# Absolutely, Positively Square - And Cheap!

 Review by jonah posted 08-31-2015 01:04 PM 13852 views 0 times favorited 13 comments

I have two of these yellow plastic speed squares. One was \$3-4 at Home Depot years ago. One I purchased a couple of months ago for \$4.

Summary/TL;DR version: these cheap plastic speed squares are absolutely 90°.

Long version:

After reading a thread in the forums a while ago extolling the virtues of “precision” layout and marking tools, I decided to resurrect my 9-10th grade geometry and trigonometry and figure out exactly how square these things are. I discovered first that the squares are absolutely identical in size. Both are exactly 7.25” x 7.375” – exactly as the HD website claims. I checked that with a measuring tape as well, my 12” Starrett combination square that I got off eBay some years ago, and a ruler. However, if you look at the picture, you can see that one corner is not a 45° angle but is clipped off at 90°. Using two rulers, I determined that if that side continued out at the angle it was at that the side would be about 1/8” longer.

Here are our options for discovering the angles and sides of this triangle:

1) Law of triangles (all angles add up to 180°)
2) Pythagorean Theorem (for right triangles)
3) Law of Cosines/Sines
4) Using trusted 90° angle, compare to the speed square to see if they differ
5) Using trusted flat/straight board, use the “two line” test to see if opposite sides of the square make parallel lines on the board

If the angle on the speed square is indeed a 90 degree angle (which it turns out it is, but lets not take that as a given for the moment), we could use the Pythagorean Theorem to find the measurement of the third side of the triangle. If that number differed from the actual measurement we’d know that the angle wasn’t 90.

I decided to not take a 90 degree angle as a given for the moment and to use a much more complicated Law of Cosines formula. Here's a good website that explains it.

3) Law of Cosines

c^2 = a^2 + b^2 – 2ab cos©

I ended up tracing the triangle onto a piece of paper using a really fine mechanical pencil, extending the line of the clipped off corner, and measuring that. The hypotenuse of the triangle ended up being just above 10 27/64”, so I took that to mean 55/128”. 10 55/128” is 10.4297.

After a bunch of simplification of the above formula we end up with with ~90.01° or ~89.99, depending on which angle you set to be C. We pass. That’s pretty square!

2) Pythagorean Theorem

I have sides of 7.375”, 10.4297”, and what I suspect is another 7.375”.

a^2 + b^2 = c^2

10.4297^2 – 7.375^2 = b^2

b = 7.3748 = 7.375

We pass the Pythagorean Theorem test.

4) Trusted 90° Angle

My most trusted 90° angle is the aforementioned Starrett combination square. Holding the square up to the speed square, I see no gap between them all the way down to the end of the blade. We pass this test.

5) Parallel lines test

Again using the Starrett square as well as my best straight edge, I found a piece of plywood that was absolutely flat and straight and square, with the face 90° to the edge. I drew a line with the speed square. I flipped it over and drew another. Both are parallel to my eye. I tried ones that were very close together as well as 1/4” apart. I could not see any obvious divergence. I tried the same test with my Starrett combo square. Same thing. We pass this test.

Conclusion: any divergence from 90° in this speed square is so slight that I cannot detect it with the measuring tools I own and cannot see it with my 20/15 vision. Five stars, especially considering the price.

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