Roof Pitch Calculator

Enter a rise and run, an angle, or a pitch like 6 in 12 and get the pitch, angle, percent grade, roof area multiplier, and rafter length per foot of run, plus roof area from a footprint and the shingle and fall protection code lines your pitch lands on.

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How roof pitch works

Roof pitch is a ratio: how many inches a roof rises for every 12 inches it runs level. A 6 in 12 roof (also written 6/12 or 6:12) climbs 6 inches over each foot of level distance. Carpenters settled on the 12 because a framing square is marked in inches and a foot of run is easy to lay out. The angle, the percent grade, and the area multiplier on this page are all the same slope wearing a different outfit.

Give the calculator any one of those descriptions and it returns the rest, plus the two things people usually want next: how much roof sits over a footprint, and which code lines your pitch lands on. Rise and run can be in any unit you like, as long as both use the same one, because the units cancel out of the ratio.

The formula

pitch = 12 × rise ÷ run · angle = arctan(pitch ÷ 12) · grade = pitch ÷ 12 × 100 · multiplier = √(1 + (pitch ÷ 12)²)

Rise is the vertical climb and run is the level distance under it. The pitch is inches of rise per 12 inches of run, the angle is measured up from level, and the grade is the same slope as a percentage. The multiplier is the sloped length of roof for each unit of level run, so it turns a footprint into roof area and a run into rafter length. A regular hip or valley uses √(2 + (pitch ÷ 12)²) instead, because it runs corner to corner at 45 degrees in plan.

Worked example

Up in the attic, you touch one end of a 24 inch level to the underside of a rafter, hold it level, and measure straight up from the far end to the rafter: 11 inches. That is a rise of 11 over a run of 24, so the pitch is 12 × 11 ÷ 24 = 5 1/2 in 12.

The angle is arctan(5.5 ÷ 12) = 24.62 degrees, a 45.8% grade, and the multiplier is √(1 + (5.5 ÷ 12)²) = 1.1000: every foot of run needs 13.2 inches of rafter. Over a footprint of 1,800 sq ft, measured to the drip edge, that is about 1,980 sq ft of roof, or 19.8 squares before waste. Ten percent more roof than house, almost to the inch.

On the code side, 5 1/2 in 12 is past 4 in 12, so asphalt shingles need only one layer of underlayment, and OSHA calls it a steep roof: a crew working it needs guardrails with toeboards, safety nets, or harnesses. A roof plenty of people would call easy to walk is, in the regulation's eyes, a steep one.

Why 4 in 12 is the line that matters twice

Two rulebooks, written by different agencies for different reasons, draw a line at the same pitch. The International Residential Code wants two layers of underlayment under asphalt shingles from 2 in 12 up to 4 in 12, and one layer from 4 in 12 on up (R905.2.2 and Table R905.1.1(2)); below 2 in 12 shingles are not allowed at all. OSHA's construction rules call a roof steeper than 4 in 12 a steep roof (29 CFR 1926.500(b)), and a steep roof takes guardrails with toeboards, safety nets, or personal fall arrest systems for anyone working with an edge 6 feet or more above the ground (1926.501(b)(11)).

Here is the detail almost nobody notices: exactly 4 in 12 lands on the lighter side of both lines. The underlayment table gives one layer to "4:12 or greater", and OSHA's steep roof starts only above 4 in 12. A roof measured at 3.9 in 12, though, sits on the two-layer side, even if everyone on the job calls it a four. That is why the calculator tells you when your number falls within 1/8 inch per foot of a line: measure again over a longer level before you order.

One more honest note: OSHA's rules protect people working for an employer. A homeowner on their own roof is outside the regulation, but gravity reads a 6 in 12 roof exactly the same way.

