A few years ago in the paint aisle of a lumberyard I came across three women huddled over a tape measure. Two were explaining to the third how measurements were broken into smaller pieces. It was a math tutorial and fractions were the topic. The women were patient, nonjudgemental, and effective teachers. There was no condescension and the third woman walked away with information she didn’t have five minutes ago. Knowledge is a powerful tool.

Math is a constant companion when building. Anytime you need to square something up, be it a window, door, cabinet frame, or wall section, geometry comes into play. Geometry is the branch of mathematics that deals with the shape and relative arrangement of the parts of something. To square up a wall section prior to raising, we use the Pythagorean theorem. The Pythagorean theorem is a formula that explains the relationship between the three sides of a right triangle. A right triangle is a three-sided object where two of the sides meet at 90 degrees. The two sides that meet at a 90-degree, or right, angle we call ‘a’ and ‘b.’ The long side of a right triangle, called the hypotenuse, is called ‘c.’ Pythagorean’s theorem reads, “a squared plus b squared equals c squared.” If we know the length of any two sides of a right triangle, we can find the length of the third. When our wall section is framed and lying flat on the deck prior to raising, we may choose to sheath it before tilting it up. We need to square it prior to applying sheathing. To do that, we think of our wall section, a large four-sided object, as two right triangles. The line that divides the wall into two triangles runs from the outside corner of the base plate to the opposite outside corner of the top plate. When the wall is square, that diagonal dividing line, which is the hypotenuse, will be the same when measured from any of the four corners to the opposite corner. It reads more complicated than it is in practice. Don’t be intimidated by the language. A four-sided object with right angles is square when the diagonals are the same.

I’m building a large wraparound porch. It’s challenging to get the outside corners square. Rather than attempting to do that with layout lines, I can do it with the diagonals. I know that my joists are 92''. The joists make up two sides of a right triangle. Using the Pythagorean theorem, I can come up with the length of the diagonal, 10' 101⁄8''. Cutting and installing the diagonal squares up the porch. You can figure diagonals by doing the math or by using a foot and inches diagonal calculator. I use a free online version.