The roof surface is 1,503 ft² (139.6 m²), which with 10% waste is 16.53 squares: 50 bundles of shingles, 4 rolls of #15 felt and 2 bundles of ridge cap for 42 ft of ridge.
Roof cross-section
How it's calculated S
Footprint with overhangs
(40+2×1)(30+2×1)=1,344ft2
Slope factor
1+0.52=1.11803
Pitch 6 in 12 = 26.57°. A hip roof with the same pitch on all four sides has the same area factor.
Roof area
1,344×1.11803=1,502.638ft2
Squares and bundles
1001,502.638×1.1=16.529squares×3⇒50bundles
Rounded up to whole bundles.
Underlayment
⌈415.026⌉=4rolls
Roll coverage already allows for laps; rounded up to whole rolls.
Ridge
ridge=42ft
Ridge cap: 42 ft ÷ 25 ft per bundle, rounded up to 2.
About the roofing and shingle calculator
Roof area is the footprint including overhangs multiplied by the slope factor √(1 + (rise ÷ 12)²), which turns plan area into sloped surface. A hip roof with the same pitch on all four sides has the same factor as a gable. Area plus waste is divided into squares of 100 ft² and multiplied by bundles per square; the ridge and hip length divided by the coverage of one ridge-cap bundle gives the ridge bundles.
The default 40 × 30 ft gable with 1 ft overhangs at a 6/12 pitch has a slope factor of 1.118 and 1,502.64 ft² of roof. With 10% waste that is 16.53 squares, or 50 bundles at three per square, plus 4 rolls of #15 felt and 2 bundles of ridge cap.
The pitch is checked against the asphalt-shingle slope rules in 2021 IRC R905.2.2. Valleys, dormers, starter strip and drip edge are not counted.
How to calculate roof area and shingle bundles
Multiply the footprint, overhangs included, by the pitch's slope factor, add waste and divide by 100 ft² per square; most shingles take three bundles a square. A 42 × 32 ft footprint at 4/12 has 1,416.7 ft² of roof, 15.58 squares with 10% waste, so 47 bundles.
Slope factors for common roof pitches
The slope factor is √(1 + (rise ÷ 12)²). Multiplying the flat footprint by it gives the sloped surface:
3/12 (14.04°): 1.0308
4/12 (18.43°): 1.0541
5/12 (22.62°): 1.0833
6/12 (26.57°): 1.1180
8/12 (33.69°): 1.2019
9/12 (36.87°): 1.2500
10/12 (39.81°): 1.3017
12/12 (45°): 1.4142
A hip roof with the same pitch on all four sides has the same factor, so on the same footprint it has the same area as a gable.
Shingles for a gable roof, step by step
Add the overhang to both sides of each building dimension: (40 + 2) × (30 + 2) = 42 × 32 ft = 1,344 ft².
Multiply by the slope factor for 6/12: 1,344 × 1.118034 = 1,502.64 ft² of roof.
Add 10% waste and divide by 100: 1,502.64 × 1.10 ÷ 100 = 16.53 squares.
Multiply by bundles per square and round up: 16.53 × 3 = 49.59, so 50 bundles.
Ridge cap, hips and underlayment
On a gable, the ridge runs the full footprint length, 42 ft here. GAF Seal-A-Ridge covers about 25 ft per bundle, so that is 2 bundles; Owens Corning puts ProEdge at about 33 ft.
A hip roof also needs cap on its four hips. On the 42 × 32 ft footprint at 6/12, the ridge is 42 − 32 = 10 ft and each hip is 24 ft, so 106 ft in all: 5 bundles at 25 ft.
Underlayment rolls cover about 4 squares of #15 felt, 2 of #30 felt or 10 of synthetic, with laps already allowed for. Count them on the roof area before waste: the 15.03-square gable takes 4 rolls of #15 felt or 2 of synthetic.
Low-slope limits for asphalt shingles
Under 2021 IRC R905.2.2, asphalt shingles need a slope of at least 2:12, and slopes from 2:12 up to 4:12 need two layers of underlayment. Below 2:12, use a low-slope covering such as a membrane.
The double layer nearly doubles the rolls. At 3/12 the same building has 1,385.36 ft² of roof, 13.85 squares, which takes 7 rolls of #15 felt where one layer would take 4.
