# The Formula for Building a Square Wall

This first of three articles will look at a couple of tricks to square up your framing. Subsequent articles will examine how to make your walls plumb.

How many times have you heard complaints that a wall isn't square, or it isn't plumb--or the joists are unevenly spaced and not parallel? Especially if you are working with an old house whose supports have sagged, you certainly don't want to compound the problem with further tilts.

If your initial framing is not square and plumb, you will waste hours trying to accommodate the errors as your project progresses. It's best to get it right from the start--and it's not that difficult.

**Formula for Square**

Critical to creating square construction is the 90-degree angle. Too many inexperienced carpenters skip the simple mathematics, relying instead on a carpenter's square and the belief that studs are straight. They may even think their eyeball power is enough. Such misguided beliefs lead to walls that look like Shrek construction.

Carpenters can thank the ancient Greek philosopher/mathematician, Pythagoras, for a simple formula that makes "squareness" easy. If you weren't sleeping through geometry class, you should know that the Pythagorean theorem states simply that in a right triangle--a triangle that includes one 90-degree angle--the sum of the squares of the legs equals the square of the hypotenuse. The legs are the sides that come off the 90-degree angle; the hypotenuse is the side opposite from the 90-degree angle. Simply put, a^{2} + b^{2} = c^{2}.

**Square Roots!**

You may cringe, thinking that you put square roots in the mental trash basket decades ago, so here is the simplified version. Think 3, 4, and 5. If the legs are 3 and 4 feet, and the hypotenuse is 5 feet, you have a perfect 90-degree angle. The theorem works thusly: 3^{2} + 4^{2} = c^{2}, or 9 + 16 = 25, and we all know that the square root of 25 is 5. The ratio holds true for multiples of 3, 4 and 5, such as 6, 8 and 10. The longer your measurements, the closer you will be to an exact 90-degree angle.

Putting Pythagoras' theorem to practical use, you can measure 8 feet down the base of a wall, and then mark 6 feet up the other side. Pulling your tape measure from the 8-foot mark to the 6-foot mark, pivot the 6-foot mark until the line matches up with the 10-foot mark on the tape measure. At that point, you have a 6, 8, 10 triangle and a square (90-degree) angle. (Support the tape measure in mid span to keep it from sagging or you'll throw off your measurements.)

If you are putting the wall together on a floor to be raised into position when finished, you can temporarily tack the boards to the floor to hold them at 90-degree angles.

**Measure Diagonals**

When you have framed your rectangle (the wall), the final test for squareness is to measure the diagonals. (If you label the corners of the rectangle A, B, C, and D, in a clockwise direction, the diagonals will be the lines that would connect AC and BD). If the diagonals are equal, then the corners are all square. You may need to tap a corner with the hammer to move it an an eighth of an inch or so to make it perfect. When you have it all squared, tack some scrap 1x4s or 2x4s at angles across the studs to hold the wall in position till it is raised into place.

You see, it's really simple to build square. Makes you wonder why more carpenters can't do it. In part two of this three-part series, you'll learn how to use a level to make your walls plumb.

**About the Author**

Jim Mallery, a semi-retired journalist and onetime registered contractor, has extensive experience remodeling, repairing, and rebuilding homes.