A roof pitch factor chart lists the multiplier that turns a horizontal roof measurement into a sloped one. At 6:12 the factor is 1.1180, so a 1,200 sq ft roof plan has about 1,342 sq ft of roof surface before waste and a 12 ft run becomes a 13.4164 ft rafter. The chart below covers every pitch from 1:12 to 24:12 and includes the hip and valley factor. Every value is calculated from the formula, and you can print the chart as a PDF.
Roof pitch factor chart: 1:12 to 24:12
Every pitch from 1:12 to 24:12. The angle is atan(rise ÷ 12) and the percent slope is rise ÷ 12 × 100. The slope factor converts a horizontal run or plan area into a sloped length or area. The hip and valley factor does the same for a hip or valley rafter on a regular roof.
| Pitch | Angle | Percent slope | Slope factor | Hip/valley factor |
|---|---|---|---|---|
| 1:12 | 4.76° | 8.33% | 1.0035 | 1.4167 |
| 2:12 | 9.46° | 16.67% | 1.0138 | 1.4240 |
| 3:12 | 14.04° | 25.00% | 1.0308 | 1.4361 |
| 4:12 | 18.43° | 33.33% | 1.0541 | 1.4530 |
| 5:12 | 22.62° | 41.67% | 1.0833 | 1.4743 |
| 6:12 | 26.57° | 50.00% | 1.1180 | 1.5000 |
| 7:12 | 30.26° | 58.33% | 1.1577 | 1.5298 |
| 8:12 | 33.69° | 66.67% | 1.2019 | 1.5635 |
| 9:12 | 36.87° | 75.00% | 1.2500 | 1.6008 |
| 10:12 | 39.81° | 83.33% | 1.3017 | 1.6415 |
| 11:12 | 42.51° | 91.67% | 1.3566 | 1.6853 |
| 12:12 | 45.00° | 100.00% | 1.4142 | 1.7321 |
| 13:12 | 47.29° | 108.33% | 1.4743 | 1.7815 |
| 14:12 | 49.40° | 116.67% | 1.5366 | 1.8333 |
| 15:12 | 51.34° | 125.00% | 1.6008 | 1.8875 |
| 16:12 | 53.13° | 133.33% | 1.6667 | 1.9437 |
| 17:12 | 54.78° | 141.67% | 1.7341 | 2.0017 |
| 18:12 | 56.31° | 150.00% | 1.8028 | 2.0616 |
| 19:12 | 57.72° | 158.33% | 1.8727 | 2.1230 |
| 20:12 | 59.04° | 166.67% | 1.9437 | 2.1858 |
| 21:12 | 60.26° | 175.00% | 2.0156 | 2.2500 |
| 22:12 | 61.39° | 183.33% | 2.0883 | 2.3154 |
| 23:12 | 62.45° | 191.67% | 2.1619 | 2.3819 |
| 24:12 | 63.43° | 200.00% | 2.2361 | 2.4495 |
Download this chart as a one-page PDF to print for the truck or the site office. To start from your own rise and run, use the roof pitch calculator.
How to use the pitch factor
There are two jobs: find a sloped length, or find a roof surface area. Each is one multiplication, and both start from horizontal measurements.
Sloped length = horizontal run × slope factor Roof surface = horizontal plan area × slope factor
Rafter length. A common rafter with a 12 ft run at 6:12 has a sloped length of 12 × 1.118034 = 13.4164 ft, which is 13′ 5″. That is the geometric length from the wall line to the ridge centerline. Ridge thickness, overhang and the cuts are separate steps; the rafter length calculator handles them.
Roof area. A 1,200 sq ft horizontal plan at 6:12 has 1,200 × 1.118034 = 1,341.64 sq ft of roof surface before waste, about 13.4 roofing squares. The same plan at 8:12 has 1,442.22 sq ft.
Where the factor comes from
A pitch of 6:12 means 6 in of rise for every 12 in of horizontal run. Those two legs and the sloped surface form a right triangle, so the sloped length for each 12 in of run is √(12² + 6²) = √180 = 13.4164 in. Divide by 12 to get the factor per inch of run: 1.1180.
Slope factor = √(12² + rise²) ÷ 12 Hip/valley factor = √(2 × 12² + rise²) ÷ 12
A hip or valley rafter runs diagonally across the plan. On a regular roof, where both planes have the same pitch and meet at 90° in plan, its horizontal run is √2 times the common run, which is where the 2 × 12² comes from. At 6:12 that gives √324 ÷ 12 = 1.5000, so a hip over a 12 ft common run is 18.00 ft long.
These are geometric lengths. If the two planes have different pitches, or the building is not square, a hip or valley needs its own calculation.
Worked example: a 36 × 28 ft house at 7:12
Assume a simple roof with one pitch, a 1 ft horizontal overhang on all sides and an illustrative 10% waste allowance.
| Step | Calculation | Result |
|---|---|---|
| Plan area with overhang | (36 + 2) × (28 + 2) ft | 1,140 sq ft |
| Slope factor at 7:12 | from the chart | 1.1577 |
| Roof surface | 1,140 × 1.1577 | 1,319.78 sq ft |
| Roofing squares | surface ÷ 100 | 13.20 |
| With 10% waste | 13.20 × 1.10 | 14.52 squares |
| Bundles at 3 per square | 14.52 × 3, rounded up | 44 bundles |
Three bundles per square is an example input, not a rule for every shingle, so check the coverage printed on your product. The roofing squares calculator runs the same steps from your own dimensions.
Mistakes that give the wrong area or length
- Multiplying twice. If you measured the roof surface itself, or a satellite tool already reports sloped area, the factor is already in the number.
- Leaving out the overhang. The roof extends past the walls. Measure the plan to the edge of the eaves, not to the wall line.
- Using one factor for several pitches. Calculate each plane or section with its own pitch, then add the results.
- Reading the pitch as degrees. 6:12 is 26.57°, not 6° and not 50°. The chart shows the angle and the percent slope next to each pitch.
- Using the hip/valley factor for a common rafter. The slope factor is for common rafters and plan area. The hip/valley factor is only for a hip or valley on a regular roof.
Frequently asked questions
What is a roof pitch factor?
It is the multiplier that converts a horizontal roof measurement into a sloped one. Multiply a horizontal run by it to get the sloped length, or multiply a horizontal plan area by it to get the roof surface area. It is also called the slope factor or roof pitch multiplier.
What is the pitch factor for a 6/12 roof?
1.1180. A 6:12 roof has about 11.8% more surface than its horizontal plan. At 4:12 the factor is 1.0541, at 8:12 it is 1.2019 and at 12:12 it is 1.4142.
How do I convert roof pitch to degrees?
Divide the rise by 12 and take the arctangent. For 6:12, atan(6 ÷ 12) = 26.57°. The chart lists the angle for every pitch from 1:12 to 24:12.
What is the hip and valley factor?
It is the length of a hip or valley rafter for each unit of common-rafter run, on a regular roof with equal pitch on both planes. At 6:12 it is 1.5000, so a 12 ft common run needs a 18.00 ft hip before ridge and seat adjustments.
Do I multiply roof area I already measured on the roof by the factor?
No. The factor converts a horizontal plan measurement. If the area was measured along the roof surface, it already includes the slope. Multiply once, then add waste once.
Does the chart include waste or overhang?
No. The factors are geometric. Measure the plan to the eave edge to include overhang, and add a waste allowance that suits the roof shape and the product.