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So I am trying to figure out the square miles of my homebrew game world map but I drew it on hex paper and now I'm not sure how many square miles it is. I did a search online to find a conversion but all I could really find was an old forum thread that offered up a bunch of mathematical formulae for determining the area of a hex and debate to their accuracy for game purposes with no real answer.
Can anyone here help a brother out? If I can get an answer than hopefully other folks wandering about the interwebs with just such a problem will be able to find an answer as well.
What I am looking for is a simple means of calculating hex miles to square miles. If I have x number of hexes, each y number of miles across, my map is z number of square miles. That sort of thing, but a formulae that isn't too complicated and involving figuring the area based on the length of the sides and so on and so on geometry. Something the non mathies will be able to do. If a website with a calculator or such exists that would be great too.
The map I made for my homebrew world is 1,178 hexes large with each hex representing miles. How many square miles is my map?
lt's 3/4, assuming you measure a hex side-to-side. The map is 883.5 square miles.
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You did not give me the size of your hexagon. Is "y" the diameter (from one point to its opposite point) or is "y" the height (from the center of one side to its opposite side's center), or is "y" the length of one side? The math is different for each one.
But I guess it doesn't matter, you can do it yourself. Check out this link for all you need to know.
Just pick one of the radio buttons (h for height or s for side or d for diameter) and click the compute button, it will figure out the exact square mileage of your hexagon. Multiply by 1,178 for the square mileage of your map.
The area of a hexagon is (3*sqrt(3)*b^2)/2, where b is the length of one edge, or (sqrt(3)*h^2)/2, where h is the distance from one side to the other. I think you're referring to the latter distance as one mile, which would make each hex 0.866 square miles. That comes out to 1020.18 square miles for the total map.
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If the side of a hex is 1 mile then the hex is 2.6 square miles. (3063 sq mi)
If the height of each hex is 1 mile then each hex is .86 square miles. (1013 sq mi)
If the diagonal of the hex is 1 mile then each hex is .65 square miles. (766 sq mi)
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Now what is the DC to jump that? (joking)
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I did my map the way (I assume) most hex maps are measured. The distance is from one side of the hex to the opposite side of the hex, or the center of one hex tot he center of an adjacent hex, which is the same thing. So that would be the height according to the linked site.
Thank you very much for the link, it calculates exactly what I am looking to calculate. :D
To use my above example, I have 1,178 hexes, each 20 miles across, my map is Just over 408,071.1 square miles, or about three Californias. So, bigger than I intended it to be, but since it's a coastal region there is a fair amount of ocean and islands.
