Reference
Roof Pitch Factor Table
Every common roof pitch with the multipliers that turn plan measurements into roof area, rafter length and hip length.
How to use the table
Find your pitch in the first column. Multiply a horizontal measurement by the factor in the same row:
- a footprint area by the pitch factor to get the sloped roof area;
- a rafter’s horizontal run by the pitch factor to get its line length;
- a common run by the hip and valley factor to get the length of a regular hip or valley.
Pitch from 1/12 to 24/12
| Pitch | Angle | Slope | Pitch factor | Hip / valley factor | Rafter per ft of run | For roofing |
|---|---|---|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.0035 | 1.4167 | 12.04 in | Flat for roofing: membrane only |
| 2/12 | 9.5° | 16.7% | 1.0138 | 1.4240 | 12.17 in | Low slope: shingles with double underlayment |
| 3/12 | 14.0° | 25.0% | 1.0308 | 1.4361 | 12.37 in | Low slope: shingles with double underlayment |
| 4/12 | 18.4° | 33.3% | 1.0541 | 1.4530 | 12.65 in | Walkable |
| 5/12 | 22.6° | 41.7% | 1.0833 | 1.4743 | 13.00 in | Walkable |
| 6/12 | 26.6° | 50.0% | 1.1180 | 1.5000 | 13.42 in | Walkable |
| 7/12 | 30.3° | 58.3% | 1.1577 | 1.5298 | 13.89 in | Steep: roof jacks and harness |
| 8/12 | 33.7° | 66.7% | 1.2019 | 1.5635 | 14.42 in | Steep: roof jacks and harness |
| 9/12 | 36.9° | 75.0% | 1.2500 | 1.6008 | 15.00 in | Steep: roof jacks and harness |
| 10/12 | 39.8° | 83.3% | 1.3017 | 1.6415 | 15.62 in | Very steep: staging |
| 11/12 | 42.5° | 91.7% | 1.3566 | 1.6853 | 16.28 in | Very steep: staging |
| 12/12 | 45.0° | 100.0% | 1.4142 | 1.7321 | 16.97 in | Very steep: staging |
| 14/12 | 49.4° | 116.7% | 1.5366 | 1.8333 | 18.44 in | Mansard-like: staging, priced as a wall |
| 16/12 | 53.1° | 133.3% | 1.6667 | 1.9437 | 20.00 in | Mansard-like: staging, priced as a wall |
| 18/12 | 56.3° | 150.0% | 1.8028 | 2.0616 | 21.63 in | Mansard-like: staging, priced as a wall |
| 21/12 | 60.3° | 175.0% | 2.0156 | 2.2500 | 24.19 in | Over 21/12: six nails and hand-sealing |
| 24/12 | 63.4° | 200.0% | 2.2361 | 2.4495 | 26.83 in | Over 21/12: six nails and hand-sealing |
Pitch from degrees
For plans and inclinometer readings given in degrees:
| Angle | Rise per 12 | Pitch factor | Hip / valley factor |
|---|---|---|---|
| 10° | 2.12/12 | 1.0154 | 1.4252 |
| 15° | 3.22/12 | 1.0353 | 1.4394 |
| 20° | 4.37/12 | 1.0642 | 1.4603 |
| 22.5° | 4.97/12 | 1.0824 | 1.4736 |
| 25° | 5.60/12 | 1.1034 | 1.4891 |
| 30° | 6.93/12 | 1.1547 | 1.5275 |
| 35° | 8.40/12 | 1.2208 | 1.5781 |
| 40° | 10.07/12 | 1.3054 | 1.6444 |
| 45° | 12.00/12 | 1.4142 | 1.7321 |
| 50° | 14.30/12 | 1.5557 | 1.8494 |
| 60° | 20.78/12 | 2.0000 | 2.2361 |
Worked lookups
- A 1,768 sq ft footprint at 6/12: 1,768 × 1.1180 = 1,977 sq ft of roof.
- A rafter with a 12 ft run at 8/12: 12 × 1.2019 = 14.42 ft of line length.
- A hip on a 12 ft common run at 6/12: 12 × 1.5000 = 18 ft.
Sources and notes
The factors are exact geometry, computed to four decimals. The roofing notes follow the International Residential Code (R905.2.2: no asphalt shingles below 2/12; R905.1.1: double underlayment from 2/12 to below 4/12), shingle manufacturers’ installation instructions (six nails and hand-sealing above 21/12), and roofing estimating practice for walkability. The hip factor assumes a regular hip or valley, where two planes of the same pitch meet at a right-angled corner.
Calculators that use this table
- The roof pitch calculator converts any pitch and gives both factors.
- The pitch factor calculator applies them to a footprint or a run.
- The roof area calculator multiplies the footprint by the pitch factor.
- The rafter length calculator and the hip and valley rafter calculator use the factors for lengths and cuts.
- The shingle calculator, the ice and water shield calculator and the valley flashing calculator apply them to areas, courses and valley lengths.
- The metal roof panel calculator uses the pitch factor for panel length.
The guide roof pitch explained shows where the factors come from.