Slope factor computed, not tabulated. IRC R905 requirements by pitch
Every roofing calculator takes your pitch and uses it for exactly one thing: multiplying the footprint to get the area. IRC Section R905 hangs three more decisions on that same number. Below 2:12 asphalt shingles are not permitted at all, between 2:12 and 4:12 the underlayment is doubled, and the ice barrier is measured to a point 24 inches inside your wall, which on most houses is wider than the roll.
Roof quantities and the code requirements at this pitch
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ft
in
in
%
no.
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Plain roof planes only. Hips, valleys, dormers and ridge cap are extra, and valley cut waste is much higher than the flat allowance.
Specification summary
Generated from on .
Reopen that address to reproduce these figures exactly.
Entered
Result
A gable section, and where R905.1.2 puts the barrier
Prices for roof coverings and tear-off
The published figures for roof coverings and tear-off are on the roof replacement cost calculator, with the byline, the publication date and the caveats that go with them. They are not repeated here, because the same table on two pages is worth less than one table you can find.
Material alone is $0.15 to $2.75 per sq ft in the source; the rest of each installed price is prep and labor.
Worked example
A 40 ft by 28 ft house at 6:12 with a 24 in overhang, 10% waste, 3-bundle squares, 36 in strip shingles at 5 in exposure, in an area where an ice barrier is required and the roll is 36 in.
Slope factor. √(144 + 36) / 12 = 1.1180, so 11.8% more roof than ground.
Plan area. The overhang adds 2 ft each side: 44 × 32 = 1,408 sq ft covered.
Roof area. 1,408 × 1.1180 = 1,575 sq ft, which is 15.75 squares, or 17.32 with waste.
Bundles. 17.32 × 3 = 52 bundles.
Fasteners. Each shingle covers 36 × 5 / 144 = 1.25 sq ft, so 1,387 shingles, and R905.2.6's four per strip is 5,548 nails.
Ice barrier. 24 in overhang plus 24 in inside the wall is 48 in horizontal, times 1.1180 = 53.7 in up the slope. A 36 in roll gives one course, so you need two.
The ice barrier is the line worth re-reading. R905.1.2 measures to a point 24 inches inside the exterior wall line, not 24 inches up from the eave, so the overhang is added before the slope factor is applied. A 36 in roll covers only 32 inches of horizontal run at this pitch. Almost every house with a normal overhang needs two courses, and the second one is the one nobody orders.
The formula
One piece of trigonometry, then four code checks against the same number:
A = (L + 2o)(W + 2o) × √(144 + r²) / 12 squares = A / 100
L, W
building footprint, ft, measured to the wall line
o
eave overhang, converted to ft. It is roof area too
r
pitch as rise per 12 in of run
√(144 + r²)/12
the slope factor. The hypotenuse over the base, exactly
100
square feet in a roofing square. A definition
The overhang is inside the area term, not outside it, because eaves are roof. On the worked example the 24 in overhang adds 232 sq ft of plan area, which is 16% of the roof, and leaving it out is the commonest way a roof order comes up short.
The pitch is the input, and it decides four things
Ask a roofing calculator for a quantity and it wants a footprint and a pitch. It uses the pitch once, as a multiplier, and hands you a number of squares.
That multiplier is right and it is exact: a roof plane is the hypotenuse of a triangle whose base is the footprint, so the area is the footprint times the square root of 144 plus the rise squared, over 12. No table is needed and none is used here.
But IRC Section R905 reads the same pitch and makes three more decisions with it. It refuses asphalt shingles below 2:12 outright. It doubles the underlayment between 2:12 and 4:12. And above 21:12 it stops prescribing attachment and hands you back to the manufacturer. None of those change the area, and all of them change the order.
Then there is the ice barrier, which does not depend on pitch alone but on pitch and overhang together, and which is the one requirement on this page that people measure wrong with a tape in their hand.
Slope factor by pitch, and what R905 attaches to each
Pitch
Slope factor
Angle
Area over footprint
What R905 says at this pitch
1:12
1.0035
4.8°
0.3%
below the 2:12 minimum for asphalt shingles
2:12
1.0138
9.5°
1.4%
double underlayment required
3:12
1.0308
14.0°
3.1%
double underlayment required
4:12
1.0541
18.4°
5.4%
5:12
1.0833
22.6°
8.3%
6:12
1.1180
26.6°
11.8%
7:12
1.1577
30.3°
15.8%
8:12
1.2019
33.7°
20.2%
9:12
1.2500
36.9°
25.0%
10:12
1.3017
39.8°
30.2%
12:12
1.4142
45.0°
41.4%
15:12
1.6008
51.3°
60.1%
18:12
1.8028
56.3°
80.3%
21:12
2.0156
60.3°
101.6%
24:12
2.2361
63.4°
123.6%
manufacturer's instructions govern
Read 2026-09-08. The factor is sqrt(144 + rise squared) divided by 12, computed rather than tabulated.
