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Calculate roof area from footprint and pitch, number of roofing squares needed, and total with waste factor.
Roofing Formulas:
Pitch Factor = sqrt(rise^2 + run^2) / run
Roof Area = Footprint x Pitch Factor
Squares = Roof Area / 100
One roofing square = 100 square feet of roof surface
A roofing square is a unit of area equal to 100 square feet (9.29 m²). Roofing materials such as shingles and underlayment are sold by the square.
Roof pitch (slope) is the ratio of vertical rise to horizontal run, typically expressed as rise over 12 (e.g. 6/12 means the roof rises 6 inches for every 12 inches of horizontal run).
A standard waste factor is 10-15% for simple roofs. Add 15-20% for complex roofs with many hips, valleys, and dormers. Extra material covers cuts and mistakes.
Standard three-tab asphalt shingles come in bundles. Three bundles typically cover one square (100 sq ft). Architectural shingles may require 4 bundles per square.
The footprint area is the horizontal projected area of the roof, which equals the floor area of the top story of the building. The actual roof surface area is larger because of the slope.
Common residential pitches range from 4/12 to 9/12. Low-slope roofs are 2/12 to 4/12. Steep roofs above 9/12 require special installation techniques and safety precautions.