Measuring & pitch
Roof pitch explained: ratios, degrees and the pitch factor
Pitch is written four ways and used in almost every roofing calculation. One right triangle explains all of it.
One triangle
Take any roof plane and look at it from the gable end. Between the top of the wall and the ridge there is a right triangle: the horizontal side is the run, the vertical side is the rise, and the sloping side is the rafter, or the roof surface. Every way of writing pitch, and every multiplier this site uses, is a ratio of two sides of that triangle.
In the United States pitch is written as the rise per 12 inches of run: a 6/12 roof rises 6 inches for every foot it runs horizontally. Plans draw it as a small triangle with the 12 on the long side. Everywhere else, and on many inclinometer apps, pitch is an angle in degrees. Civil and flat-roof drawings use percent slope, rise ÷ run × 100. And older carpentry books use “pitch” for rise over the whole span, so a “quarter pitch” is 6/12 (6 inches of rise per 24 inches of span).
The pitch factor, the number that does the work
The pitch factor is the length of the sloping side divided by the run: how much longer the roof is than its plan. Multiply a horizontal footprint by it and you get the roof area; multiply a rafter’s run by it and you get the rafter’s line length. That is why the roof area calculator and the rafter length calculator both start by computing it.
| Pitch | Angle | Slope | Pitch factor | Hip factor | What it means |
|---|---|---|---|---|---|
| 2/12 | 9.5° | 16.7% | 1.0138 | 1.4240 | The lowest pitch for shingles, with double underlayment |
| 4/12 | 18.4° | 33.3% | 1.0541 | 1.4530 | Standard underlayment from here up; easy to walk |
| 6/12 | 26.6° | 50% | 1.1180 | 1.5000 | The most common US pitch |
| 8/12 | 33.7° | 66.7% | 1.2019 | 1.5635 | Steep: roof jacks and fall protection |
| 10/12 | 39.8° | 83.3% | 1.3017 | 1.6415 | Very steep: worked from staging |
| 12/12 | 45° | 100% | 1.4142 | 1.7321 | A 45° roof; priced as a wall |
The factor grows slowly at first and fast later: 4/12 adds 5 percent to the plan, 6/12 adds 12, 12/12 adds 41. The pitch factor calculator gives it for any pitch, and the pitch factor table lists every common one.
Converting a phone reading
An inclinometer app on the rake board reads 35 degrees.
- Rise per 12: tan 35° × 12 = 8.4, so about 8½/12
- Slope: 70%
- Pitch factor: 1 ÷ cos 35° = 1.221
- A 2,000 sq ft footprint under this roof is 2,000 × 1.221 = 2,442 sq ft of roofing
The pitch calculator does the conversion in any direction.
Why hips have their own factor
A hip rafter runs diagonally across the plan, from the corner of the building to the ridge, at 45 degrees to the walls. For every foot the common rafters run, the hip runs √2 feet, about 17 inches, while rising the same amount. Its length per foot of common run is therefore √(rise² + 12² + 12²) ÷ 12, which is 1.5 at 6/12 against the common rafter’s 1.118.
The same geometry explains why carpenters write hip pitch as “6 in 17”: the hip rises 6 inches per 16.97 inches of its own run, a flatter 19.5 degrees. The hip and valley rafter calculator uses it for the plumb cut, and the hip factor gives the hip lengths for ridge cap and valley materials.
How pitch changes materials
Pitch is not only a multiplier; it decides what can go on the roof.
- Below 2/12 asphalt shingles are not allowed (IRC R905.2.2). Use a membrane, or metal with sealed laps; the flat roof membrane calculator covers it.
- From 2/12 to 4/12 shingles need double-coverage underlayment (IRC R905.1.1), which halves the coverage of each roll.
- From 4/12 up single-coverage underlayment is enough, and most tile and slate begin here.
- Above 21/12 shingle makers require six nails per shingle and hand-sealing.
Pitch also sets the ice barrier: the code’s 24 inches inside the wall is horizontal, so on a steeper roof the same requirement runs further up the deck.
How pitch changes labor
Up to about 6/12 a roof can be walked; from 7/12 to 9/12 crews work from roof jacks with harnesses; above that they work from staging. Estimators add roughly 30 and 60 percent to labor for those bands, which is why the labor cost calculator asks for the pitch. OSHA treats any roof over 4/12 as steep for fall protection purposes, and the guide to ladders and roof safety covers what that means for anyone getting on one.
Metric pitch and the same roof
In countries that use degrees, a “30-degree roof” is the standard reference, and it sits between 6/12 and 7/12. Nothing in the arithmetic changes: the pitch factor is 1 ÷ cos(angle), so a 30-degree roof has a factor of 1.155, and a footprint of 150 square metres under it is 173 square metres of roofing. When a plan gives a pitch in degrees and a product’s instructions give a minimum in rise per 12, convert one to the other before comparing; a 15-degree roof is 3.2/12, below the 4/12 most tile and standard shingle installations need.
Reading pitch without measuring
On a plan, the pitch triangle sits beside each roof plane. In a photo taken square to a gable, measure the gable’s height and half its width on the screen in any unit: their ratio times 12 is the pitch. And on an existing roof, the measuring guide shows how to take it with a level from a rake board.