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The accuracy of an engineer's square is typically rated in thousandth's of an inch per inch of blade length, and comes in different grades, priced accordingly. The beam and blade width is held to a close tolerance so that the part can be measured on either side of the beam or scale. A search on Google will give you information on the different grades available, and you can check the various manufacturers for the costs. I would say that the typical woodworker doesn't need the higher grades, but buy what your budget allows - on the other hand, a good grade of square is worth the money when setting up, for example, the fence on a jointer when you are prepping stock to be glued into panels as that will have a direct affect on the tightness of the glue joint. However, you can get the same result, for a lot less money, by running two boards through the jointer, flipping one and checking the tightness of the joint - keep adjusting the fence until you get zero (or as close as your eyes can judge) gap between the faces.

I have a rafter square that I used for checking the squareness of the cross-cut on my radial arm saw - "adjustments" were made with a center punch and ball pein hammer until the outer edges were exactly (or as close as my eyes could tell) 90° to each other. Remember though that the rafter square is stamped out of a sheet of steel and then trued within maunfacturer's tolerance - the legs are not particularly parallel and so the outer faces being square don't necessarily equate to the inner surfaces being square. A precision square it is not, but it works for what I was using it for. I was also getting inconsistencies with a 12" aluminum speed square and realized that all 3 of the locating surfaces were not square to the edge. I took this down to a small local machine shop and they trued it up on a mill for me, taking a skim cut on the three surfaces - they put the square on a CMM when I picked it up and showed me that all three surfaces ran to the edge within .002" max, and all for the princely sum of $25. The edges of both squares in the last two photos are hooked on the edge of the saw table, checking as compared to the Woodpecker's square.

As an aside, I remember a video from years back showing the machinist checking/adjusting the squareness on a Bridge City Tool Works square - they had a checking fixture with a dial indicator that read on the outer end of the blade; the reading out at the end of the blade had to be some ridiculously low number. Probably why I had to pay so much money for it, and rarely use it because a) it's so pretty and b) I'm afraid I'll knock it out of true.
 

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