close enough to a circle) or by explaining to them that when they say southwest, you’re actually going to be using 30 degrees south of west, and to adjust expectations accordingly, but either way it’s a mess that no one wants to deal with.

OK then, well what about just mapping on white paper, like Robbins’ says he did in the comment thread linked above? This discards those three advantages of hex mapping listed above. It also requires either huge paper or a ton of eyeballing or scanning, resizing etc… on a computer to zoom in or out in scale. Alternately, some mapping software can provide the best of both worlds with the ability to zoom in and out easily with nary a hex anywhere, but both of those solutions require outlaying some cash (and while I technically have a copy of CC2 laying around here somewhere, I’ll be damned if I want to try to get it running on Windows 10).

But, it turns out there’s a simple solution that retains all the advantages of a hex map, with additional advantages that hex maps don’t have. It’s so simple that it makes me wonder why our hobby ever started using hex maps in the first place. I suspect it’s a legacy from RPGs’ wargaming roots, where the hex offers additional facing options that are completely useless to overland mapping but I‘d be happy to be educated on the finer points of it by anyone grognardier than I.

That solution is the standard graph paper grid. Using it for overland maps has the same advantages of the hex map, but also has the following advantages:

- If you’re using the squares as regions players are aware of (similar to usual hex use) it’s possible, but much more difficult to get to the “no man’s land” between areas. On a hex map if you travel east or west, a third of the time you’re between hexes. On a grid players would actively have to try to get there, with no payoff. Of course once there they could stay indefinitely much easier than with hex maps.
- Your basic 4 cardinals and 4 ordinals are much easier to deal with than with a hex map.
- Same paper for dungeons and overland
- While a variety of “scale maps” for hexes with two different scale hexes to facilitate zooming in and out between regions of different sizes can be found online and it’s not terribly difficult to produce your own, making your own is easier with grids.

One of may favorite articles about the scale of hex maps is In Praise of the 6 Mile Hex over at The Hydra’s Grotto. If you’re going to use a hex map, that’s a good place to start. There they discuss the measurements of a 6 mile hex, that a 6 mile hex is about the limit of visual range, so you can see out of it only if you find a high vantage point, and discuss breaking it down into sub-hexes. I wanted to find a similar “perfect size” for a grid map, and It turns out that it’s the 5 mile square. A 5 mile square is 25 sq miles (as opposed to 31 for the 6 mile hex), is 2.5 miles from the center to a side, 7 miles diagonally from corner to corner, and 3.5 miles from center to corner. Since it’s nearly the same size as the 6 mile hex, a 5 mile square is also about the limit of vision without finding a vantage point. I had some trouble with scaling the 5 mile grid up and down at first. I had assumed since the Grotto’s article mentioned scaling the 6 mile hex up to a 72 mile hex and down to a half mile hex that those were also nicely proportioned hexes, so I was trying to find some magic ratio of grid sizes that had a common factor, were 3 useful scales, and all worked out well as far as “round” distances were concerned. Turns out the best set are 3, 12, and 48, though the numbers on 48 are fudged a bit and the difference in scale between 3 and 12 could be larger.

But it turns out, as I was fiddling with the measurements of varying hexes, trying to discover why they worked so well scaled up and down while grids didn’t, I discovered that my assumption that hexes scale well isn’t all that true, so as long as the level at which the majority of your navigation will be done has convenient measurements, that should be sufficient and other scales don’t need to be as clean. For ease, here are a handful of clean square grid sizes with useful dimensions:

Width/Height | Radius to Side | Diagonal | Radius to Corner |

5 | 7 | 2.5 | 3.5 |

7 | 10 | 3.5 | 5 |

12 | 17 | 6 | 8.5 |

24 | 34 | 12 | 17 |

36 | 51 | 18 | 25.5 |

Because it’s really easy to make custom “scale maps” with grids, it’s not essential to keep your jumps in scale to a consistent factor, like is suggested for hex maps. Instead, choose a scale you like for travel and scale up and down by whatever factor works best for you. If you want to go 1/2 mile, 5 mile, 25 mile, go right ahead.

Here’s a sample map that I had lying about on which I overlaid a grid map. Estimations of distance is quick and easy without any weirdness in the angles, so it can be used either as is or using the grid for your own reference only.

Matt, thanks so much. Always great to consider WHY we do what we do in the hobby. I tend to use a non-gridded or hexed overland map like Tolkien’s and only grid out the combat likely areas.

Pretty sure hex maps are a leftover from wargaming that predates original D&D. I’m not sure why they are used there, though.

I think you are in danger of over-thinking this one.

Drawing or figuring “square” directions is no more difficult on a hex grid than on square paper, really. No arcs are required. Simply draw a square on the hex grid by counting off the hexes for the corners and assemble your compass rose from there.

