Lesson 4 of 13
Squaring a Layout
A building that starts out of square stays out of square, and every trade that follows pays for it. This is how you check a corner with nothing but a tape, and how you work out which way to move it.
Step one
Read the material
Three ideas, and the third one is the one that saves the day.
Concept one
3-4-5 and every multiple of it
Measure three feet along one line, four feet along the other, and when the distance between those two marks is exactly five feet, the corner is square. It works because three squared plus four squared is five squared, which is the right triangle again.
Any multiple works and bigger is better, because a small triangle magnifies a small error. On a house use 12-16-20 or 15-20-25. On a deck 6-8-10 is usually enough. The ratio never changes; only the scale does.
Concept two
The diagonal check
3-4-5 squares one corner. The diagonal check squares the whole rectangle at once, and it is faster.
Set your two sides, then compute what the diagonal ought to be: the square root of one side squared plus the other side squared. Measure the actual diagonal. If your tape reads the computed number, the layout is square. On a rectangle you can also just measure both diagonals and compare them to each other, because in a true rectangle they are equal.
Concept three
How far out, and which way to move
Knowing it is out of square is only half the job. Subtract the computed diagonal from the measured one and you have the error.
If the diagonal you measured is longer than it should be, that corner is open, and you pull it in. If it is shorter, the corner is closed, and you push it out. And here is the part worth remembering: moving the corner by roughly half the error usually lands you on square, because the diagonal changes about twice as fast as the corner does. Nudge, re-measure, nudge again.
Step two
Work it with your hands on it
Set the two sides, then set what your tape actually read across the diagonal. The drawing shows you the shape you really have.
Hands on it, off the screen. Lay out a rectangle on the ground with four stakes and a string, any size you like. Measure both sides, compute the diagonal, then measure it. Move one stake until the tape agrees with the arithmetic.
Do it once with your hands and you will never take somebody else's word that a layout is square again.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can square a corner with a tape, check a whole rectangle in one measurement, and say which way the corner has to move. Lesson five is slope and pitch.
Trades Geometry
Lesson four of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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