Reading roof pitch, degrees and the pitch multiplier
Roof pitch is written as rise over a 12 inch run, so a roof that climbs 6 inches for every 12 inches of horizontal travel is a "6:12" or "6 in 12" pitch. If you measure over a different run, scale it back to 12 first: rise ÷ run × 12. The angle in degrees is the arctangent of rise ÷ run, which is why 6:12 works out to about 26.6°, and a 12:12 roof, the one that looks dramatically steep, is exactly 45°. You can measure a pitch on an existing roof from inside the attic by holding a level out 12 inches horizontally from a rafter and measuring straight down to the rafter's underside.
The pitch multiplier is the number that makes roof material estimates come out right. A roof's surface is always larger than the footprint it covers, by a factor of √(rise² + run²) ÷ run: at 6:12 that is about 1.118, so 1,000 ft² of footprint is roughly 1,118 ft² of actual roof. Estimating from a floor plan without applying it is the single most common way people under-order shingles or sheathing. Two cautions on the result: the footprint must include the overhang of the eaves, not just the heated area, and this calculation covers the sloped planes only, so hips, valleys and ridge caps still need their own waste allowance on top. Pitch also drives what material is permitted, since low slopes below roughly 4:12 generally need extra underlayment or a different roofing system entirely.
Geometric estimate only. Minimum slope for a given roofing material, underlayment requirements and snow or wind loads are set by local building code and manufacturer instructions. Always confirm measurements on site, and take care working at height.