How the numbers are worked out
- Measure rise and run. Hold a level flat with one end touching the roof or rafter, and measure straight down from the 12 inch mark on the level to the roof surface. That number is the rise per 12 inches of run, the x in x/12.
- Convert the pitch. Divide the rise by the run. The roof angle is the arctangent of that ratio, and the slope percent is the ratio times 100. A 6/12 pitch is 26.57 degrees and a 50% slope.
- Find the rafter length. Multiply the run by the square root of 1 plus the ratio squared. Per foot of run that is the square root of 144 plus the pitch squared, in inches: 13.42 inches for a 6/12 roof.
- Mark the cuts. Set a speed square or framing square to the pitch to mark the plumb cut at the ridge and the seat cut at the wall, then check the first rafter in place before cutting the rest.
The run of a common rafter is the level distance from the outside of the wall to the face of the ridge board: half the building span, less half the ridge board thickness. The rafter length is measured along the rafter over that run, plus the overhang. Allow extra board for the plumb cut at the ridge and the tail cut.