Roof Pitch Calculator
Convert roof pitch between rise-over-run, x-in-12 ratio, degrees, and percent grade. Find the slope factor for rafters and roof area, with common pitch references.
Rise and run can be in any matching units. Pitch is the ratio between them, so the result is the same in inches or centimeters.
Roof pitch describes how steep a roof is. It compares the vertical rise of the roof to the horizontal distance it covers, which builders call the run. In the United States the run is always set to 12, so a pitch written as 4:12 tells you the roof goes up 4 inches for every 12 inches it travels sideways. The first number changes with the steepness; the second number stays at 12 by convention.
That single ratio carries a lot of practical weight. It decides which roofing materials are allowed, how much surface area you are actually covering, how long the rafters need to be, and how safe the roof is to walk on. A gentle 2:12 roof and a dramatic 12:12 roof can sit on the same size building yet need different shingles, different underlayment, and very different amounts of material.
This calculator takes whatever you already know, whether that is a rise and run measurement, an x-in-12 pitch, an angle in degrees, or a percent grade, and converts it into all of the other formats at once. The math is the same trigonometry behind the slope calculator, applied to the specific language roofers use.
The same roof slope can be written four different ways, and each audience tends to prefer one of them. A framer wants the x-in-12 pitch, an engineer often wants degrees, a drainage plan may list a percent grade, and a field measurement usually starts as a plain rise and run. Here is how they connect.
Because all four come from the same slope value, converting between them is just arithmetic. The one mistake to avoid is mixing up the run with the sloped surface length. Run is the flat, horizontal distance, not the diagonal you would measure by laying a tape along the roof itself.
Most residential roofs land in a narrow band of common pitches. This table shows the angle, percent grade, and slope factor for the pitches you will run into most often.
| Pitch | Angle | Percent | Slope factor |
|---|---|---|---|
| 2:12 | 9.46° | 16.67% | 1.014 |
| 4:12 | 18.43° | 33.33% | 1.054 |
| 6:12 | 26.57° | 50.00% | 1.118 |
| 8:12 | 33.69° | 66.67% | 1.202 |
| 9:12 | 36.87° | 75.00% | 1.25 |
| 12:12 | 45.00° | 100.00% | 1.414 |
Notice that a 12:12 pitch is exactly 45 degrees and a 100 percent grade. That gives you a handy mental anchor: if someone says a roof is half as steep as a 12:12, they are describing something close to a 6:12 in feel, even though the angle is not literally half.
The slope factor is the most useful output for anyone buying materials. A roof's footprint, the flat area you would see looking straight down, is smaller than the real sloped surface you have to cover. The slope factor is the multiplier that bridges the two. It equals the square root of one plus the slope squared, which is the same as one divided by the cosine of the roof angle.
Worked area example
Say a simple gable building has a footprint of 1,500 square feet under the roof and a 6:12 pitch. The slope factor for 6:12 is 1.118, so the actual roof surface is 1,500 multiplied by 1.118, or about 1,677 square feet. That extra 177 square feet is real material you need to order, and it is easy to forget if you only measure the floor plan.
The slope factor also relates to rafter length. A rafter spanning a given run is the run multiplied by the slope factor, before you add any overhang. Once you have the roof surface area, the roofing calculator can turn it into shingle bundles, underlayment rolls, and a waste allowance.
You do not need to stand on a roof to measure its pitch. The safest method works from inside the attic. Hold a level horizontally against the underside of a rafter, mark the 12-inch point on the level, and measure straight down from that mark to the rafter. That vertical distance is your rise over a 12-inch run, so a 5-inch drop means a 5:12 pitch.
If you ever do climb up, treat anything above 6:12 with care. Steep roofs are slippery and the fall risk rises quickly. The OSHA fall protection rules referenced below set the baseline for when guarding and harnesses become mandatory on the job.
Pitch is not only an aesthetic choice. It controls how water and snow shed off the roof and which materials your covering manufacturer will warranty. Below roughly 2:12, water drains slowly and standard shingles are not rated, so low-slope roofs lean on membrane systems or fully sealed underlayment. From about 4:12 up to 9:12 you are in conventional territory, where most asphalt shingles, metal panels, and tiles perform well and tradespeople can still walk the surface.