I do it all the time when I use a grid in my Savage Worlds games – a hex grid is just easier in every way but one than squares. That one case? Drawing rectangles along grid lines a-la D&D dungeon map. Impossible on hexes, but rectangles are easy to draw on hex grids. It’s making the players understand there is no problem that takes time.

You are not limited to 60 degree directions on a hex-grid, something I have to explain time and again to people when I show off my old “Triplanetary” space-race board game. SPI’s Freedom in the Galaxy RPG fighter tactical display actually spelled this out with a direction rose. “

What, we can move along the lines as well as across the faces of the hexes?“.What hexagons do really really well and (non-staggered) squares do very badly: Give true ranges (unless you go all Pythagorean). That’s why I like to go diagonally on the grid in post 4e games – I get a two-fifths acceleration for free. Staggered squares fix the Pythagoras problem, but then you have ugly flattened hexes anyway.

In Pathfinder/D&D 3.n they work in a bit of Greek by the “every other square costs double” rule. It is surprisingly accurate for a kluge.

Snapshot solved the same issue by charging two action points for a move orthogonally on the grid and three for a diagonal move.

Either way, if you don’t account for it your “actual range” from a-b will be wrong if you don’t factor in some triangle math. With hexes, provided you always move toward the target, it doesn’t matter which path you take across the grid, the answer will be the same (estimated) value of the true distance.

The reason you have hex sheets in RPGs is because the grandaddy of them all suggested Outdoor Survival as a good mapping machine (an Avalon Hill board game) and it used hexes. All wargames did because of the range/Pythagoras thing.

And here are a couple more things for consideration:

Tactical hex grids present a more realistic “how many enemies can gang up” limit than squares.

Vis-a-vis large scale/strategic mapping: the hex grid is not useful for the fine-grained information you want to include for the same reason squares aren’t. But what they can do is convey enough high-level information that the GM gets useful info

if the movement scheme is appropriately chosen.What is needed isn’t “how long does it take to travel from place to place inside a hex” but “how long does it take to move from this hex into another”. Which is how wargames came up with movement points and D&D came up with wilderness movement rates.

And all this is in danger of becoming irrelevant when you factor in real-world wilderness adventuring stuff such as people walking along trails and roads rather than blagging across country (for very good real world reasons rarely crossing the minds of “shortest path” obsessed gamers), and natural scenery that won’t cooperate with people trying to cross it such as rivers, cliffs, bogs and dense foresting.

Real world navigational maps such as the truly incomparable Ordinance Survey maps of the UK do use square grids, but orienteers do not use them for ranging, they either eyeball it or, if they actually need to care, measure off the distance from here to there with the ruler built into their compass. Yes, I’ve done this for real back before the invention of D&D. The difference between 1 and the square route of two can get you killed on a bad day.

It’s obvious I like hex grids more than I like square grids for game maps. I think they solve a bunch of problems presented by square grids. And there’s a really neat and elegant implementation of the very idea you are struggling with, along with a journey attrition scheme that puts the “epic” back in epic fantasy in The One Ring RPG.

Truly a game-changing idea and one all GMs would do well to look at. The wilderness could be dangerous and make sense at the same time, posing a serious threat to adventurers without the need for ravening hordes of wandering monsters inexplicably eking out a living in the wasteland to up the ante. Of course, you can have them too if you want. But adventuring is much more nerve-wracking if the journey itself is a wandering monster.

I’m not sure I’m following everything you’re saying here. Let me respond to a few points and then you can clarify if I’ve bungled your intent all to heck.

“Simply draw a square on the hex grid by counting off the hexes for the corners and assemble your compass rose from there.”

So if I get you, you’re saying do the reverse of what I did above. Instead of drawing a line 60 mi SW, just draw a line 42 mi W, another 42 mi S and that’s 60 mi SW? I suppose, but then am I not pulling up a calculator and dividing by root 2 at the table, then drawing a square? Wouldn’t it just be easier to be able to draw a line SW in a known unit, which is what I propose?

“That one case? Drawing rectangles along grid lines a-la D&D dungeon map. Impossible on hexes,”

Actually, it’s fairly easy to adapt a hex map to an isometric perspective grid map if you want to get all fancy or if you have no graph paper handy.

â€œWhat, we can move along the lines as well as across the faces of the hexes?â€œ

You’ll find that I already have an example of that. Traveling across the faces in the example I give is 30 degrees south of west. Traveling on the line is 60 south of west. I then went on to point out that neither of those is 45 degrees south of west.

