Roof pitch calculator
A roof plan gives you the horizontal run, but rafters and sheeting follow the slope. The multiplier converts one to the other: on a 6:12 roof it is 1.118, so 20 feet of horizontal run needs 22 feet 4 inches of rafter. It is also the factor for turning a plan area into a real roof area when ordering felt or tiles — miss it and every roof order is short by the same 12%.
Roof pitch is the rise over a 12-unit run. A 6:12 roof rises 6 inches for every 12 horizontal, an angle of 26.57 degrees and a 50% slope. The rafter multiplier for that pitch is 1.118, so multiply any horizontal run by it to get the sloping length.
How to find roof pitch
Pitch decides what covering is allowed. Below about 10 degrees a roof is low-slope and needs a continuous membrane rather than tiles, because water no longer runs off fast enough for lapped coverings to work. Interlocking concrete tiles generally want 17.5 degrees or more, plain clay tiles closer to 35, and slate somewhere between depending on the lap. Going below a covering minimum does not fail immediately — it fails in the first driving rain from the wrong direction, which is the hardest kind of leak to trace.
Questions
26.57 degrees. A 4:12 is 18.43, a 9:12 is 36.87, and a 12:12 is exactly 45.