Roof Pitch Calculator (rise & run to x/12, degrees & percent)
Enter a rise and a run and read your roof pitch four ways at once — as a builder’s x/12, as an angle in degrees, as a percent grade, and as the pitch multiplier you need to turn a flat footprint into true roof area.
Calculator
A rise of 6.00 over a run of 12.00 is a 6.0/12 pitch — 26.6°, 50% grade, multiplier 1.1180 (multiply your flat footprint by 1.1180 for the true roof area).
Roofers describe slope as pitch — the number of inches a roof rises for every 12 inches it runs horizontally. A roof that climbs 6 inches over a 12-inch run is a 6/12 pitch; one that climbs 9 over 12 is a 9/12. The run is always taken as the horizontal, not the sloped, distance, which is why the same rise over a longer run yields a gentler pitch.
The rise and run don’t have to be measured in inches — any consistent unit works, because pitch is a ratio. Measuring a 6-foot rise over a 12-foot run gives exactly the same 6/12 pitch as 6 inches over 12 inches. What matters is that both numbers use the same unit. This calculator normalizes whatever you enter back to the standard per-12 form so it matches the language your framing crew, shingle wrapper and building inspector all speak.
You get four outputs. The x/12 pitch is the trade standard. The angle is the same slope expressed in degrees, handy for setting a rafter or a saw. The grade is rise over run as a percent, the way drainage and accessibility are often written. And the pitch multiplier is the single most useful number for take-offs: multiply your flat, plan-view footprint by it and you get the true, sloped roof surface area to order material against.
Formula
From a rise r and run run:
- Pitch (x/12):
x = r ÷ run × 12 - Angle:
θ = arctan(r ÷ run) - Grade:
% = r ÷ run × 100 - Multiplier:
M = √(1 + (x/12)²)
The multiplier is the length of the sloped rafter line per unit of horizontal run — a direct consequence of the Pythagorean theorem on the rise-run-rafter right triangle.
Worked example
Measure a 6-inch rise over a 12-inch run:
- Pitch:
6 ÷ 12 × 12 = 6/12 - Angle:
arctan(6 ÷ 12) = 26.57° - Grade:
6 ÷ 12 × 100 = 50% - Multiplier:
√(1 + 0.5²) = 1.1180
So a 6/12 roof stands at 26.57°, a 50% grade, and its surface is 1.118× the flat footprint below it. A gentler 4/12 works out to 18.43° and a 1.0541 multiplier.
Measuring pitch & using the multiplier
Measuring safely. You rarely need to climb onto the roof to find pitch. Hold a level horizontally against a rafter or gable, mark 12 inches along it, and measure straight down from that mark to the roof line — that vertical drop is your rise over a 12 run. From the ground you can do the same on a scaled photo taken square-on to the gable end, or read it off the framing plans. The measuring guide walks through all three methods.
Why the multiplier matters. Aerial images and county records give you the building’s footprint — the flat area it covers. A pitched roof is always larger than its footprint, and steeper roofs are larger still. Skipping the multiplier is the classic reason a material order comes up short. Feed the multiplier into the roof area calculator, then convert to roofing squares and bundles.
Common pitches. Most residential asphalt roofs fall between 4/12 and 9/12. Below about 2/12 a roof is considered low-slope and usually needs a membrane rather than shingles; above 9/12 it is a steep-slope roof that raises labor and safety demands. The reference table shows the angle and multiplier for every standard pitch.
Reference table
| Pitch (x/12) | Angle | Grade | Multiplier |
|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.0035 |
| 2/12 | 9.46° | 16.7% | 1.0138 |
| 3/12 | 14.04° | 25.0% | 1.0308 |
| 4/12 | 18.43° | 33.3% | 1.0541 |
| 5/12 | 22.62° | 41.7% | 1.0833 |
| 6/12 | 26.57° | 50.0% | 1.1180 |
| 7/12 | 30.26° | 58.3% | 1.1577 |
| 8/12 | 33.69° | 66.7% | 1.2019 |
| 9/12 | 36.87° | 75.0% | 1.2500 |
| 10/12 | 39.81° | 83.3% | 1.3017 |
| 12/12 | 45.00° | 100.0% | 1.4142 |
| 14/12 | 49.40° | 116.7% | 1.5366 |
| 16/12 | 53.13° | 133.3% | 1.6667 |
| 18/12 | 56.31° | 150.0% | 1.8028 |
| 24/12 | 63.43° | 200.0% | 2.2361 |
Multiplier = √(1 + (rise/12)²). Multiply your flat footprint by it for the true roof surface. See the full pitch-multiplier table.