Skew Calculator for Parallelogram

So I’m having one of those moments where my high school math is eluding me…

I’m trying to figure out the correct M666 offset for my long axis on the LR.

I cut a 100mmx100mm square which measures close to perfect side but the diagonals are like 141 x 140. My Gantry is around 1475mm. Through trial and error I found the offset to be around 3.2mm across the gantry.

With my portable lowrider setup I need to square the gantry each time I setup the LR so I’d like to create a calculator that figures the offsets but I’m finding that my math skills aren’t what they used to be.

Before I go on a remedial math journey, does anybody know what the formula is for finding the skew of a parallelogram?

You can use the diagonals and side length to get the angle, then substitute that angle and your axis length to get the offset. Parallelogram Calculator

But the easier and probably more accurate way would be to drill a tiny hole at the extents of your build and then measure your skew. The difference in that number is like half the offset, or something like that. I usually get it closer than I can measure in one try. Using a very small square is hard to get very accurate without a few tries.

On a 4’x2’ build, I am happy with a mm or less diagonal difference.

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If you know the side length a of your work area as well as the side length h of your parallelogram, you can do the following using the Pythagorean theorem:

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Thank you both I hadn’t considered I knew the side length of the rail as it should be my movement distance. I was trying to solve the whole parellegram to get the outside angle. With an extra side to work with it becomes easy.

Because of the portable rail system I use, my tables squareness is slightly different each time I assemble so I think I have to do it the hard way.