How to use this calculator
- Measure the building's footprint including the eaves overhang, or take it from the plans.
- Enter the pitch in degrees or as rise per 12.
- Choose gable or hip; the extra fills in (hip roofs have more cutting).
- For shingles, keep 3 bundles per square unless the wrapper says otherwise.
The formula
Pitch factor = 1 ÷ cos(pitch angle) = √(1 + (rise ÷ run)²)
Roof area = footprint × pitch factor
Squares = roof area × (1 + extra %) ÷ 100 ft²
Bundles = squares × bundles per square, rounded up
A sloping roof is bigger than its footprint. The pitch factor says how much bigger: a 6/12 roof (26.6°) is 1.118 times its footprint, a 45° roof 1.414 times.
For a simple gable or hip roof with one pitch everywhere, the footprint method is exact. Dormers, valleys and different pitches need each part measured separately.
Worked example
A 40 ft × 30 ft footprint at 6/12 has a pitch factor of 1.118, so the roof is 1,341.6 ft².
With 10% extra that's 14.76 squares — 45 bundles of shingles.
Tips before you buy
- Add starter strips, ridge caps, underlayment and flashing — they are separate items.
- Very low pitches may need a different roof covering; check the product's minimum pitch.
- Ask two roofers for quotes and compare their measured areas with this one.
Frequently asked questions
›What is a roofing square?
100 square feet of roof. Shingles are priced and packed by the square, usually 3 bundles per square.
›How do I convert pitch to degrees?
Angle = arctan(rise ÷ run). 4/12 ≈ 18.4°, 6/12 ≈ 26.6°, 8/12 ≈ 33.7°, 12/12 = 45°.
›How much waste for shingles?
About 10 % for simple gable roofs and 15 % for hip roofs or roofs with valleys and dormers.
Sources
Formulas last reviewed: September 29, 2026. How we check our formulas