Convert a roof pitch (rise per 12 of run) into an angle in degrees, a slope-area multiplier, and a rafter length.
angle = atan(rise ÷ run); multiplier = √(rise² + run²) ÷ run
Pitch is written as rise:12 — a 6:12 roof rises 6 inches for every 12 inches of horizontal run, an angle of about 26.6°.
The slope multiplier converts a flat footprint area into actual sloped roof area — feed it into the roofing calculator.
A 6:12 pitch means the roof rises 6 inches for every 12 inches of horizontal run. The angle is arctan(6/12) = 26.57 degrees. The slope multiplier — the number that converts flat footprint area to actual roof area — is the square root of (6² + 12²) divided by 12, which is 1.118.
So a roof plane covering 1,000 square feet of footprint actually has 1,118 square feet of surface. That multiplier is the single most useful output here: feed it straight into the roofing and shingle calculators.
These are exact trigonometric results — no estimation. A 12:12 roof is exactly 45° with a 1.414 multiplier.
Roof pitch is expressed as rise over run — the inches of vertical rise per 12 inches of horizontal run. A 6/12 roof rises 6 inches for every foot of run. You can measure it with a level and tape on a rafter, or from the ground using a known span and height. Pitch sets both the material area (through the pitch factor) and the walkability and shedding behavior of the roof.
The pitch factor converts footprint area to true sloped area: it is the hypotenuse length per unit of run. A 4/12 pitch has a factor of about 1.054, a 6/12 about 1.118, a 12/12 about 1.414. The same pitch also corresponds to an angle in degrees (a 12/12 is 45°), useful for cuts and for comparing to slope limits on materials.
About 26.57 degrees, with a slope multiplier of 1.118.
Pitch is the rise over run — the inches a roof rises vertically per 12 inches of horizontal run. A 6/12 pitch rises 6 inches per foot.
Use the pitch factor, the sloped length per unit of run. A 4/12 roof's factor is about 1.054 and a 12/12 is about 1.414; multiply the footprint by it to get true roof area.
Roofs up to about 6/12 are generally walkable with care; steeper than roughly 8/12 usually needs roof jacks, harnesses, or staging for safe work.