Roof pitch calculator

The same slope has three names and each trade insists on its own. Roofers and carpenters in the United States talk in rise per 12 of run and write it 6/12 or "six in twelve", because 12 inches is a convenient span to lay a level across. European roofing works in degrees, which is also what tile manufacturers publish their minimum pitches in and what you dial into a mitre saw or a bevel gauge. Percentage belongs to civil engineering and drainage, where a gutter fall of 1 in 80 reads more naturally as 1.25 per cent than as a ratio over 12. All three describe one number, and this converts between them.

One piece of vocabulary genuinely does mean two different things. In older British carpentry, "pitch" meant the rise over the full span rather than over the half-span run, so a quarter-pitch roof rose a quarter of its width and a half-pitch roof rose half of it. In modern terms those are 6:12 and 12:12, or 26.57 and 45 degrees. Reading a Victorian roofing description with the modern definition halves every slope instead: taken as rise over run, a quarter pitch reads as 3:12 and 14.04 degrees when the roof it describes is 6:12 and 26.57. Nothing about either usage announces which one is in play.

The multiplier is where the calculation earns its keep. A roof plan gives you horizontal distances, and rafters, battens, felt and tiles all follow the slope instead. Multiply the run by the square root of one plus the pitch ratio squared and you have the sloping length: on a 6:12 that factor is 1.118, so 20 feet of run wants 22 feet 4 inches of rafter. The same factor turns plan area into roof area, since only one of the two axes is tilted. Order a 6:12 roof off the plan area and every material on it arrives about 12 per cent short.

Pitch also decides what covering is permitted, and the limit belongs to the product rather than to a general rule. Lapped coverings work by shedding water fast enough that it never travels far enough sideways to reach a joint, so as the slope falls the required headlap rises until the covering stops making sense. Interlocking concrete tiles are commonly rated from 15 to 22.5 degrees depending on profile and lap, plain tiles want around 35 because they are small and rely on lap alone, and slate sits between the two according to slate size. Below roughly 10 degrees no lapped covering applies and the roof needs a continuous membrane. Going under a covering minimum does not leak on day one; it leaks in the first driving rain from the wrong quarter, which is the hardest kind of leak to trace back to its cause.