When I first started doing carpentry in the mid-1970s, I had never seen a hand-held calculator. Like a lot of carpenters, I learned to do some layouts without using math. To do others, I figured out how to use the geometry stored on my framing square. Using the tables on the square often required multiplication and division, which I did with a pencil and paper. Using this method, I was able to lay out things like foundations and roof frames precisely, and I was usually able to do the necessary math in a few minutes because it was fairly simple.

I used geometry, to be sure, but I didn’t actually do geometry. The geometric proportions were etched on the framing square, and all I had to do was expand them using the multiplication I had mastered in grammar school. To do this, of course, I had to convert from fractions to decimals. Doing this, again, required grammar-school math, and after doing it for a while, I found it as easy and natural as driving a truck with a manual transmission.

More importantly, I learned how to visualize how the geometry stored on my framing square fit the structure I was laying out. For as long as I can remember, people have overstated the difficulty of the underlying math (especially of roof framing) and assumed that, once they overcame that obstacle, they’d be able to lay out foundations and roof frames. But the math is not the main obstacle. Almost everyone I know, whether they work in the trades or not, can do the math required for these tasks. What they struggle with is visualizing how that math can be applied to the layout.

In this article—the first of a two-part series—I’ll walk down memory lane in part simply to show how things were done before we had calculators and also to explain the meaning of the mysterious tables on framing squares. The main thing I want to show, however, is how geometry—whether it’s compiled in manuals such as Riechers’ Full Length Roof Framer, etched in the tables on a framing square, or stored in the electronic memory of a calculator—can be applied to a foundation; in Part 2, I’ll show how a framing square applies to the roof framing process; and in Part 3, how the framing square applies to octagon layouts. In my own career, making that connection was key to my development as a builder.