π Roof Pitch Calculator
Pitch, angle in degrees, and slope multiplier for true roof area.
Roof Pitch (X/12)
How to Use This Calculator
Enter the rise (vertical height) and run (horizontal distance) in inches. The default run of 12 matches the standard X/12 pitch convention, but you can enter any run if you measured over a different distance. The calculator normalizes everything to the X/12 format and also gives the pitch angle in degrees, the slope multiplier, and the rafter length per foot of run.
Enter the rise in inches. If you measured 6 inches of rise over a 12-inch level in the attic, enter 6.
Enter the run in inches. Leave it at 12 for the standard pitch reading, or enter your actual measured horizontal distance.
Read your pitch (e.g. 6/12), the angle in degrees, and the slope multiplier. Multiply your roof footprint square footage by the multiplier to get the true roof area for material estimates.
The Formulas
The slope multiplier comes from the Pythagorean theorem. If the rise and run form a right triangle, the rafter (hypotenuse) is longer than the run by exactly this ratio, and that ratio is the same no matter how long the rafter is. So one multiplier converts any horizontal measurement into its true slope length.
Common multipliers worth memorizing: 4/12 is 1.054, 6/12 is 1.118, 8/12 is 1.202, 10/12 is 1.302, and 12/12 is 1.414. Notice how fast it grows past 8/12: a steep roof has dramatically more surface area than its footprint suggests, which is why steep roofs cost so much more to shingle.
Worked Example
Rise of 7 inches, run of 12 inches. Pitch = (7/12) x 12 = 7/12. Angle = atan(7/12) = 30.3 degrees. Slope multiplier = sqrt(7^2 + 12^2) / 12 = sqrt(193)/12 = 13.89/12 = 1.158. So a 1,500 square foot ranch footprint with a 7/12 roof has a true roof area of about 1,737 square feet, roughly 17.4 squares of shingles (a square is 100 sq ft), plus 10 to 15 percent waste.
Tips
When ordering shingles, add 10 percent waste for a simple gable roof and 15 percent for hips, valleys, and dormers. On pitches over 8/12, plan on safety equipment: roof jacks, staging, or a harness, since falls from steep roofs are a leading cause of DIY injuries. Also check your shingle bundle label for its coverage at your pitch; steep pitches sometimes need extra nails per shingle (6 instead of 4) to meet wind ratings.
Estimates for planning only. Roof work is hazardous; use proper fall protection and check local building codes before re-roofing.
Frequently Asked Questions
What does roof pitch mean, like 6/12?
Roof pitch is written as rise over a 12-inch run. A 6/12 pitch means the roof rises 6 inches for every 12 inches of horizontal distance. Pitches under 4/12 are considered low slope, 4/12 to 8/12 are typical for most homes, and anything over 9/12 is steep and usually needs special safety equipment to walk.
How do I measure my roof pitch?
Hold a level horizontally against the underside of a rafter in the attic and mark 12 inches along it, then measure straight down from the 12-inch mark to the rafter. That vertical distance in inches is your pitch number. From outside, you can estimate with a smartphone pitch app against the rake board, but the attic method is more accurate.
What is the roof slope multiplier used for?
The multiplier converts horizontal (plan) square footage into true roof surface area. A 6/12 pitch has a multiplier of 1.118, so a 1,000 square foot footprint is actually 1,118 square feet of roofing. Shingle, metal, and underlayment estimates all need this number, because materials cover the slope, not the floor plan.
How do you convert roof pitch to degrees?
Take the arctangent of rise divided by run and convert to degrees: degrees = atan(rise/run) x 180/pi. A 4/12 pitch is 18.4 degrees, 6/12 is 26.6 degrees, 8/12 is 33.7 degrees, and 12/12 is exactly 45 degrees. This calculator does the math for any rise and run you enter.
What is the minimum pitch for asphalt shingles?
Most shingle manufacturers require a minimum 2/12 pitch, and require special underlayment (double layer or ice and water shield) between 2/12 and 4/12. Below 2/12, shingles are not recommended at all; use a membrane system like TPO or modified bitumen instead.