Roof Pitch Calculator
Find the pitch of a roof from its rise and run, or convert a pitch between x/12 and degrees, with the slope in percent. With the run, the calculator also finds the rafter length, with the overhang and the ridge board. For the roof area and how many bundles of shingles to buy, use the Roofing Calculator.
For rafters, the run is half the building width for a gable roof, measured to the center of the ridge.
- Choose US or Metric. You can still change the unit of any single field.
- Choose Rise and run to find the pitch from two measurements, or Pitch to convert a pitch you already know, as x/12 or in degrees.
- For the rafter length, enter the Run. For a gable roof, that is half the width of the building, measured to the center of the ridge.
- Optionally, enter the Overhang, measured level from the outside of the wall, and the Ridge board thickness.
Length fields accept whole numbers, decimals, fractions, and mixed
numbers, such as 12, 10.5, 3/4, or
1 1/2. The pitch takes whole numbers and decimals, such as
6 or 22.5.
How to calculate roof pitch
Roof pitch is the rise of the roof over its horizontal run. In the US and Canada it is written as the rise for every 12 inches of run, such as 6/12. The calculator works from the ratio of rise to run:
Pitch = rise ÷ run × 12, written as x/12
Angle = atan(rise ÷ run), slope = rise ÷ run × 100%
Pitch factor = √(1 + (rise ÷ run)²)
The pitch factor is how many times longer a line running up the roof is than the same line seen from above. It gives the rafter length for a run, and the roof area for an area measured from above. Times 12 in, it is the rafter length per foot of run. Common pitches are:
| Pitch | Angle | Rafter per ft of run |
|---|---|---|
| 3/12 | 14.04° | 12.37 in |
| 4/12 | 18.43° | 12.65 in |
| 5/12 | 22.62° | 13.00 in |
| 6/12 | 26.57° | 13.42 in |
| 7/12 | 30.26° | 13.89 in |
| 8/12 | 33.69° | 14.42 in |
| 9/12 | 36.87° | 15.00 in |
| 10/12 | 39.81° | 15.62 in |
| 12/12 | 45.00° | 16.97 in |
How to measure roof pitch
From the attic, hold a level against the underside of a rafter so that the level is horizontal. Mark 12 inches along the level, then measure straight up from that mark to the rafter. That height is the rise for a 12-inch run. Enter it as the rise and 12 as the run, both in inches. You can also measure the full rise and run of the roof, in any unit.
In the UK and Australia, pitch is usually given in degrees, such as 30° or 35°. In traditional carpentry terms, pitch can also mean the rise over the whole span of the building, so a 1/4 pitch is the same as 6/12.
Rafter length
A common rafter runs from the wall to the ridge, and its length is the diagonal of the rise and run: √(run² + rise²), or the run times the pitch factor. Swanson Tool's rafter table gives the same numbers per foot of run, such as 13.42 in for a 6/12 roof.
- Ridge board. Swanson Tool moves the top plumb cut back by half the thickness of the ridge board. The calculator takes half the thickness off the run, level, before multiplying by the pitch factor.
- Overhang. The tail past the wall is the overhang, measured level, times the pitch factor.
Measure and mark the rafter along its top edge. The lengths do not include the extra you need for cutting.
Examples
Finding a pitch
A roof that rises 6 in over a 12 in run has a pitch of 6/12, an angle of 26.57°, and a slope of 50%.
Rafters for a 24 ft wide house
At 6/12, a run of 12 ft needs a rafter of 144 in × √1.25 = 160.997 in, or 13 ft 5 in to the center of the ridge. With a 1 1/2 in ridge board and a 12 in overhang, the rafter is 13 ft 4 3/16 in to the ridge board, the tail is 1 ft 1 7/16 in, and the total length is 14 ft 5 9/16 in. Each length is rounded to 1/16 in on its own, so the parts can add up to 1/16 in more or less than the total.
Metric dimensions
A 30° roof is 6.93/12, a slope of 57.74%. With a run of 4,000 mm, the rise is 2,309.4 mm and the rafter is 4,618.8 mm.
FAQ
A 4/12 pitch is about 18.43°, a slope of 33.33%. The table above lists other common pitches.
From the attic, hold a level horizontally against a rafter, mark 12 inches along it, and measure straight up from the mark to the rafter. That rise over 12 is the pitch.
In traditional carpentry terms, pitch is the rise over the whole span of the building. A 1/4 pitch rises a quarter of the span, which is 6/12.
The run is half the width, 12 ft. At 6/12 the rafter is 13 ft 5 in to the center of the ridge, before the overhang and the ridge board.
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