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The short answer is that they look quite alike having a thin blade and a thicker base, the blade and base being fastened at one corner and the blade and base being an accurate 90 degrees from each other. The difference being that the try square is usually used for woodworking and usually has a stable hardwood short base leg (rosewood most popular, sometimes beech or maple), and the engineer's square (also called a machinists square) usually has a metal base.

The longer story is that the try square usually has 3 or four brass rivets holding the base to the blade, and a brass facing on the top of the base for wear. Some try squares have double brass facing meaning that there is also a brass face on the bottom. The machinists square usually being carbon steel (sometimes combinations of carbon steel and a stainless steel blade and/or a aluminum base), being metal does not need a wear plate.

An accurate 90 degree inside angle is claimed for both, the engineer's square also claims that the outside angle is also square. Both blade and base will have very high parallelism. Usually it is claimed that the engineer's square's two angles will have something like .001" to .0002" deviation per linear inch - the try square usually .001 to .0005" per liner inch on the inside square. THe wood expansion and contraction with humidity and temperature will result in perhaps another ~.001" per inch movement - the second brass facing is probably an attempt to limit this.

Nonetheless, I think its considered the engineer's square to be the more accurate of the two but try squares are probably sufficient for woodworking which normally has looser tolerances due to the greater movement of wood.

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Q: How is an engineers try square different from a typical woodworkers try square?
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