Some pitches come out perfectly round

Most multipliers are endless decimals, but a few pitches are famous right triangles in disguise. A 9 in 12 roof is the 3-4-5 triangle scaled up (9, 12, 15), so every foot of run takes exactly 15 inches of rafter and the multiplier is exactly 1.25. A 5 in 12 roof is the 5-12-13 triangle: exactly 13 inches per foot. The hips hide a couple too. A hip covers 16.97 inches of its own run for each foot of common run, and 16.97 squared is 288, so at 6 in 12 the hip measures √(288 + 36) = √324 = exactly 18 inches per foot of common run, and at 1 in 12 it is √289 = exactly 17. Framers who remember a few of these can sanity-check a rafter number in their head.

Pitch, angle, and grade for common roofs

Pitch	Angle (degrees)	Grade	Area multiplier	Rafter per foot of run	Hip or valley per foot of common run
1 in 12	4.76	8.3%	1.0035	12.04 in	17.00 in
2 in 12	9.46	16.7%	1.0138	12.17 in	17.09 in
3 in 12	14.04	25.0%	1.0308	12.37 in	17.23 in
4 in 12	18.43	33.3%	1.0541	12.65 in	17.44 in
5 in 12	22.62	41.7%	1.0833	13.00 in	17.69 in
6 in 12	26.57	50.0%	1.1180	13.42 in	18.00 in
7 in 12	30.26	58.3%	1.1577	13.89 in	18.36 in
8 in 12	33.69	66.7%	1.2019	14.42 in	18.76 in
9 in 12	36.87	75.0%	1.2500	15.00 in	19.21 in
10 in 12	39.81	83.3%	1.3017	15.62 in	19.70 in
11 in 12	42.51	91.7%	1.3566	16.28 in	20.22 in
12 in 12	45.00	100.0%	1.4142	16.97 in	20.78 in

Every cell is computed by the same code as the calculator above, and our test suite recomputes the whole table on every build. A 12 in 12 roof is the one place the pitch, the 45 degree angle, and the 100% grade all say the same thing in three accents.

Area multipliers and pitch factors: which question each one answers

The multiplier here is pure geometry: the sloped area of a roof plane divided by the level area under it. It works on a gable, a hip, or any mix of planes, as long as they share one pitch, because every plane tilts its own slice of the footprint by the same factor. That leads to a surprise: a hip roof and a gable roof with the same pitch over the same footprint have exactly the same roof area. The hip trades gable-end walls for two more roof planes, but the arithmetic comes out even.

Published pitch factor tables answer a slightly different question, which is what to plan for, and many of them round up. Our own roofing cost calculator is a fair example, and we would rather say it out loud: its four pitch bands use factors of 1.05, 1.15, 1.3, and 1.45, which sit 1.9% to 4.0% above the steepest roof in each band (1.0308 at 3 in 12, 1.1180 at 6 in 12, 1.25 at 9 in 12, 1.4142 at 12 in 12) and as much as 12.3% above the shallowest. That cushion is on purpose, to cover eaves and overhangs a footprint can miss, and for a cost estimate rounding up is the safe direction. For measuring and ordering, use the exact multiplier on a footprint measured to the drip edge, then add your roofer's waste allowance once, not twice.

Measuring pitch without a risky climb

You rarely need to stand on a roof to know its pitch. In the attic, the level-and-tape method in the worked example is accurate to a fraction of an inch per foot, and a longer level makes it better. An angle finder or a phone level app laid along a rafter reads the angle directly; switch the calculator to degrees. House plans usually print the pitch on the elevation drawings as a small triangle marked 12 on one side and the rise on the other. If you need a rafter length next, our rafter length calculator takes the pitch from here, and the slope calculator handles slopes that are not roofs.

Sources

Where the numbers on this page come from. We go to the body that publishes the figure, not to another calculator. See how we verify.

