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By MusicMan
There have been several questions on how to ensure that a square is accurate, and also several members who just assume that it is when it often isn't. How to check it? There are a few ways.

1. Obtain a piece of board with one straight edge; the manufactured edge of standard ply or MDF boards is fairly good. Draw a line square to the edge. Flip the square over (so that the bottom piece is pointing in the opposite direction) and draw the line again starting from the bottom. The difference between the two lines is twice the error from true 90 degrees.

2. If the square is on a tablesaw sled, or is used to set up a sled or a crosscut saw, make five cuts on the largest piece of wood you can The first four are rotated 90 degrees each cut, the fifth cut is parallel to the fourth. If the square is true, this will result in a parallel slice being cut. Measure the width of their slice at each end and any difference is four times the error in squareness over the length of the cut. There are plenty of youtube videos demonstrating this, for example

3. The way that I like is similar to the five-cut method in that it magnifies the error by four, but you make a jig that can be used repeatedly without further cutting. This post will show the method, which I got from a 1906 precision engineering handbook, originally for metalworking, and have applied it to wooden jig.

The first picture shows the final jig in its place on the workshop wall.

Square setting jig - 01.jpg

It consists of a square made out of four straight pieces of wood fixed to a flat backing piece. The bottom side is screwed and glued in place. The others are pivoted at one end and adjustable at the other. If all four corners are exactly 90 degrees, then a true square will fit exactly in each corner, since four right angles add up to 360 degrees. If the square is not true, the 'closure gap' will be four times the error at the end of the square. But because the sides are pivoted, they can be adjusted to make the square perfect within the measurement tolerance and can then be used to check any square without other adjustment. I show an example in the next post.

I started with the following materials: a good piece of 18 mm ply, and hardwood strips about 18 mm thick for the sides. Make the sides as long as the largest square that you want to check. I happen to have a fair bit of 160-year old teak strip flooring (from architectural salvage, used to make a wood floor in my house) so I use it for jigs and tools as I know it is well seasoned! It would be simpler to use flat, straight metal such as a length of 3/4" T track. The inside edges must be as straight, flat and perpendicular to their faces as you can make it. I used the engineering technique of lapping with emery supported on a surface plate, but some of you can probably just plane it right first time.
Square setting jig - 02.jpg

Square setting jig - 3.jpg

Square setting jig - 4.jpg

The bottom side is screwed and glued to the base.
Square setting jig - 7.jpg

The remaining three sides are fixed with wing nuts fitting on M6 threaded rod taken through the baseboard and engaging with T nuts recessed on the under side. As shown, the ends of the threaded rod are spoiled so that they jam in the nuts. Use a square to set out this sides but it does not have to be super accurate as it will be adjusted later. Leave a small gap between the edges so the sides and top can plot slightly about the fixing point.
Square setting jig - 8.jpg

Square setting jig - 9.jpg

Square setting jig - 10.jpg

One of the bolt holes is a close fit to the threaded rod, while the other is larger (9 mm in my case) to allow a small angular adjustment, as shown in this figure:
Square setting jig - 11.jpg

Fit the 'loose' bolts and the jig is complete. The next post will illustrate its use.
By MusicMan
This post shows how the jig is used. The square is a Bridge City 14" square in which the angle is settable by means of Allen grub screws. So it can be set very accurately, but you need to be sure it is correct! A non-adjustable square has to be set by grinding with emery cloth on a flat surface, pressing on the end that needs adjusting.

Starting at the fixed base, set the right hand side to match the square nicely. I find it best to loosen the wing nuts slightly then tap the side with a light hammer to close the gap.
Square setting jig - 15.jpg

Square setting jig - 16.jpg

Square setting jig - 17a.jpg

When arriving at the last corner, we find a 1 mm gap at the end of the square. This is four times the error at the end of the square, which is much less than 0.1 degrees.
Square setting jig - 17.jpg

But it can be got much better. Using feeler gauges one can set the gap to 0.25 mm (a quarter of the error0 and go round again. I found that about three circuits enabled it to be set very well: here's the final angle after resetting the square.
Square setting jig - 18.jpg

I estimate that the final error is about 0.003 degrees. Close enough for Government work! It really depends on the straightness of the sides, which in my case I estimated at about 0.02 mm (just under a thou) over their length, using a precise straight edge and feeler gauges. One could do better in metal.

Now that the jig is set accurately, one can use it to check a square quickly and simply. Here's another one from the Bridge City set:
Square setting jig - 19.jpg

Note the slip of wood placed under the end of the square to ensure that it is parallel to the base when you make the adjustments. The setting is sensitive enough that this matters. My slip is tapered to handle different size squares.

If you make the sides carefully parallel (or use straight metal bars or T-track) you can also check the insides of squares by using the outside of the sides. And also check large T squares.

And finally, be careful to clean the edges of the square before checking them - a speck of dirt makes all the difference.
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By SpoonsbySven
Thank you for an excellent pair of posts. Extremely clearly explained, and top quality pictures. I have a couple of squares I have been meaning to sort out, and I am really glad to have seen your post before getting around to it.