Hex maps use the length of a side to indicate their size. This seems pretty terrible (IMO) as a way of figuring speed, and is about to be a real PITA for me in converting a bunch of hex-mappery from sources I'm reading into the system I've cooked up for handling them.

So how do I calculate:
1) The area of a hex with 4 miles between facing sides.
2) The side length.

And when I cook up my map, how should I go about conversion?

Thanks in advance to anyone who can help out. I've never really run a hexcrawl before.

My lazy bastard approach here would be to work out three hexes, one of 3 cm on a side, one of 5cm and one of 7cm, and figure the distance between sides by dead reckoning or a quick copy and paste. From that you should be able to rapidly figure a translation formula or relevant ratio. Working it backwards to find the side length is a slightly more messy but still doable aproach.

Of course a better idea all round would be to simply abandon hexes and use a ruler or piece of string.

x = distance side-to-side

Area = (.9306049x)^2

And for the rest: http://www.drking.org.uk/hexagons/misc/dims.html

Thanks for your help guys, but it looks like I jumped the gun on posting this thread. I just found a calculator for this sort of thing here: http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php

Looks like the side length was something like 2.3 and the area is about 14 square miles.

EDIT: KenHR, your link is good too. Thanks for chipping in.

Quote from: beejazz;653069So how do I calculate:
1) The area of a hex with 4 miles between facing sides.
2) The side length.

I am sorely tempted to say "ask your high school trig teacher" because this is 9th grade math, but if you're seriously having trouble looking this up on Google I can walk you through the steps.

Quote from: daniel_ream;653101I am sorely tempted to say "ask your high school trig teacher" because this is 9th grade math, but if you're seriously having trouble looking this up on Google I can walk you through the steps.

Sorry to have wasted your time. I did eventually find the answer on google (the issue I was having was figuring out how to phrase the question when searching).

I wasn't bad at math in school, but it's been years and years since I've really applied anything of this nature. I really should brush up on it at some point.

EDIT: And now I'm remembering some stuff I could have done to solve this on my own. Truly I am shamed by what a week (or so) of summer and a day long road trip will do to me.

Quote from: beejazz;653069Hex maps use the length of a side to indicate their size.

No. Hex maps use the distance from one side to the opposite side to indicate their size.

Quote from: Justin Alexander;653147No. Hex maps use the distance from one side to the opposite side to indicate their size.

I must have read the stuff I was using wrong then, too.

EDIT: Nope, looks like I was (at least partly) correct. BotRN at least lists hexes as 12 miles on a side. AER has a few potential hex sizes measured side to side.

A hexigon isn't quite a circle, but the "diameter" of the hexigon (one corner to the opposite corner) is also the same distance as the distance from the center of one hex to the center of the next hex. It makes more sense when you realize that a hexigon is actually six equilateral triangles.

In other words, suppose a hex has a facing side of 5 km, so its "diameter" would be 10 km. Going from the center of one hex to the edge would be 5 m again, so going from one center to the next is like one radius added to another one (one from each hex) or would be 10 km again.

Sigh...I just got through trying, and failing, to convince college admin that there are mathematical applications in gaming. Really wish they'd stop giving Ph.D.s in Administration...

Quote from: finarvyn;653209A hexigon isn't quite a circle, but the "diameter" of the hexigon (one corner to the opposite corner) is also the same distance as the distance from the center of one hex to the center of the next hex. It makes more sense when you realize that a hexigon is actually six equilateral triangles.

In other words, suppose a hex has a facing side of 5 km, so its "diameter" would be 10 km. Going from the center of one hex to the edge would be 5 m again, so going from one center to the next is like one radius added to another one (one from each hex) or would be 10 km again.

Yep. And I figured out that I could discern the bit I was looking for by cutting one of those equilateral triangles in half, and calculating the length of one side based on the length of the other two. It's high school math I know, but it stops being intuitive when you haven't used it in a few years.

To learn something more general purpose from this, consider: what is a hexagon?

You can beak it down into 6 triangles, equiangular (60 degrees each corner) and equilateral (sides of the same length).

Quote from: finarvyn;653209A hexigon isn't quite a circle, but the "diameter" of the hexigon (one corner to the opposite corner) is also the same distance as the distance from the center of one hex to the center of the next hex.

... if you're moving through the corners of the hex.

If you're moving across the face of the hex, then the distance moved is √3 * side. (Where size is the length of one face of the hex.) Or √3 * 0.5 * diameter (because the diameter is 2 * side).

Quote from: beejazz;653162EDIT: Nope, looks like I was (at least partly) correct. BotRN at least lists hexes as 12 miles on a side. AER has a few potential hex sizes measured side to side.

I'm not sure what BotRN is.

I'm assuming AER is an An Echo Resounding, which does use face-to-face.

If you're looking for hexmap resources, you'll generally find two sorts: First, using hexes in computer games. Second, hexmaps for tabletop games.

Resources for computer game hexes will generally measure a hex by the length of its side because the length of the side is a convenient basis for doing all sorts of hexagon-based math. That's useful for computers because the programmers need to do all sorts of math in order for the computer to understand how the hexes work.

Tabletop hexmaps, OTOH, almost universally measure distance from face-to-face or center-to-center through a face (which, it turns out, is the same thing). This is because DMs generally have no interest in performing a lot of complicated math at the tabletop: The point of using a hexmap is to simplify the handling of movement through the wilderness.

If you actually manage to find some tabletop game that's using a hexmap with a scale set to the length of the hexagon's side, then you're almost certainly looking at a tabletop game which was never actually playtested.

Quote from: Justin Alexander;653862I'm not sure what BotRN is.

I'm assuming AER is an An Echo Resounding, which does use face-to-face.

If you're looking for hexmap resources, you'll generally find two sorts: First, using hexes in computer games. Second, hexmaps for tabletop games.

Resources for computer game hexes will generally measure a hex by the length of its side because the length of the side is a convenient basis for doing all sorts of hexagon-based math. That's useful for computers because the programmers need to do all sorts of math in order for the computer to understand how the hexes work.

Tabletop hexmaps, OTOH, almost universally measure distance from face-to-face or center-to-center through a face (which, it turns out, is the same thing). This is because DMs generally have no interest in performing a lot of complicated math at the tabletop: The point of using a hexmap is to simplify the handling of movement through the wilderness.

If you actually manage to find some tabletop game that's using a hexmap with a scale set to the length of the hexagon's side, then you're almost certainly looking at a tabletop game which was never actually playtested.

Book of the River Nations. It's a supplement that compiles the rules from Kingmaker. Not sure how well tested Kingmaker's rules are, but unless this was a mistake they should be more or less identical. You're right about An Echo Resounding (both the acronym and the hex system). I read Kingmaker first, have been doing a lot of skimming, and must have carried an assumption of similarity where there was a difference.