Check Whether a Framing Square Is Actually Square With a Compass and Straightedge

The Problem

A framing square, combination square, or speed square that's been dropped or knocked out of true still looks like a normal square sitting on the bench — nothing about it visibly signals that it's lying to you. Two squares can look identical and both read as fine, but only one of them is actually cutting 90 degrees.

The Technique

This uses Thales' theorem — a piece of geometry roughly 2,600 years old: any angle drawn from the two ends of a semicircle's diameter to a third point on the arc is always exactly 90 degrees, no matter where on the arc that third point falls.

1. Draw a straight line on a flat surface (this becomes the semicircle's diameter).
2. Set a compass to any radius and swing a semicircle using the line as the diameter, marking point A and point B where the arc meets the line.
3. Pick any third point on the arc.
4. Draw a line from point A to that third point, and another from the third point to point B — the angle where those two lines meet is guaranteed to be exactly 90 degrees.
5. To test your square: line up its short arm on point B with the corner of the square resting on the arc, then sight down the long arm. If the square is true, the long arm lands exactly on point A. If it lands off to one side, that gap shows you how far out of square the tool actually is.