How to calculate a hexagon side to side?

[briansommers]

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.

[mlangsdorf]

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.

[briansommers]

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.

[whswhs]

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.

[Anthony]

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.