Roof pitch calculator
Convert a roof pitch between x/12, degrees and percent, then get rafter length and roof area from the same slope.
Angle
- Angle
- 26.57°
- Slope in percent
- 50%
- Pitch
- 6/12
- Rise to run
- 1 : 2
- Slope factor
- 1.118Rafter length per unit of run
Rafter length and roof area
Half the building width for a simple gable roof.
The roof seen from above, including overhangs.
Rafter length and roof area
- Rafter length before overhang
- 13.42 ft13 ft 5 in
- Roof surface area
- 1,073.3 sq ft10.7 roofing squares (100 sq ft each)
Estimate only. Check product labels and local building rules before you buy or build.
Quick answer
Roof pitch is the rise in inches for every 12 inches of horizontal run. To turn it into degrees, take the arctangent of rise ÷ run: a 6/12 pitch is arctan(6 ÷ 12) = 26.57°, which is also a 50% slope. Multiply the run by the slope factor √(1 + (rise ÷ run)²), 1.118 for 6/12, to get the rafter length.
How to use the roof pitch calculator
- Choose how you know the pitch: as x/12 from plans, as an angle from a phone or digital level, as a percent, or as a rise and run you measured yourself.
- Type the value. The angle, percent slope, x/12 pitch, rise-to-run ratio and slope factor update as you type.
- For rafter length, enter the horizontal run from the outside of the wall to the centre of the ridge. For roof area, enter the footprint of the roof seen from above, overhangs included.
How is roof pitch calculated?
Pitch, angle and percent are three ways of writing the same ratio: how far the roof rises for each unit it runs horizontally. In the United States the ratio is written as inches of rise per 12 inches of run, so a roof that rises 6 inches over 12 inches is a 6/12 pitch, read "six in twelve".
The angle is the arctangent of that ratio, and the percent slope is the ratio multiplied by 100. The slope factor is the length of the sloped side of a right triangle whose run is 1, so multiplying any horizontal measurement by it gives the matching sloped measurement.
pitch (x/12) = rise ÷ run × 12angle = arctan(rise ÷ run)slope % = rise ÷ run × 100slope factor = √(1 + (rise ÷ run)²)rafter length = run × slope factorroof area = footprint area × slope factorRoof pitch chart: x/12 to degrees and percent
Every value below comes from the formulas above, rounded to two decimals for the angle and four for the slope factor.
| Pitch | Angle | Slope | Slope factor |
|---|---|---|---|
| 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 |
| 11/12 | 42.51° | 91.7% | 1.3566 |
| 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 |
Worked examples
Rafters and shingles for a 6/12 gable roof
A house is 24 ft wide and 40 ft long with a simple gable roof at 6/12. The run of each rafter is half the width, 12 ft. The slope factor for 6/12 is 1.118, so each rafter is 12 × 1.118 = 13.42 ft, about 13 ft 5 in, before you add the overhang.
Seen from above, the roof covers 24 × 40 = 960 sq ft. The sloped surface is 960 × 1.118 = 1,073.3 sq ft, or 10.7 roofing squares. Order shingles for the sloped area, not the footprint, and add a waste allowance as the shingle maker recommends.
Finding the pitch with a level and a tape
In the attic, hold a 12-inch level horizontally with one end touching the underside of a rafter. Measure straight up from the other end of the level to the rafter. If that measurement is 7 inches, the pitch is 7/12, an angle of 30.26° and a slope of 58.3%.
What is the lowest pitch for asphalt shingles?
Under the International Residential Code section on asphalt shingles (R905.2), shingles may only be used on roofs of 2/12 or steeper, and roofs from 2/12 up to 4/12 need a double layer of underlayment. Your local code edition and the shingle manufacturer’s instructions can be stricter, so check both before you buy. For structural roof work, local building rules and a qualified roofer or engineer take priority over this calculator.
Questions
What is a 6/12 roof pitch in degrees?
A 6/12 roof pitch is 26.57 degrees. The roof rises 6 inches for every 12 inches of run, so rise ÷ run is 0.5, and arctan(0.5) is 26.57°. The same roof is a 50% slope, and its slope factor is 1.118, which means every foot of horizontal run is 1.118 ft of rafter.
How do I convert roof pitch to degrees?
Divide the rise by 12 and take the arctangent of the result. For a 4/12 pitch, 4 ÷ 12 = 0.333, and arctan(0.333) = 18.43°. Most phone calculators have a tan⁻¹ key. To go the other way, take the tangent of the angle and multiply by 12: tan(30°) × 12 = 6.93, so 30° is about a 7/12 pitch.
Is roof pitch the same as roof slope?
In everyday use, yes: both usually mean rise per 12 inches of run, such as 6/12. In traditional carpentry, pitch meant the rise divided by the full span of the building, so a 6/12 slope was called a 1/4 pitch. If a plan writes a single fraction such as 1/3 pitch, ask which meaning it uses before you cut rafters.
What does a 12/12 roof pitch mean?
A 12/12 roof rises 12 inches for every 12 inches of run, so it is a 45-degree roof with a 100% slope. Its slope factor is 1.4142, which means the roof surface is about 41% larger than the area it covers. Roofs this steep usually need roof jacks or other fall protection to work on.
How much larger is the roof than the house footprint?
Multiply the footprint by the slope factor for your pitch. A 4/12 roof is 5.4% larger than its footprint (factor 1.0541), a 6/12 roof is 11.8% larger (1.118) and an 8/12 roof is 20.2% larger (1.2019). Include overhangs in the footprint, and add hips, valleys and dormers separately because they change the shape.
Sources
- City of Hopkins, Minnesota, Asphalt Shingles (R905.2) (checked October 19, 2026)Minimum 2:12 slope for asphalt shingles and double underlayment from 2:12 to 4:12, under the International Residential Code.
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