If you do not have a good 90 degree square, do not despair. Even with the help of an out of order square, you can easily build a wooden square to precisely measure a 90 degree angle.

All you need are two boards straightened on all sides. One of the boards, which will form the “useful” side of the square, is preferable to be thin ( yet it has to be thick enough not to bend).

Using the method described in the article about checking the accuracy of a square, I draw the two lines. If they do not overlap on their entire length, you will need to determine the perpendicular line between them and after that you can build your own square.

By measuring the distance between the two lines and dividing it into two, you will find the point where the correct line of the new wood square must end. In my case, it was two millimeters, so the point would be midway, 1 millimeter across from both lines.

I measure the difference between the two stripes
The measurement of the distances between the two lines

I placed the thin beech wood piece along the newly drawn line and I fixed it with glue and three screws on the base, also a piece of wood. Note that it is better to fix the first screw, the center one, after which small adjustments can be made until screwing the other two additional screws.

 I made small adjustments after the two pieces of woods were fastened together using only one screw
I fastened the two pieces with one screw and then I made the small required adjustments
I checked that the angle is 90 degrees and then I screwed the three screws, waiting the glue to dry
After I was sure the angle was exactly 90 degrees, I tightened all the three screws and then I waited for the adhesive to harden

Once the glue has hardened, I was able to check whether I made a wood square that is truly perpendicular or not. In my case, the two stripes overlapped very well, but not perfect.

the two stripes used to check the perpendicularity of the new wood square
I checked that the angle of the square is 90 degrees. The two stripes on the left are made with a bought square, the two on the right are made with the square built in 3 minutes

It is important to note that the better (thinner) the pencil is, the higher the accuracy of the square is.

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