“What hexagons do really really well and (non-staggered) squares do very badly: Give true ranges (unless you go all Pythagorean). Thatâ€™s why I like to go diagonally on the grid in post 4e games â€“ I get a two-fifths acceleration for free. Staggered squares fix the Pythagoras problem, but then you have ugly flattened hexes anyway.”

I’m going to have to disagree here. Neither do it particularly well, but neither does it better than the other. On a hex, the true distance from center to face and from center to corner is off by a factor of (root 3)/2. That’s why the 6 mile hex is so great, because it’s 3 mi from center to face, 3.5 mi from center to corner.

For grids, center to face and center to corner are off by a factor of root 2. That’s why the 5 mi hex is equally nice. It’s 2.5 mi from center to face, 3.5 from center to corner. In both cases those measurements are fairly accurate, but there are infinite hex sizes and grid sizes where those numbers go all to hell and you’d need to kludge as you describe above for hexes as well as for grids.

Picking one of these well fitting hexes or grids eliminates the need for any kludgey adjustment regardless of hexes or grids.

“Tactical hex grids present a more realistic â€œhow many enemies can gang upâ€ limit than squares.”

I’m going to admit ignorance on if 6 or 8 people circling someone in melee is “more realistic”. In any case, as far a overland hex maps go, this isn’t really relevant unless you’ve dropped from overland to tactical scale, and that’s not really the issue at hand.

Sorry for the delay Matthew, I got hung up with work.

No, the compass rose is not constructed the way you have it. I was suggesting you construct a small square, easy to do on hexes, and extend your line using it as your origin.

I think where we part company is on your trying to place a hex (or square) grid over real territory and then make statements about what’s going on in the hex, whereas the great strength of the idea is in spitballing how long it takes to cross the hex itself. That is why some games used to run rivers along hex sides (but others with slightly different MP mechanics didn’t).

Pythagorean argument: again, you are over-thinking. Don’t get hung up an what is happening inside the hex (or square). Measure center to center for a spitballed range. If you need to talk about distances inside a hex (or square) increase mag and reduce the grid size and go back to center-to-center measurement.

Not forgetting that without contour lines you have no real idea how “far” something is from something else just by looking at the horizontal separation anyway. The ground moves in the Z axis with wanton abandon.

People rarely have the option of traveling as the crow flies. Open terrain is never that cooperative. Roads get built the way they are for a reason. Roman roads? Yep straight as a die (you can still travel along ’em in parts of the UK (see: Watling Street) but the Romans spent much time and energy banging on the infrastructure to make it work. Everyone else traveled in squiggles to avoid hills and floods and rivers and rocky ground.

As for enemies ganging up, close packing says that if everyone is the same size it’s six (molecular close packing follows the same rules though the matrix can look cubic if you aren’t used to looking at it right). Actual in-the field combatants claim four or even three is more realistic, and I can see why.

Anyway, interesting article even if we differ on details.

Ever considered using bricked graph paper, where one row of squares is offset to the neighboring rows half a square, so each square borders to 6 other squares like hexes do?

There are even more interesting graph papers available at http://incompetech.com/graphpaper/

Wargaming (Freikriegspeil in the Prussian tradition) adopted the ‘chess’ grid before Frederick the First as a teaching tool. It was imperfect at best, as was every promising replacement until the Rand Corporation got the contract and ran it past mathematicians and other proto-geeks. That started the geeks asking questions and coughing up their own ‘games’, the heir to which be or modern tabletop gaming. Now we have computers that will allow us to do all the drudge work of mapping, marching and starving the unprepared (remember Oregon Trail?). Did I just date myself?

If reader want to draw hex maps easily and quickly there is a in-browser app available at http://hextml.playest.net

It takes a little getting use to since there is many features but the basics are easy to grasp.

It has to do with the original d&d (Chainmail). For overland travel and encounters, players were told to use a board game from Avalon Games. It was a wilderness survival game that used a hex map for different terrain and also had random encounters.

Yes! I don’t know why more people don’t know about the Outdoor Survival roots of Dungeons and Dragons. In the early 70s you had to have Avalon Hill’s game Outdoor Survival to do any overland travel in Dungeons and Dragons. Outdoor Survival was a game with a single hex based map as the game board. That is the only reason why we use hexes instead of grids, or lines, or 😮 a freaking ruler with a scale marked for whatever your distances are (which incidentally I find to be easiest).

It doesn’t have to be difficult really and I don’t know why we have to do all the 30 degrees off of south west stuff just to conform to the grid. Just get rid of the grid entirely. Draw the map, choose true north, decide on the scale, and be done with it.