Every row is the 40 × 30 ft building with 1 ft overhangs, three bundles per square and #15 felt. "Default" is the 6/12 gable with 10% waste.
Each other row changes one thing: the hip row keeps 10% waste, "Low pitch three" is 3/12 and "Single layer four" is 4/12.
Scenario
Roof area, ft²
Shingle bundles
Underlayment rolls
Ridge-cap bundles
Default
1502.637681
50.000000
4.000000
2.000000
Equal pitch hip
1502.637681
50.000000
4.000000
5.000000
Low pitch three
1385.363490
46.000000
7.000000
2.000000
Single layer four
1416.700392
47.000000
4.000000
2.000000
No waste
1502.637681
46.000000
4.000000
2.000000
The 3/12 roof has less area than the 4/12 roof but needs more underlayment, because it falls in the double-layer range.
Mistakes that inflate or shrink a roof order
Applying the slope factor twice. A length measured up the slope already includes the pitch. Multiplying the 1,502.64 ft² roof by 1.118 again gives 1,680 ft², 11.8% too much.
Adding the overhang once. A 1 ft overhang makes a 40 ft wall a 42 ft roof edge. Using 41 × 31 ft gives 1,271 ft² of footprint instead of 1,344 ft².
Using gable waste on a hip roof. Hips cut every course along their length. At the 15% hip allowance, the hip roof above takes 52 bundles instead of 50.
Assuming three bundles per square. Most 3-tab and architectural shingles take three, but read the wrapper for your product.
Forgetting the accessories. Starter strip, drip edge, valleys, dormers and flashing are separate items on top of the shingle count.
Inputs worth a second look
Building length and width are horizontal measurements; the overhang is per side.
Pitch can be rise per 12 in of run or an angle in degrees: 45° is 12/12.
Ridge cap coverage per bundle is printed on its wrapper.
Related calculators
Check the horizontal footprint of an L-shaped or multi-part house with the room area calculator, then apply the slope factor to each part.
Checked against: 11 × 9 m ÷ cos 30° = 114.3154 m² = 1230.48 ft² × 1.1 ÷ 100 × 3 = 40.6 → 41
Questions
How many bundles of shingles do I need?
Divide the roof area by 100 to get squares, add waste, and multiply by the bundles per square printed on the wrapper (three is the default here). A 40 × 30 ft gable with 1 ft overhangs at 6/12 has 1,502.64 ft² of roof, or 16.53 squares with 10% waste: 49.6 bundles, bought as 50. The waste presets are 10% for gables and 15% for hips, where every course is cut along the hips.
How do you convert roof pitch to degrees and a slope factor?
Pitch is the rise in inches per 12 in of run. A 6/12 roof rises at arctan(6 ÷ 12) = 26.57°, and its slope factor √(1 + 0.5²) = 1.118 means each square foot of plan carries 1.118 ft² of roof. A 4/12 roof is 18.43° with a factor of 1.054; a 12/12 roof is 45° with a factor of 1.414.
What is the minimum roof pitch for asphalt shingles?
2:12, about 9.5°. Under 2021 IRC R905.2.2, asphalt shingles may be used only on slopes of 2 in 12 or steeper, and slopes from 2:12 up to 4:12 need double underlayment. Flatter roofs need a low-slope covering such as a membrane. In the 2:12 to 4:12 range this calculator doubles the underlayment rolls.
What is a roofing square?
100 ft² of roof surface, about 9.29 m². Shingles and underlayment are ordered by the square, so a roof of 1,502.64 ft² is 15.03 squares before waste and 16.53 after 10% waste. With the #15 felt option at 4 squares per roll, that roof takes 4 rolls of underlayment.
How do you calculate the area of a hip roof?
Use the same slope factor as a gable: when all four sides share one pitch, sloped area = plan area × √(1 + (rise ÷ 12)²). A 40 × 30 ft hip roof at 6/12 with no overhang is 1,200 × 1.118 = 1,341.64 ft². Its ridge is 40 − 30 = 10 ft and each of the four hips is 22.5 ft, so ridge cap covers 100 ft.
About this calculator
A=(L+2o)(W+2o)1+(p/12)2,bundles=⌈bundles per square⋅100A(1+waste)⌉
Sources
International Code Council — 2021 IRC R905.2.2: asphalt shingles on slopes of 2:12 or steeper, double underlayment from 2:12 up to 4:12
This calculator includes 4 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.
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