Pitch multiplier and angle, 1/12 to 12/12#
Roof pitch is written as rise over a 12 inch run, like "6 in 12." The multiplier converts a flat footprint into actual roof surface area, and the angle is the same slope expressed in degrees.
4 in 12
1.054×18.4°6 in 12
1.118×26.6°12 in 12
1.414×45.0°| Pitch | Multiplier | Angle | 30×40 ft roof area |
|---|---|---|---|
| 1 in 12 | 1.003 | 4.8° | 1,204 sq ft |
| 2 in 12 | 1.014 | 9.5° | 1,217 sq ft |
| 3 in 12 | 1.031 | 14.0° | 1,237 sq ft |
| 4 in 12 | 1.054 | 18.4° | 1,265 sq ft |
| 5 in 12 | 1.083 | 22.6° | 1,300 sq ft |
| 6 in 12 | 1.118 | 26.6° | 1,342 sq ft |
| 7 in 12 | 1.158 | 30.3° | 1,389 sq ft |
| 8 in 12 | 1.202 | 33.7° | 1,442 sq ft |
| 9 in 12 | 1.250 | 36.9° | 1,500 sq ft |
| 10 in 12 | 1.302 | 39.8° | 1,562 sq ft |
| 11 in 12 | 1.357 | 42.5° | 1,628 sq ft |
| 12 in 12 | 1.414 | 45.0° | 1,697 sq ft |
The area column shows roof surface before any waste allowance. A footprint here means the building's flat outline as measured from the ground or a site plan, not the sloped surface itself.
Skip the manual math
Get your squares, bundles & underlayment
Enter your roof footprint and pitch and get roof area, squares, shingle bundles, and underlayment rolls, with a waste allowance built in.
The formula#
The multiplier comes from basic trigonometry. A roof plane is the hypotenuse of a right triangle where the run is 12 inches and the rise is whatever the pitch calls for. The multiplier is:
multiplier = √(rise² + 12²) ÷ 12
Multiply your footprint area by this number to get the actual sloped roof area. The angle, if you'd rather think in degrees than in a rise-over-run ratio, is the arctangent of rise divided by 12:
angle = arctan(rise ÷ 12)
Both describe the same slope. Contractors and shingle manufacturers use the rise-in-12 pitch almost exclusively; framers and rafter tables sometimes switch to degrees.
Worked example#
Take a simple gable roof over a 30 by 40 foot footprint (1,200 square feet) at a 6 in 12 pitch, the most common residential pitch in the US.
- Multiplier for 6 in 12: √(6² + 12²) ÷ 12 = √180 ÷ 12 = 1.118
- Roof area: 1,200 × 1.118 = 1,342 sq ft
- Add 10 percent waste for a simple gable roof: 1,342 × 1.10 = 1,476 sq ft
- Squares: 1,476 ÷ 100 = 14.8 squares
- Bundles at 3 per square: 45 bundles
- Underlayment at 400 sq ft per roll: 4 rolls
That 45-bundle figure is exactly what the roofing calculator returns for the same footprint and pitch. Run your own footprint through it to skip these steps and get squares, bundles, and underlayment together.
Where the multiplier does not apply#
Use this multiplier for anything you buy by roof surface: shingles, underlayment, sheathing, ice and water shield. Do not use it to size gutters.
Rain falls vertically, so a roof collects water over its horizontal footprint. A 12/12 roof and a flat roof on the same footprint catch the same rain, even though the steep one has 41 percent more surface. Sizing a gutter off sloped area oversizes the whole system.
Gutters do get a pitch adjustment, but it is a different and much smaller one, running 1.00 up to 1.30 rather than 1.00 up to 1.414. It covers wind-driven rain and the speed water reaches the eave, not surface area. The gutter calculator prints both columns side by side so the two numbers cannot be mixed up.
Sizing gutters, not shingles
Get gutter feet, downspouts & the 5 or 6 inch call
Enter your footprint, pitch, and eave runs and get linear feet, downspout count, hangers, and whether the roof needs a 5 or 6 inch trough.
Save the roof pitch chart#
Pitch multipliers for six common roof pitches, plus what each does to a 30x40 roof. Save it and stop guessing at roof area.
Save to PinterestOpens Pinterest with the chart and link ready to go.
Common questions#
What is a roof pitch multiplier?#
The number you multiply a roof's flat footprint area by to get its true, sloped surface area. It's the square root of rise squared plus 144, divided by 12. A 6 in 12 pitch has a multiplier of 1.118, so a 1,200 square foot footprint covers 1,342 square feet of actual roof.
What angle is a 6/12 roof pitch?#
26.6 degrees. The angle is the arctangent of rise over run, and for a 6 in 12 pitch that's the arctangent of 6 divided by 12, or 0.5, which comes to 26.57 degrees.
How do I convert roof pitch to degrees?#
Take the arctangent of rise divided by run, both in inches. A pitch of X in 12 converts with angle = arctan(X / 12). A 4 in 12 pitch comes to 18.4 degrees, a 9 in 12 pitch to 36.9 degrees, and a 12 in 12 pitch to exactly 45 degrees.