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For metric, use mm - For English, use Inches English Example: [ 1inch / (thickness of nut) ] x (number of turns for the bolt to get through the nut ) typical numbers are 18, 24, and 32. Metric: (thickness of nut in mm) / (number of turns for the bolt to get through the nut) typical numbers are 1, 1.25, 1.5, and 2.
A hexagonal nut has the shape of an equilateral hexagon
How to calculate spanner size regarding bolts and nuts
If they were square they would take up more area and the edges may get in the way or take up space, also if you had a square head then it would be easier for the metal to get stripped or deformed which would make it harder for the tool to loosen it. If the head was round, the you couldn't get a tool to grip the edges of it, so you couldn't screw it in good or loosen it. Basically, hexagonal is the most efficient shape for a nut.
One method would be with water displacement. Fill a graduated cylinder with a known amount of water. Drop in the nut. Push below surface with wire, or something with negligible volume. Read volume, and subtract.