Steeper pitches above 9:12 shed water and snow aggressively and give a roof a tall, dramatic profile, but they add cost. Material quantities climb with the slope factor, labor slows down because of staging and fall protection, and some shingles need extra fasteners to stay put. In heavy snow regions a steeper pitch can be a feature rather than a burden, since it keeps loads from building up.
Match the pitch to the climate, the look you want, and your budget, then confirm the covering you have in mind is approved for that slope before you commit.
A few quick examples show how the formats line up. Suppose you measure a rise of 7 inches over a 12-inch run. The slope is 7 divided by 12, or about 0.583. Multiply by 12 and you still have a 7:12 pitch. The angle is the inverse tangent of 0.583, about 30.26 degrees, and the percent grade is 58.33 percent. The slope factor is the square root of one plus 0.583 squared, roughly 1.158.
Now suppose a plan only gives you an angle of 22 degrees. The tangent of 22 degrees is about 0.404, so the pitch is 0.404 multiplied by 12, which is close to 4.85, or a hair under 5:12. The percent grade is about 40.4 percent. Working backward from a single angle like this is common when you inherit drawings that list degrees instead of the x-in-12 framers expect.
Finally, imagine a flat-roof drainage note that calls for a 2 percent fall. Two percent is a slope of 0.02, which is only about 0.24 in 12, or roughly a 1-degree angle. That is far below shingle territory and firmly in low-slope membrane territory, which is exactly why the calculator flags very gentle slopes differently from walkable ones.
Treat the calculator output as a clean conversion, not the final word on the roof. The arithmetic is exact, but it can only work from the numbers you enter. If your rise and run came from a quick tape measurement, the pitch carries whatever small error that measurement had. When the result will drive a material order or a framing cut, take the measurement twice and compare.
Keep your run honest. The most common error is measuring along the sloped surface of the roof instead of the horizontal distance underneath it. On steep roofs that difference grows fast, and it quietly inflates every number downstream. If you only have the diagonal length, you can recover the run, but it is better to measure the horizontal distance directly when you can.
When you share a pitch with someone else, give them the format they use. A framer hears 6:12 clearly, an engineer may prefer 26.57 degrees, and a roofing supplier might quote off the slope factor. Because this tool shows all of them together, you can hand over the version each person needs without redoing the math, which keeps a roofing conversation moving instead of stalling on units.
Finally, revisit the numbers if the design changes. Raising or lowering a pitch by even a couple of inches in 12 shifts the roof area, the rafter lengths, and sometimes the allowed materials. A fresh pass through the calculator after a design tweak is faster than discovering the mismatch when the shingles arrive short.
A 4:12 pitch means the roof rises 4 units for every 12 units of horizontal run. The second number is always 12 because roof pitch in the United States is standardized to a 12-unit run. So 4:12 climbs 4 inches over each foot of horizontal distance, which works out to about 18.43 degrees and a 33.33 percent grade.
Divide the rise by the run to get the slope, then take the inverse tangent (arctangent). For a 6:12 pitch, that is 6 divided by 12, which is 0.5; the arctangent of 0.5 is about 26.57 degrees. This calculator does the trigonometry for you and also shows the percent grade and slope factor for the same pitch.
People often use the terms interchangeably, but builders sometimes draw a distinction. Slope is the ratio of vertical rise to horizontal run, usually written as x:12. Pitch, in the stricter sense, is the ratio of rise to the full span (twice the run). In everyday roofing conversation and in this calculator, pitch is treated as the x-in-12 slope, which is how most contractors, suppliers, and codes describe it.
The slope factor is a multiplier that converts a flat, horizontal area into the actual sloped surface area of the roof. It equals the square root of one plus the slope squared, or one divided by the cosine of the roof angle. A 6:12 roof has a slope factor of about 1.118, so the real roof surface is roughly 12 percent larger than its footprint. Multiply your plan area by the slope factor to estimate material quantities and rafter lengths.
Roofs below 2:12 are generally treated as low-slope or flat and need membrane systems or special sealed underlayment rather than standard shingles. Pitches from about 4:12 to 9:12 are conventional and walkable for most trades. Anything above 9:12 is steep-slope work that usually requires staging, harnesses, and extra labor. A 12:12 pitch is exactly 45 degrees.
Yes. You can measure from inside the attic by placing a level against a rafter and measuring the rise at the 12-inch mark on the level. You can also use a smartphone inclinometer app held against a gable end or rafter to read the angle in degrees, then convert that angle here. Measuring from the ground against a gable wall photo is less precise but works for a rough estimate.
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