Roof pitch factor chart
The multiplier that turns a flat measurement into a length on the slope, for every common pitch, with the hip and valley factor and the angle.
Pitch factor = √(1 + (rise ÷ 12)²). Multiply a flat length or a flat area by it to get the sloped length or area. At 6/12 the factor is 1.118.
| Pitch | Rafter and area factor | Hip and valley factor | Angle |
|---|---|---|---|
| 1/12 | 1.0035 | 1.0017 | 4.8° |
| 2/12 | 1.0138 | 1.0069 | 9.5° |
| 3/12 | 1.0308 | 1.0155 | 14.0° |
| 4/12 | 1.0541 | 1.0274 | 18.4° |
| 5/12 | 1.0833 | 1.0425 | 22.6° |
| 6/12 | 1.1180 | 1.0607 | 26.6° |
| 7/12 | 1.1577 | 1.0817 | 30.3° |
| 8/12 | 1.2019 | 1.1055 | 33.7° |
| 9/12 | 1.2500 | 1.1319 | 36.9° |
| 10/12 | 1.3017 | 1.1607 | 39.8° |
| 11/12 | 1.3566 | 1.1917 | 42.5° |
| 12/12 | 1.4142 | 1.2247 | 45.0° |
| 14/12 | 1.5366 | 1.2964 | 49.4° |
| 16/12 | 1.6667 | 1.3744 | 53.1° |
| 18/12 | 1.8028 | 1.4577 | 56.3° |
| 20/12 | 1.9437 | 1.5456 | 59.0° |
| 24/12 | 2.2361 | 1.7321 | 63.4° |
How to use the chart
- Rafter length. Flat run from the eave to the ridge × rafter factor. A 15 ft run at 8/12 is 15 × 1.2019 = 18.03 ft, or 18 ft 0 3/8 in.
- Roof area. Flat area × rafter factor. A 1,200 sq ft footprint at 8/12 is 1,442 sq ft of roofing, 14.4 squares. The squares calculator does this one.
- Hip or valley length. The hip's length in plan × hip factor. A hip that measures 21.2 ft on the plan at 8/12 runs 21.2 × 1.1055 = 23.44 ft. The hip factor applies when both slopes are the same pitch and meet at a square corner.
- Metal panel length. Same as the rafter: run × factor, then add the overhang at the eave. The metal panel calculator gives the count and the length together.
Where the factor stops working
A single factor assumes one pitch. A roof with a 4/12 porch kicked out under an 8/12 main roof has two factors and a transition line between them. A hip between a 6/12 and a 10/12 slope is a bastard hip: it does not run at 45 degrees in plan and no table has its factor. Valleys between different pitches are the same. Those need the roof built in three dimensions, which is what All Roof Pricer's geometry engine does from a traced outline and the pitches you type.
Questions
What is a roof pitch factor?
The pitch factor, also called the slope factor or roof pitch multiplier, is the number you multiply a flat measurement by to get the length on the slope. It is the square root of 1 plus the pitch squared, with the pitch written as rise over 12. A 6/12 roof has a factor of 1.118.
How do I convert roof pitch to degrees?
The angle is the arctangent of rise over run. A 4/12 roof is 18.4 degrees, 6/12 is 26.6 degrees, 8/12 is 33.7 degrees and 12/12 is 45 degrees.
Why is the hip and valley factor different?
A hip or valley runs diagonally across the roof in plan, so its horizontal run per foot of rise is longer than a rafter's. For two slopes of the same pitch meeting at 90 degrees, the hip factor is the square root of 1 plus half the pitch squared: at 6/12 it is 1.061 against the rafter factor of 1.118. A hip between two different pitches, a bastard hip, has no simple factor; it has to be solved in three dimensions.
Does All Roof Pricer use the pitch factor?
It uses the full three-dimensional geometry, which gives the same answer as the factor on a plain roof and the right answer on a mixed-pitch roof. Every facet is built as a plane at its pitch, and every line length and area is read off that plane.