Enter a rise and a run in the same units and get the roof pitch as x:12, the angle in degrees, the slope as a percentage and the rafter length multiplier.
Roof pitch in the x:12 convention states how many units the roof rises for every 12 units of horizontal run, which is the rise divided by the run, multiplied by 12. The angle is the arctangent of rise over run, the slope percentage is rise over run multiplied by 100, and the rafter length multiplier is the square root of rise squared plus run squared, divided by the run: multiplying a horizontal distance by it gives the length along the slope. Rise and run can be in any units as long as both use the same one. Steeper pitches shed water and snow faster but need more material per unit of plan area, which is exactly what the multiplier quantifies.
What does a 6:12 roof pitch mean? The roof rises 6 units for every 12 units of horizontal run, which is an angle of about 26.6 degrees and a 50% slope. The x:12 form lets any rise and run be compared on the same 12-unit baseline.
What is the rafter length multiplier used for? Multiplying a horizontal run by the multiplier gives the length along the slope. For a 6:12 pitch the multiplier is about 1.118, so a 10 ft horizontal run needs about 11.18 ft of rafter, before overhangs and cuts.
Is slope percentage the same as pitch? No. Slope percentage is rise divided by run times 100, so a 6:12 pitch is a 50% slope, and a 12:12 pitch is a 100% slope at 45 degrees. Pitch, angle and percentage are three expressions of the same steepness.