The slope factor, which is the only exact thing on a roof
A roof plane is the hypotenuse of a right triangle whose base is the footprint it covers. So its area is the footprint times:
slope factor = √(144 + rise²) / 12
That is trigonometry, not a table, and it is exact. A 6:12 roof is √(144+36)/12 = 1.1180, so 11.8% more area than the ground it covers. A 12:12 is 1.4142, over 41% more.
Which is the whole of what most roofing calculators do with the pitch you give them. The code does considerably more with it, and the last column of the table below is the part they leave out.
What the code hangs on the same number
Pitch is not just an area multiplier. Four requirements in IRC Chapter 9 change with it, and three of them change what you buy:
R905.2.2
Asphalt shingles shall be used only on roof slopes of two units vertical in 12 units horizontal (17-percent slope) or greater. For roof slopes from two units vertical in 12 units horizontal (17-percent slope) up to four units vertical in 12 units horizontal (33-percent slope), double underlayment application is required in accordance with Section R905.1.1.
R905.2.5
Fasteners for asphalt shingles shall be galvanized steel, stainless steel, aluminum or copper roofing nails, minimum 12-gage [0.105 inch] shank with a minimum 3/8-inch-diameter head, complying with ASTM F1667, of a length to penetrate through the roofing materials and not less than 3/4 inch into the roof sheathing. Where the roof sheathing is less than 3/4 inch thick, the fasteners shall penetrate through the sheathing.
R905.2.6
Asphalt shingles shall have the minimum number of fasteners required by the manufacturer's approved installation instructions, but not less than four fasteners per strip shingle or two fasteners per individual shingle. Where the roof slope exceeds 21 units vertical in 12 units horizontal (21:12, 175-percent slope), shingles shall be installed in accordance with the manufacturer's approved installation instructions.
R905.1.2
In areas where there has been a history of ice forming along the eaves causing a backup of water as designated in Table R301.2(1), an ice barrier shall be installed for asphalt shingles, metal roof shingles, mineral-surfaced roll roofing, slate and slate-type shingles, wood shingles and wood shakes. The ice barrier shall consist of not fewer than two layers of underlayment cemented together, or a self-adhering polymer-modified bitumen sheet shall be used in place of normal underlayment and extend from the lowest edges of all roof surfaces to a point not less than 24 inches inside the exterior wall line of the building.
R905.10.2
Minimum slopes for metal roof panels shall comply with the following: 1. The minimum slope for lapped, nonsoldered-seam metal roofs without applied lap sealant shall be three units vertical in 12 units horizontal (25-percent slope). 2. The minimum slope for lapped, nonsoldered-seam metal roofs with applied lap sealant shall be one-half unit vertical in 12 units horizontal (4-percent slope). Lap sealants shall be applied in accordance with the approved manufacturer's installation instructions. 3. The minimum slope for standing-seam roof systems shall be one-quarter unit vertical in 12 units horizontal (2-percent slope).
R905.3.2
Clay and concrete roof tile shall be installed on roof slopes of two and one-half units vertical in 12 units horizontal (25-percent slope) or greater. For roof slopes from two and one-half units vertical in 12 units horizontal to four units vertical in 12 units horizontal, double underlayment application is required.
R905.9.1
Built-up roofs shall have a design slope of not less than one-fourth unit vertical in 12 units horizontal (2-percent slope) for drainage, except for coal-tar built-up roofs, which shall have a design slope of a minimum one-eighth unit vertical in 12 units horizontal (1-percent slope).
R905.2.8.2
Valley linings shall be installed in accordance with the manufacturer's instructions before applying shingles. For open valleys (valley lining exposed) lined with metal, the valley lining shall be not less than 24 inches (610 mm) wide.
R905.2.8.3
Base flashing against a vertical sidewall shall be continuous or step flashing and shall be not less than 4 inches (102 mm) in height and 4 inches (102 mm) in width and shall direct water away from the vertical sidewall onto the roof or into the gutter. Where siding is provided on the vertical sidewall, the vertical leg of the flashing shall be continuous under the siding.
R905.2.8.5
A drip edge shall be provided at eaves and rake edges of shingle roofs. Adjacent segments of drip edge shall be overlapped not less than 2 inches (51 mm). Drip edges shall extend not less than 1/4 inch (6.4 mm) below the roof sheathing and extend up back onto the roof deck not less than 2 inches (51 mm). Drip edges shall be mechanically fastened to the roof deck at not more than 12 inches (305 mm) o.c.
