Approximating the area of a hexagon

I needed to figure out how many square miles are in a hexagon. Turns out, nobody wants to give a straight answer when all you know about the hexagon is the distance face-to-face, which is what we all use in the hex and chit world.

After relearning some geometry, this is the simplest possible approximation I can give you: a = (w / 1.732) * (3w)

That is, the area is the width “face to face” divided by 1.732, then multiply that by three times the width.

Example: A Greyhawk 30-mile hex has width 30. It’s area is about 1558.8914 square miles.

a = (30 / 1.732) * (3 * 30)

a = (17.3210) * (90)

a = 1558.8914

Which means if your stronghold-building wilderness-clearing 9th level Fighter wants a Greyhawk hex all to himself, he’s clearing almost 1600 square miles of monsters. Get to it, Gutboy Barrelhouse!

This is the kind of formula I’d put on the second DM screen that you pull out only in extremis. Like how composition books have commonly-used formulae on the inside covers.

Watch this become by far the most useful thing I have ever done :/


3 Responses to “Approximating the area of a hexagon”

  1. Black Vulmea Says:

    Or you could’ve just checked my blog.

  2. JDJarvis Says:

    Your formula is off. You are getting an area much larger than the actual area. Draw a hex on some grid paper and count the squares.

  3. Red Orc Says:

    I have a page bookmarked for working out the area of a hexagon because it’s only gamers that measure the size of a hexagon centre-to-centre through a perpendicular edge.

    Pretty sure you want to know A from twice the ‘inradius r’. For a 30 mile face-to-face distance (ie, r=15), that gives an area of 779.4 square miles.

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