The drawing is a gable roof seen from the end, to scale. The colored side is one rafter, the dashed line in the middle is the rise, and the angle at the eave is the one you'd set a saw or an angle finder to.
Roof pitch to degrees chart
Pitch in the US is written as inches of rise for every 12 inches of run, so 6/12 means the roof climbs 6″ for each foot you go in from the wall. Here's every whole pitch from 1/12 to 12/12, a few steeper ones, and two low slopes that flat roofs use for drainage.
| Pitch | Angle | Percent grade | Rafter factor | Rafter per foot of run |
|---|---|---|---|---|
| 0.25/12 | 1.19° | 2.1% | 1.0002 | 12.00″ |
| 0.5/12 | 2.39° | 4.2% | 1.0009 | 12.01″ |
| 1/12 | 4.76° | 8.3% | 1.0035 | 12.04″ |
| 2/12 | 9.46° | 16.7% | 1.0138 | 12.17″ |
| 3/12 | 14.04° | 25% | 1.0308 | 12.37″ |
| 4/12 | 18.43° | 33.3% | 1.0541 | 12.65″ |
| 5/12 | 22.62° | 41.7% | 1.0833 | 13.00″ |
| 6/12 | 26.57° | 50% | 1.1180 | 13.42″ |
| 7/12 | 30.26° | 58.3% | 1.1577 | 13.89″ |
| 8/12 | 33.69° | 66.7% | 1.2019 | 14.42″ |
| 9/12 | 36.87° | 75% | 1.2500 | 15.00″ |
| 10/12 | 39.81° | 83.3% | 1.3017 | 15.62″ |
| 11/12 | 42.51° | 91.7% | 1.3566 | 16.28″ |
| 12/12 | 45.00° | 100% | 1.4142 | 16.97″ |
| 14/12 | 49.40° | 116.7% | 1.5366 | 18.44″ |
| 16/12 | 53.13° | 133.3% | 1.6667 | 20.00″ |
| 18/12 | 56.31° | 150% | 1.8028 | 21.63″ |
| 24/12 | 63.43° | 200% | 2.2361 | 26.83″ |
The two gray rows at the top are 1/4″ and 1/2″ per foot. Nobody calls those a roof pitch out loud, but it's how flat roofs and decks get specified, so they're worth having in the same table.
The last column is the rafter length for each foot of run, in inches. Most steel framing squares have a rafter table stamped on the blade, and its first line gives these same numbers: 13.42 for 6/12, 16.97 for 12/12.
The roof pitch formulas
Every number on this page comes from one right triangle. The run is the level side, the rise is the upright side, and the rafter is the long side. Once you have rise ÷ run, everything else follows.
- Angle in degrees = atan(rise ÷ run). For 6/12 that's atan(0.5), which is 26.57°.
- Percent grade = rise ÷ run × 100. A 6/12 roof is a 50% grade.
- Rafter factor = √(1 + (rise ÷ run)²). For 6/12 that's √1.25, or 1.1180.
- Back from degrees: rise per foot = 12 × tan(angle). A 30° roof rises 6.93″ per foot.
The rafter factor is just the Pythagorean theorem done once per foot. A 12″ run and a 6″ rise give a long side of √(144 + 36), about 13.42″, and 13.42 ÷ 12 is the 1.118 in the chart. Multiply any run by it and you get the rafter length.
If you'd like a calculator to do the atan, most phone calculators have it as tan⁻¹ in their scientific mode. Make sure it's set to degrees, not radians.
A worked example
Say you're in the attic with a 2 foot level. You hold it under a rafter with one end touching the rafter's bottom edge and the bubble centered, then measure straight up from the other end of the level to the rafter: 9″. These are the numbers already in the calculator.
- Turn it into a pitch.
9″ of rise over 24″ of run is 0.375. Times 12, that's 4 1/2″ per foot, so the roof is 4.5/12.
- Find the angle.
atan(0.375) is 20.56°. That's also the plumb cut on the rafter, and the seat cut is 90° minus that, 69.44°.
- Get the grade and the factor.
