Roof Area from Footprint and Pitch

The same square root that stretches a rafter stretches the whole roof. Measure the building's footprint from the plan, multiply by $\sqrt{1 + (p/12)^2}$, and you have the sloping area to be covered. A 1000 ft² footprint under a 9:12 roof is 1250 ft² of shingles, or 12.5 squares in roofing currency, since a "square" is 100 ft².

The multiplier is why steep roofs cost more than they look. It runs from 1.03 at 3:12 to 1.41 at 12:12, so going from a low slope to a 45° roof adds better than a third to the material before any of the labour premium for working on a pitch that steep. Add your hips, valleys and starter courses on top, usually 10 to 15 percent, and remember that this formula gives the plan-to-slope conversion only. Dormers, overhangs and rake extensions have to be measured and added separately.