05-24-2023, 02:46 PM | #1 |
Join Date: Dec 2009
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How to calculate a hexagon side to side?
If I have a hexagon that is flat on bottom & top.
How do I calculate the distance from bottom to top? There used to be a brilliant website that did all of this but it seems to have vanished. |
05-24-2023, 03:04 PM | #2 |
Join Date: Aug 2004
Location: Austin, TX
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Re: How to calculate a hexagon side to side?
I don't quite understand the question. Normally, GURPS measures the size of a hexagon from one side to another, so distance between the top and bottom of the hexagon is 1 yard or whatever.
The long diagonal of a polygon is the further distance between any two points, and that's 1.15x the distance between opposite sides. The length of a side is half of the long diagonal, or 0.577x the distance between opposite sides. Hope that helps. Also, see https://www.omnicalculator.com/math/hexagon - the left hand diagram lets you input whatever you know about the hexagon and get whatever other values you want.
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05-24-2023, 03:13 PM | #3 |
Join Date: Dec 2009
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Re: How to calculate a hexagon side to side?
I have a grid app for my iPad
But it needs the distance ‘a’ Now I can put in the correct distance a hex to measure exactly 1” across ‘S’ That site pretty much did what my other site did, thanks. |
05-24-2023, 04:15 PM | #4 |
Join Date: Jun 2005
Location: Lawrence, KS
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Re: How to calculate a hexagon side to side?
If a hexagon is distance 1 from side to side, then the distance from its center to the center of an adjacent hexagon is also 1.
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Bill Stoddard I don't think we're in Oz any more. |
05-24-2023, 04:56 PM | #5 |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: How to calculate a hexagon side to side?
A hexagon can be exactly filled by six equilateral triangles, and the ratio of height to side length for an equilateral triangle is sqrt(3 ) / 2, so if a hexagon is 1 yard between opposed sides, it is 1.155 yards between opposed vertices, and if it's 1 yard between opposed vertices, it is 0.866 yards between opposed sides.
While we're at it, the area of an equilateral triangle is sqrt( 3 ) / 4 * side length squared, so the area of a hexagon is sqrt(3) * 3/2 * side length squared, so a hexagon with an area of one square yard has a side length of 0.62 yards, and is 1.07 yards between opposed sides, 1.24 yards between opposed vertices. |
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