# Angles We Have Heard on High

Roofing. Man, there is nothing so humbling as the roof over my head, and I don’t mean that in a metaphorical sort of way. Next time you’re in a garage without a finished ceiling, look up and see how the rafters meet the center ridge and wall plates at precise cuts, some 90° angles some 45° angles. It’s amazing to think someone executed that fine geometry using 2 x 6’s and a Skil saw.

Even more humbling, is that they likely did the whole thing while standing on the ground. If it were me, I’d be clinging to the roof with pencil and saw, then with eraser and glue, trying to keep from sliding off, cussing the whole damn time.

But math is pure, and triangles don’t lie, so you can calculate and make all your cuts from the safety of the ground, as long as you know the pitch of your roof. That is, how far does it rise to every foot of run?

The model roof we are building in our classroom has a 4 pitch, which means it rises 4 inches to every 1 foot. So every calculation we need to cut common and hip rafters for 16 inches on center is on the 4-pitch page of The Roof Framer’s Bible. It looks like the agate of a stock quote table from a newspaper. (Remember those? Stock quote tables? Newspapers?)

If the roof rises 4 inches for every foot, then for every 1 foot of run, the diagonal rafter–the hypotenuse of your rise-run triangle–will be 12.65 inches.

Because, Pythagorus. And because it says so, right there on the 4-pitch page of The Roof Framer’s Bible.

We were marking it with a framing pencil for future reference, when the instructor asked us not to make marks in his book. At that point, another classmate admonished, rather earnestly, “You NEVER write in The Bible, dude.”

Anyway, there are other references for finding that 12.65 number, including an old-school framing square and the dazzlingly elegant tool known as the Adjustable Hip Square.

We’ll get to those later…