R905.2.8.1
Base flashing shall be of either corrosion-resistant metal of minimum nominal 0.019-inch (0.5 mm) thickness or mineral-surfaced roll roofing weighing not less than 77 pounds per 100 square feet. Cap flashing shall be corrosion-resistant metal of minimum nominal 0.019-inch thickness.
R905.3.6
Nails shall be corrosion resistant and not less than 11-gage, 5/16-inch head, and of sufficient length to penetrate the deck not less than 3/4 inch or through the thickness of the deck, whichever is less. Attaching wire for clay or concrete tile shall not be smaller than 0.083 inch.
R905.2.2 is the one that costs money. Between 2:12 and 4:12 the underlayment is doubled. That is not a recommendation and it is not in the shingle manufacturer's literature, it is the code, and a calculator that hands you one roll for a 3:12 porch roof has given you half the material.
Below 2:12 asphalt shingles are not permitted at all, whatever the manufacturer says. That is a different roof covering, not a thinner one.
The overhang is roof, and it is bigger than it looks
The footprint you measure is to the wall line. The roof is bigger, by the overhang, on every side it has one.
A 24 in overhang on a 40 by 28 ft house turns a 1,120 sq ft footprint into 44 by 32 ft, which is 1,408 sq ft of plan area. That is 232 sq ft more, 21% on top, before the slope factor touches it. Multiply by 1.1180 and the overhang alone is 259 sq ft of roof, more than two and a half squares.
Rake overhangs at the gable ends work the same way and are counted here, because the input adds the overhang on all four sides. If your roof only overhangs at the eaves, reduce the width input accordingly.
Waste, valleys, and why the flat allowance is not enough
The 10% default here is ours, and it covers ordinary cutting on plain planes: starter courses, ridge, and the ends of runs.
It does not cover valleys. A valley is cut on both sides at an angle, and the offcut is usually unusable, so a roof with several valleys can run well past 15%. Nor does it cover hips, which need cap shingles cut from field bundles at roughly one bundle per 35 linear feet depending on exposure.
A simple gable roof is the case the 10% is written for. A cut-up roof with dormers and returns is a different estimate and the honest thing to do is add the valley and hip lengths and allow for them separately.
Ridge cap is not in the bundle count above either. It is usually a separate product and it is sold by the linear foot.
Fasteners, and the number that is a floor rather than an answer
R905.2.6 sets a minimum of four fasteners per strip shingle, or two per individual shingle, and then says the manufacturer's approved instructions govern the actual number.
In practice many manufacturers specify six per strip in high-wind areas, and a warranty is void without them. Six against four is a 50% increase in nails, which on the worked example is 8,322 rather than 5,548.
R905.2.5 is equally specific about the nail itself: 12-gauge shank, 3/8 in head, ASTM F1667, long enough to penetrate 3/4 in into the sheathing or all the way through if the sheathing is thinner. That last clause is the one that catches people re-roofing over 3/8 in plywood.
The ice barrier is measured from inside the house, and that is the trap
Read R905.1.2 again, slowly. The barrier runs from the lowest edge of the roof to a point not less than 24 inches inside the exterior wall line.
Not 24 inches up the roof. Not one roll. Twenty-four inches past the wall, measured horizontally, which means the width you need is:
width = (overhang + 24 in) × slope factor
On a house with a 24 in overhang at 6:12, that is (48 in) × 1.1180 = 53.7 in of barrier measured up the slope. A 36 in roll does not reach. You need two courses with a lap, and the second course is the one everybody forgets to order.
The overhang is what drives it. A 12 in overhang at the same pitch needs 40.2 in, still over a single 36 in roll. A house with no overhang at all needs 26.8 in, and one roll does it.
Whether you need one at all is not a national question. R905.1.2 applies in areas with a history of ice damming as designated in Table R301.2(1), which is a jurisdiction-by-jurisdiction table. It is a question for your building department, and this calculator asks you rather than guessing.
Where the code text came from
Read 2026-09-08. 2018 Seattle Residential Code, Chapter 9 Roof Assemblies, Seattle Department of Construction and Inspections. Prints IRC Chapter 9 in full, including R905.1.2 ice barriers and R905.2 asphalt shingles. Used because codes.iccsafe.org returns HTTP 403 and cannot be read.
It is one city's adopted code printing the model text, which is the best that can be done from here, and your jurisdiction may have amended any of it. The ice barrier requirement in particular is triggered by a table of local values, so the answer to whether you need one is local by construction.
Frequently asked questions
How do I calculate roof area from the footprint?
Multiply the plan area, overhangs included, by the slope factor, which is the square root of 144 plus the rise squared, all over 12. A 6:12 roof has a factor of 1.1180, so 11.8% more area than the ground it covers. A 12:12 is 1.4142, over 41% more.