The main benefit to me, with hex grids for overland use, is when you are explicitly treating each hex as a unit for exploration, all adjacent hexes are equidistant from you and you can use “one hex” as the basic unit of distance for overland travel. You pick a hex size that divides nicely into your standard travel pace, and everything gets rounded to even numbers of hexes per day, or hours per hex. It gives you six equal directions, rather than a square grid with four equally distant adjacent hexes and four adjacent diagonals.

If you routinely need to navigate to a specific point within one hex, rather than treating the hex as a unit, you aren’t going to get much benefit from using a hex map. You can either zoom in and use a grid with smaller hexes, so you CAN treat each hex as a unit, or put a scale mark at the bottom of the map and actually measure distances with it, or you can throw whatever grid pleases you over the map just as a way of giving some sense of scale and distance. I still like a hex grid for this, but whatever grid you choose, if you aren’t using each grid section as a distinct unit, you will have weirdness about travelling in a direction other than one that follows the grid. (On a hex grid, distance to the next east or west hex is almost exactly 1.75 hexes, though I usually figure it as 2 hexes minus a bit.)

Referring to “southwest” in a hex crawl – where you are explicitly using hexes as a discrete unit for exploration and travel – everyone has to understand that “southwest” means 60 degrees west of south. In mid-high latitudes, you could just as well call the direction “winter sunset”. You just need six terms to describe the six general directions you can go from one hex.

Using a hex as a unit of overland travel works best when the PCs can’t navigate with perfect precision, and when the terrain doesn’t favor a dead straight line of travel. They can pick which adjacent hex they want to move into, and there is likely a navigation roll (modified by conditions) that means they might end up in a different adjacent hex.

They don’t have a GPS. They don’t know exactly where they are on a map. They don’t know precisely how far they have travelled. They don’t have a wristwatch. If they have any kind of map at all, it was not made with modern surveying and satellite imagery.

If the PCs are capable of travelling EXACTLY 60 miles, precisely SW, with no landmarks to put them on course, and no obstacles to push them off that line, then any grid you use is just for eyeballing. Travel by dead reckoning, your target isn’t going to be exactly in a cardinal direction. It’s going to be something like 157 degrees east of north. And in real life overland travel, even with a modern map and compass, you know you aren’t going to stick precisely to your line, so you plan your route by landmarks and “catching features”. Besides, the large square grid on navigational maps isn’t for estimating distance between points or dividing the map up into discrete units. They are to have a reference point for measuring angles and coordinates.

Go 2 hex. With grain (orthogonal) has a distance of 2. With off grain (diagonal) has a distance of sqrt(3), approximately 1.732. The value 1.75 is relatively further away from sqrt(3) than 1.4 is from sqrt(2), but relatively closer to sqrt(3) than 1.5 is to sqrt(2).

Actually, going 60 miles southwest is too far if truly on a spherical world, since it is clearly less than 59 miles, and greater than 42 miles since crossing the north pole is implicitly forbidden by the example. Real life has lots of grid-lock movements.

The example shown: 42 miles north, 48 miles “hex drunken walk” east, follow by 60 miles south west west. Going south west west instead of going southwest is a problem. The correct path is 66 miles of “hex drunken walk” southwest. Clearly, travel distance increased by grid-lock movement.

Showing up to this interesting party seven years later (where is everyone?) …

Can anyone explain Roxysteve’s method of ‘simply’ drawing a square on a hex grid?: “Simply draw a square on the hex grid by counting off the hexes for the corners and assemble your compass rose from there.” I can draw a rectangle if the long diagonal lines and the edges of hexes are allowed, but I don’t see how to draw a square.

More importantly, does anyone know a simplified hack for estimating 45 deg movement on a hex map? For example, I’m hoping there is something like the hack for 45 deg movement on square grids, which estimates 3 distance units for every 2 diagonal squares.

Also, a significant typo – I almost never post about such things but this one can confuse readers: In the table of square dimensions near the end, the column headers “Radius to Side” and “Diagonal” are reversed.

But that is a compliment – it means I read and thought about every word in the article, right to the end, because it was so insightful and engaging. Thank you!

If I hazard a guess, I think Roxysteve meant: count over and down x hexes, say for example 4, and then draw a square from there and make a compass rose in said square. But I could well be wrong because I’m not sure that would work. Maybe he’ll hop in and explain if he happens to have notifications on on this article.

Alas, I know of no such rule for estimating movement on hex grids. Sorry.

As for the typo: You’re absolutely correct. And I would swear I’ve fixed it at least twice at this point. I think I’m just going to have to leave it broken. 🙁

Wow I’m not the only one agonizing about this. I feel validated.

One thing I haven’t seen mentioned: If you are not using a grid as an overlay but fill in the squares/hexes piece by piece, a hex map looks better. Squares look pixelated while hexes look somewhat like natural borders.

If I draw a map myself, I don’t think I’ll use hexes again.