Understanding your result
The headline is the pitch factor, with the pitch in both notations and the hip and valley factor beneath it. The stats repeat the two factors and the angle and, if you entered a footprint, the roof area it gives. The table writes the factors with their formulas, converts your footprint and run, and then lists the factors for fourteen common pitches so you can see where yours sits.
The pitch factor is what the roof area calculator multiplies the footprint by and what the rafter length calculator multiplies the run by. The hip and valley factor is what the hip and valley rafter calculator uses, and what the hip length in the ridge cap calculator comes from. If you only need one number from this site to carry around, it is the pitch factor for your roof.
How we calculate this
The pitch factor comes from the right triangle of run, rise and rafter: the rafter is the hypotenuse, so its length per 12 inches of run is √(12² + rise²), and dividing by 12 gives the factor. The hip factor comes from a second triangle lying across the first: the hip’s run is the diagonal of a 12 by 12 square, 16.97 inches, for the same rise, so its length per foot of common run is √(16.97² + rise²) ÷ 12. That is why the hip factor is always larger than the pitch factor, and why it never drops below √2 even on a flat roof.
The common-pitch table at the bottom of the result is the printed table most roofers carry, computed live. The pitch factor reference page has the full table with degrees, percent and walkability notes.
The assumptions behind the numbers
| Assumption | Default | Where it comes from |
|---|---|---|
| Pitch notation | rise per 12 in of run | US plan convention; degrees in metric mode |
| Regular hip | 45° in plan | The hip factor assumes two planes of equal pitch meeting at a right-angled corner |
| Footprint | 1,768 sq ft (optional) | A 52 × 34 ft footprint, the site’s example house |
| Run | 12 ft (optional) | Half of a 24-ft span |
| Common pitches listed | 2/12 to 24/12 | The range of pitches found on houses, from low-slope to mansard |
Assumptions last reviewed October 7, 2026.
The calculator does not handle irregular hips (two planes of different pitch), for which the hip’s run is not the plan diagonal, and it reports factors, not quantities: squares with waste come from the roof area calculator and bundles from the shingle calculator. The guide roof pitch explained covers where the factors come from and how to read pitch off a plan, a photo or a level.
Two worked examples
A 6/12 roof over a 52 by 34 foot footprint
Pitch 6/12, footprint 1,768 square feet, run 12 feet.
- Pitch factor: √(1 + 0.25) = 1.1180
- Hip and valley factor: √(36 + 288) ÷ 12 = 1.5000
- Roof area: 1,768 × 1.118 = 1,977 sq ft (19.8 squares)
- Rafter line length: 12 × 1.118 = 13.42 ft
- Hip length: 12 × 1.5 = 18 ft
Every foot of run is 13.42 inches of rafter and 18 inches of hip. The hip on this roof is a third longer than the common rafter beside it.
A 30-degree roof in metric practice
Pitch 30 degrees, footprint 2,400 square feet, run 15 feet.
- Rise per 12: tan 30° × 12 = 6.93/12
- Pitch factor: 1 ÷ cos 30° = 1.1547
- Hip and valley factor: 1.5275
- Roof area: 2,400 × 1.1547 = 2,771 sq ft (27.7 squares)
- Rafter: 15 × 1.1547 = 17.32 ft; hip: 15 × 1.5275 = 22.91 ft
Thirty degrees sits between 6/12 and 7/12. Its factor is 15.5 percent, so a footprint under a 30-degree roof carries 15.5 percent more roofing than the plan shows.
Where to find your inputs
Pitch. From a level and ruler on a rake board (rise in inches over a 12-inch run), from the triangle on the plans, or from an inclinometer app in degrees; the pitch calculator converts any of them.
Footprint. Length times width of the building at the eaves, overhangs included; the roof area calculator builds it from the dimensions.
Run. Horizontal distance from the outside of the wall to the centre of the ridge; half the span on a symmetrical roof.
Common mistakes
- Multiplying by the rise instead of the factor. A 6/12 roof is not 50 percent bigger; it is 11.8 percent bigger. The factor is the hypotenuse ratio, not the rise ratio.
- Using the pitch factor for hips and valleys. They need the hip and valley factor, which is a third larger at 6/12.
- Applying the factor to a vertical dimension. It converts horizontal to sloped. Rise is already vertical.
- Reading the wrong row of a printed table. Printed tables mix “per foot of run” (inches) with “factor” (ratio). This calculator shows both.
- Interpolating between table rows. For 5.5/12 or 31 degrees, enter the exact pitch; the formula does not need a table.
- Assuming one factor for a mixed-pitch roof. Each pitch has its own. Run the porch separately.
Questions people ask
- What is the roof pitch factor?
- The pitch factor (also called the slope factor or roof pitch multiplier) is the ratio of the sloped length of a roof plane to its horizontal run, √(1 + (rise ÷ 12)²). At 6/12 it is 1.1180: every foot of horizontal run is 1.118 feet of rafter, and every square foot of footprint is 1.118 square feet of roof. Multiply any horizontal measurement by it to get the sloped one.
- What is the pitch factor for common roof pitches?
- 3/12 is 1.0308, 4/12 is 1.0541, 5/12 is 1.0833, 6/12 is 1.1180, 7/12 is 1.1577, 8/12 is 1.2019, 9/12 is 1.2500, 10/12 is 1.3017, 12/12 is 1.4142 and 18/12 is 1.8028. The calculator lists these with their hip factors under any pitch you enter.
- What is the hip and valley factor?
- A hip or valley rafter on a regular roof runs diagonally across the plan, 16.97 inches for every 12 inches of common run, while rising the same 6 inches on a 6/12 roof. Its length per foot of common run is √(rise² + 12² + 12²) ÷ 12: 1.5000 at 6/12, 1.5635 at 8/12, 1.7321 at 12/12. Multiply the common run by it for the hip or valley length.
- How do I use the pitch factor to find roof area?
- Multiply the horizontal footprint under the roof, overhangs included, by the factor. A 1,768 square foot footprint at 6/12 is 1,768 × 1.118 = 1,977 square feet of roof, 19.8 squares. The roof area calculator does the whole chain from the building dimensions; this page is the factor on its own.
- Can I use the pitch factor for a metric roof in degrees?
- Yes. The factor is 1 ÷ cos(angle), which is the same number: 30 degrees gives 1.1547, and the calculator shows the equivalent 6.93/12. Enter the pitch in degrees and a footprint in square metres and the roof area comes out in square metres.
- Why is the factor only 1.118 at 6/12 when the roof looks much bigger?
- Because the roof only grows along the slope, not along the ridge. A 6/12 plane is 11.8 percent longer from eave to ridge than its run, and no longer along the eave, so the area grows 11.8 percent. What makes roofs look big is the overhang and the height, not the pitch, until the pitch gets to 10/12 and above, where the factor passes 1.3.