Why the footprint is not the roof area
A sloped roof covers more surface than the ground it shades. The pitch multiplier converts flat (plan) area into true sloped area: it is the length of the rafter for every foot of horizontal run, √(1 + (rise ÷ 12)²). A 6/12 roof has a multiplier of 1.118, so its surface is about 11.8% larger than its footprint; a 12/12 roof is 41.4% larger.
The useful part is that the multiplier works for the whole roof at once, gable or hip, as long as every plane has the same pitch. Measure the outside of the house, add the overhang on every side, multiply by the pitch multiplier, and you have the roof area without climbing up.
How to find your roof pitch
Pitch is written as rise over a 12-inch run. From the attic, or on a rake board, hold a level horizontally, mark 12 inches along it, and measure straight up from that mark to the underside of the roof deck. If it is 6 inches, the pitch is 6/12. Phone level apps that read the angle work too: 26.6° is 6/12, 33.7° is 8/12 and 45° is 12/12.
If you only know the angle, rise = 12 × tan(angle). The table under the result shows the angle and multiplier for each common pitch.
Squares, bundles and waste
Roofing is sold by the square: the amount of shingles needed to cover 100 square feet of roof. Most three-tab and some lightweight laminated shingles come three bundles to a square, but heavier shingles can take four or five bundles per square, so read the wrapper and change the bundles-per-square field if needed.
Waste depends on the roof. A Fine Homebuilding estimating guide figures about 1% for a simple roof and 5% or more for a complex roof with open valleys. This calculator defaults to 10% because it does not count starter strips or ridge caps separately; if you will cut those from regular shingles, keep the extra, and lower it if you buy purpose-made starter and ridge products.
The formulas
Plan area = (L + 2 × o ÷ 12) × (W + 2 × o ÷ 12)Pitch multiplier = √(1 + (rise ÷ 12)²)Roof area = plan area × pitch multiplierSquares = roof area ÷ 100Bundles = round up (squares × (1 + waste ÷ 100) × bundles per square)- L, W = footprint length and width in feet
- o = overhang in inches on each side
- rise = inches of rise per 12 inches of run (the "6" in 6/12)
Example: a 40 × 30 ft house with a 6/12 roof
- Add a 12-inch overhang on every side: (40 + 2) × (30 + 2) = 42 × 32 = 1,344 sq ft of plan area.
- Pitch multiplier for 6/12: √(1 + 0.5²) = √1.25 = 1.118.
- Roof area: 1,344 × 1.118 = 1,503 sq ft, or 15.03 squares.
- Add 10% waste: 15.03 × 1.10 = 16.53 squares.
- At 3 bundles per square: 16.53 × 3 = 49.6, so order 50 bundles.
Frequently asked questions
How many bundles of shingles are in a square?
Three bundles per square (100 sq ft) is most common, which covers most three-tab and some lightweight laminated shingles. Heavier architectural shingles can take four or five bundles per square.
How many squares is a 2,000 sq ft roof?
2,000 ÷ 100 = 20 squares. With 10% for waste that is 22 squares, or 66 bundles at 3 bundles per square.
What is a 4/12 roof pitch in degrees?
The roof rises 4 inches for every 12 inches of run, an angle of about 18.4°. Its pitch multiplier is √(1 + (4 ÷ 12)²) = 1.054, so the roof surface is about 5.4% larger than the footprint.
Do I use the house's square footage?
No. Living-area square footage counts every floor and skips the garage and overhangs. Use the outside footprint of everything the roof covers, plus the overhang.
Does a hip roof need more shingles than a gable roof?
For the same footprint and pitch, the roof surface is about the same, but a hip roof has more hips and cut edges, which means more waste and more ridge cap. Raise the waste percentage for hip roofs and roofs with valleys.
Sources
Last reviewed for 2026. How we calculate.