The grade is 37.5%, and the rafter factor is 1.0680, or 12.82″ of rafter per foot of run.
- Put in the roof's run.
On a 28 foot wide gable the run is 14′ 0″. The ridge sits 5′ 3″ above the wall plates, and each rafter's line length is 14′ 0″ × 1.0680, about 14′ 11 7/16″.
That line length runs to the center of the ridge. Take off half the ridge board's thickness, and add the overhang, also times the rafter factor, before you cut. To turn a decimal like 179.42″ into tape marks, the inch fraction chart or the feet and inches calculator will do it.
How to measure the pitch of a roof
You don't need to go up on the roof. In the attic, a level and a tape on the bottom edge of any rafter give you the same triangle as the shingles on top. Mark 12″ on the level, hold it level with one end touching the rafter, and measure straight up from the 12″ mark. That reading is the pitch.
A longer level gives a better reading. With a 2 foot level, measure at 24″ and type both numbers into the rise and run fields, as in the example. Outside, the same trick works on the rake board at a gable end, or on the roof itself if it's safe to stand on.
An angle finder or a phone with an angle app works too. Put the angle in the degrees field and the pitch comes out. Just measure on a rafter, not on a sagging old ceiling.
Pitch, slope, grade and degrees
They're four ways to say how steep the same roof is. In the US, plans, roofing instructions and framing squares use rise in 12, like 6/12 or 6:12. Saws and angle finders work in degrees. Percent grade is more common for low slopes, ramps and drainage.
One old wrinkle. Strictly, "pitch" used to mean rise divided by the whole span, not the run. By that rule a 6/12 slope is a 1/4 pitch, because it climbs 6 feet over a 24 foot span. Older books still use it, so if a number looks oddly small, that may be why. Today most people say pitch and mean rise over run, and that's what this page uses.
A fun comparison: a stair with 7 3/4″ risers and 10″ treads climbs at 37.8°, about the same as a 9.3/12 roof. If you're laying out the stairs too, how many stairs for your ceiling and the stair stringer calculator use the same kind of triangle.
Plumb cuts and seat cuts
The plumb cut at the ridge is the roof angle, measured off a square end, so a 6/12 rafter gets a 26.57° plumb cut. The seat cut, where the rafter sits on the wall, is 90° minus that. On a speed square you don't even need the degrees. The scale marked Common lets you set the plumb line straight from the pitch number.
Low pitches and roofing
A pitch can be too low for the roofing on it. In the US, asphalt shingles are usually limited to 2/12 and steeper, with extra underlayment between 2/12 and 4/12. Below that, roofs count as low slope and need a membrane made for it. Metal, tile and slate each have their own limits.
Those are common values, not a rule I can promise for your house. Check the roofing maker's instructions and your local code before you pick a pitch.
What this calculator doesn't check
It does the geometry and nothing more. It doesn't size rafters, look at snow or wind loads, or work out a birdsmouth or an overhang. And the rafter length it gives is the line length to the center of the ridge, before any cut. Measure twice, and check your local code before you build.
Questions
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent. For an 8/12 roof that's atan(8 ÷ 12), or 33.69°. The chart above has every common pitch already worked out.
What pitch is a 30 degree roof?
About 6.93/12. A 30° roof rises 6.93″ per foot, which marks as 6 15/16″ on a tape, so it's a hair under 7/12. A true 7/12 is 30.26°.
What angle is a 4/12 pitch?
18.43°. Its grade is 33.3% and its rafter factor is 1.0541.
Is a 45 degree roof a 12/12 pitch?
Yes. At 45° the rise equals the run, so it climbs 12″ for every 12″, a 100% grade. The rafter factor is √2, about 1.4142.
What is a rafter factor?
It's how much longer the rafter is than the run it covers. Multiply the run by it to get the rafter length. Some people call it the slope factor or the pitch multiplier. It's the same number.
Do I measure the run to the ridge or across the whole roof?
To the ridge. The run is half the span on a gable roof: from the outside of the wall to the center of the ridge. The pitch itself doesn't change either way, but the rafter length and the ridge height do.
Construction Calculator
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