2024 International Residential Code, Chapter 9: Roof Assemblies, International Code Council. R905.2.2: asphalt shingles only on 2 in 12 or steeper, with double underlayment from 2 in 12 up to 4 in 12. Table R905.1.1(2): two layers from 2:12 up to 4:12, one layer at 4:12 or greater, or one layer of ASTM D1970 self-adhering membrane. R905.2.6: past 21 in 12, fastening follows the manufacturer. Every minimum slope in the covering table: tile 2 1/2 (R905.3.2), metal shingles 3 (R905.4.2), roll roofing 1 (R905.5.2), slate 4 (R905.6.2), wood shingles and shakes 3 (R905.7.2, R905.8.2), metal panels 3, 1/2, and 1/4 (R905.10.2), membranes 1/4 (R905.9.1, R905.11.1, R905.12.1).
2021 International Residential Code, R905.2.2 Slope, International Code Council. The same asphalt shingle slope and double-underlayment rule in the 2021 edition, which many jurisdictions still enforce. We checked every minimum slope we quote against the 2021 chapter too, and the numbers match.
2024 International Residential Code, Chapter 8: Roof-Ceiling Construction, International Code Council. R802.4.4: where the roof pitch is less than 3:12, ridges, hips, and valleys shall be designed as beams.
29 CFR 1926.500, Scope, application, and definitions (Subpart M, Fall Protection), Occupational Safety and Health Administration. Paragraph (b): a steep roof is a roof having a slope greater than 4 in 12, and a low-slope roof one having a slope less than or equal to 4 in 12.
29 CFR 1926.501, Duty to have fall protection, Occupational Safety and Health Administration. (b)(10): low-slope roofing work 6 feet or more up may use warning lines with a safety monitor among other systems. (b)(11): on a steep roof, guardrail systems with toeboards, safety net systems, or personal fall arrest systems. (b)(13): residential construction 6 feet or more up.

Frequently asked questions

How do you calculate roof pitch?

Measure how far the roof rises over a known level run, then scale it to 12: pitch = 12 x rise / run. Rest one end of a 24 inch level against a rafter, hold it level, and measure straight up from the far end to the rafter; 11 inches over 24 is 12 x 11 / 24 = 5 1/2 in 12. Rise and run can be in any unit, as long as both use the same one.

What is a 6/12 roof pitch in degrees?

A 6/12 pitch is 26.57 degrees, a 50% grade. Its area multiplier is 1.1180, so each square foot of footprint carries 1.118 square feet of roof, and every foot of run takes 13.42 inches of rafter. For comparison, 4/12 is 18.43 degrees, 8/12 is 33.69 degrees, and 12/12 is exactly 45 degrees.

What is the minimum roof pitch for asphalt shingles?

2 in 12. The International Residential Code allows asphalt shingles only on slopes of 2 in 12 or steeper (R905.2.2), and from 2 in 12 up to 4 in 12 it wants two layers of underlayment, or in the 2024 edition one layer of self-adhering membrane. At 4 in 12 and steeper, one ordinary layer does. Flatter roofs need a low-slope covering such as roll roofing (1 in 12), standing-seam metal, or a membrane (1/4 in 12).

What roof pitch is considered steep?

For fall protection, anything steeper than 4 in 12. OSHA defines a steep roof as a slope greater than 4 in 12 (29 CFR 1926.500(b)), and workers on one with an edge 6 feet or more up need guardrails with toeboards, safety nets, or personal fall arrest systems. Exactly 4 in 12 still counts as low-slope. Roofers also talk about walkable and non-walkable roofs, but that is judgment, not a rule.

How do I convert roof pitch to degrees?

Take the arctangent of the pitch divided by 12: angle = arctan(pitch / 12). A 4 in 12 roof is arctan(0.3333) = 18.43 degrees, and 6 in 12 is 26.57. To go the other way, pitch = 12 x tan(angle), so a 30 degree roof is a 6.93 in 12 pitch.

How do I calculate roof area from the pitch?

Multiply the footprint by the pitch multiplier, the square root of 1 + (pitch / 12) squared. Measure the footprint to the drip edge so the overhangs count. A 1,800 square foot footprint under a 5 1/2 in 12 roof, multiplier 1.1000, has about 1,980 square feet of roof, or 19.8 squares, before your roofer's waste allowance.

Do a hip roof and a gable roof with the same pitch have the same area?

Yes, over the same footprint and at the same pitch. Every roof plane tilts its own slice of the footprint by the same multiplier, so the total is footprint x multiplier whether the planes are two or four. The hip roof has more ridge and hip length to cap, and the gable roof has two gable-end walls to side instead.