The formula: plan area times the pitch factor
A drawing gives a roof's plan, the footprint seen from above. A sloped roof has more surface than its plan, and the pitch factor says how much more. It is the rafter length for each foot of run, from the right triangle of run, rise and rafter.
- Pitch factor = √(rise² + 12²) ÷ 12 = √(rise² + 144) ÷ 12, with rise in inches per 12 in. of run.
- Roof surface = plan area × pitch factor. Measure the plan with the overhangs included.
- Squares = roof surface ÷ 100. A roofing square is 100 square feet of roof surface.
- With waste = squares × (1 + waste percent ÷ 100), and bundles = squares with waste × bundles per square, rounded up.
The same factor works for a gable or a hip roof when every plane has the same pitch, because each plane's surface is its plan area times the factor. For planes at different pitches, run each one separately and add them.
Worked example 1: a 5 in 12 roof
The plan with overhangs is 52 ft by 36 ft and the pitch is 5 in 12. Waste is 10% and the shingle chosen packs 3 bundles to a square (an assumption for this example). These are invented study numbers.
- Plan area = 52 × 36 = 1,872 sq ft.
- Pitch factor = √(25 + 144) ÷ 12 = √169 ÷ 12 = 13 ÷ 12 = 1.0833.
- Roof surface = 1,872 × 13 ÷ 12 = 2,028 sq ft, which is 20.28 squares.
- With 10% waste: 20.28 × 1.10 = 22.31 squares, so 23 whole squares.
- Bundles = 22.308 × 3 = 66.92, so 67 bundles.
Check: 2,028 ÷ 1.0833 = 1,872, back to the plan, and 2,028 × 1.1 = 2,230.8 sq ft, which is 22.31 squares.
Worked example 2: the same plan at 12 in 12
Raise the pitch to 12 in 12 with 15% waste. Pitch factor = √(144 + 144) ÷ 12 = √288 ÷ 12 = 1.4142. Surface = 1,872 × 1.4142 = 2,647.41 sq ft, or 26.47 squares. With 15% waste, 26.47 × 1.15 = 30.45, so 31 squares and, at 3 bundles to a square, 91.34, so 92 bundles. Check: a 12 in 12 roof sits at 45 degrees, and 1 ÷ cos 45° = 1.4142. These are original arithmetic examples, not exam questions.
Roofing squares questions
Is the pitch factor the same as the slope?
No. The slope is rise over run, such as 5 in 12. The pitch factor turns that slope into extra surface: 1.0833 for 5 in 12, so the roof is 8.33% bigger than its plan.
How many bundles are in a square?
It depends on the product, so the calculator asks. Read the wrapper or the maker's data, or use the figure a question gives you.
Where is this on the NASCLA exam?
Roofing sits in Thermal and Moisture Protection, one of the twelve subject areas on the NASCLA outline, with 5 of the 115 scored questions. The Bid Bond course works this takeoff in its roofing lesson.
See the NASCLA exam outline for all twelve subject areas and their question counts.