How many bundles of shingles do I need for a 40x28 house?
At 6:12 with a 24 in overhang, about 1,575 sq ft of roof, which is 15.74 squares. With a 10% waste allowance that is 17.32 squares, so 52 bundles at three bundles to the square. Check the wrapper: not every product is three to the square.
What is the minimum roof pitch for asphalt shingles?
Two units vertical in 12 horizontal, per IRC R905.2.2. Below that asphalt shingles are not permitted at all and you need a different roof covering. Between 2:12 and 4:12 they are permitted but the underlayment must be doubled.
How far does ice and water shield have to go up the roof?
R905.1.2 requires it from the lowest edge of the roof to a point not less than 24 inches inside the exterior wall line. That is measured horizontally and inside the wall, so you add the overhang before applying the slope factor. A 24 in overhang at 6:12 needs 53.7 in up the slope, which a 36 in roll does not cover.
Do I need two rows of ice and water shield?
On most houses with a normal overhang, yes. A 36 in roll covers only about 32 inches of horizontal run at 6:12, and the requirement is the overhang plus 24 inches. Only a house with little or no overhang gets away with a single course.
How many nails per shingle does code require?
Not fewer than four per strip shingle or two per individual shingle, per R905.2.6, and the manufacturer's approved instructions govern above that. Six per strip is common in high-wind areas and is often a warranty condition. Above 21:12 the code stops prescribing and defers entirely to the manufacturer.
Does the roof overhang count in the area?
Yes, and it is substantial. A 24 in overhang on a 40 by 28 ft house adds 232 sq ft of plan area, 21% on top of the footprint, before the slope factor is applied. Leaving it out is the commonest reason a shingle order comes up short.
Is roof square footage the same as the house's square footage?
No. The footprint square footage is measured to the wall line, and the roof adds the overhang on every side and then the slope. On the 40 by 28 ft worked example, a 1,120 square foot footprint becomes about 1,575 square feet of roof at 6:12 with a 24 in overhang. Divide by 100 to get squares.
Do the shingle roof prices include labor?
Yes. This Old House states its table is built on builder-grade materials and medium labor costs for low-sloped roofs, quoted as totals for a 2,000 square foot roof, from $8,419 to $11,665 for asphalt shingles. Tear-off of the old roof is a separate row at $1 to $5 per square foot of old material. A steep or cut-up roof is outside what the table describes.
How do I calculate shingles for a hip roof?
Choose Hip as the roof shape. When all four slopes share one pitch, a hip roof has exactly the same area as a gable over the same plan, because roof area is the plan area times the slope factor whichever way the planes face. What changes is the edge: a 40 by 28 ft house with 24 in overhangs at 6:12 has a 12 ft ridge and four hips of 24 ft each, so 108 ft of ridge and hip cap against 44 ft of ridge cap on the gable.
What roof dimensions do I need to measure?
Four: the building length and width measured to the wall line, the eave overhang, and the pitch as rise per 12 in of run. Roof area, squares, bundles and the ice barrier width are all computed from those dimensions, so nobody has to measure up the slope. Rainfall runoff from the same roof is worked out on the gutter calculator.
How much do architectural shingles cost per square?
This Old House's March 2026 article gives $11,914 to $16,436 for a 2,000 sq ft roof in architectural shingles installed. A square is 100 sq ft, so that is $596 to $822 per square installed, against $421 to $583 per square for standard asphalt shingles.
How much does cedar shingle siding cost to install?
HomeAdvisor's June 2026 guide gives $3 to $30 per square foot for cedar siding and $3 to $10 for wood siding installed generally, with removal of the old siding at $1,000 to $3,000.
Check these numbers yourself
2018 Seattle Residential Code, Chapter 9 Roof AssembliesSeattle Department of Construction and Inspections. Prints IRC Chapter 9 in full, including R905.1.2 ice barriers and R905.2 asphalt shingles. Used because codes.iccsafe.org returns HTTP 403 and cannot be read.
How every figure here is verified: Sources & Method. Who builds this: Lucas Pradella, and the method is on About. Found something wrong? Tell us and it gets fixed or removed.
Figures on this page last checked against the source documents on 2026-09-08. Codes are amended locally; confirm against the edition your jurisdiction enforces.
Plain roof planes, and one city's adopted code. IRC Chapter 9 was read from the 2018 Seattle Residential Code on 8 September 2026 because codes.iccsafe.org returns HTTP 403. Hips, valleys, dormers and ridge cap are not counted. Whether an ice barrier is required at all is set by Table R301.2(1), which is jurisdiction by jurisdiction, so this page asks you rather than assuming.