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.
About 26.57 degrees, with a slope multiplier of 1.118.