Four ways of saying the same angle
Roofers say 6/12. Surveyors say 26.57 degrees. Highway and drainage people say 50 percent. Framing tables say a unit line length of 13.416 inches per foot of run. They are all the same slope described in different units, and converting between them is one line of trigonometry each way.
| From | To X-in-12 |
|---|---|
| Degrees | X = tan(degrees) x 12 |
| Percent slope | X = percent / 100 x 12 |
| Measured rise and run | X = rise / run x 12 |
Going the other way, degrees is the arctangent of X over 12, percent is X over 12 times a hundred, and the area multiplier is the square root of X squared plus 144, over 12. The one that people get wrong most often is percent, because 100 percent slope sounds like vertical and is actually 45 degrees.
| Pitch | Degrees | Percent | Multiplier | Common name |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.0035 | Low slope |
| 2/12 | 9.46° | 16.7% | 1.0138 | Shingle minimum on most products |
| 3/12 | 14.04° | 25.0% | 1.0308 | Shallow |
| 4/12 | 18.43° | 33.3% | 1.0541 | Conventional lower limit |
| 6/12 | 26.57° | 50.0% | 1.1180 | The most common residential pitch |
| 8/12 | 33.69° | 66.7% | 1.2019 | Steep, jacks usual |
| 10/12 | 39.81° | 83.3% | 1.3017 | Very steep |
| 12/12 | 45.00° | 100.0% | 1.4142 | Not walkable |
| 18/12 | 56.31° | 150.0% | 1.8028 | Steeple, tower, mansard face |
Rafter line length, and the cuts this does not give you
Multiply the horizontal run by the multiplier and you have the rafter line length: the distance along the top edge of the rafter from the outside of the plate to the centre of the ridge. That is the theoretical length, and it is where every rafter calculation starts, but it is not a cut list. Off it you still have to subtract half the ridge thickness measured perpendicular to the plumb cut, decide the height above plate at the birdsmouth, and add the tail beyond the plate for the overhang. On a hip or valley rafter the run is the diagonal of the plan square rather than the side of it, so the unit line length becomes the square root of X squared plus 288, over 12, and the backing bevel is a separate problem again.
None of that changes the multiplier. The multiplier answers area and length along the plane. The cuts answer where the wood stops, and they need a real plan.
The pitch bands, and what actually sets them
Pitch decides three practical things: whether water leaves the roof faster than wind can drive it back under the courses, whether a person can stand on it, and which covering is allowed. The first is physics, the second is your boots and your nerve, and the third is written down by other people.
Asphalt shingles are commonly rated down to 2:12 with a special low-slope detail and down to 4:12 as ordinary installation, but that is a description of what most manufacturers publish, not a rule that holds everywhere. Which pitch a given shingle is approved for, what underlayment it needs at that pitch, and whether your jurisdiction has adopted a version of the code that says something different are all things to check against the wrapper and the building department. Below the shingle range you are into standing seam, single-ply membrane, modified bitumen or a soldered flat roof, and those are different trades with different details.
Walkability is not code, it is judgement. Around 6/12 most people in clean-soled boots can work on a dry roof. By 8/12 nearly everyone wants roof jacks and planks. By 10/12 the roof is a surface you are attached to rather than standing on, and above 12/12 it stops being a walking surface at all. Frost, dew, moss, loose granules from an old roof and a light dusting of sawdust each move that assessment a full step steeper than the number suggests.
Questions people ask
What is a 6/12 pitch in degrees?
26.57 degrees. The arctangent of 6 divided by 12 is 26.565 degrees, which rounds to 26.6 for any practical purpose. Its percent slope is 50 percent, and its area multiplier is 1.1180, so a 6/12 roof has 11.8 percent more surface than the footprint under it. That is the most common residential pitch in a lot of North America, which is why those three numbers are worth remembering.
What pitch is 45 degrees?
Exactly 12/12, and exactly 100 percent slope. It is the only pitch where all three notations line up on a round number, and the multiplier is the square root of 2, or 1.41421. A 45 degree roof has 41.4 percent more surface area than the plan area beneath it, and it is comfortably past the point where anyone should be walking on it without being tied off.
What is the minimum roof pitch for shingles?
Most asphalt shingle manufacturers publish 2:12 as the absolute minimum, with a low-slope installation that usually means a doubled underlayment or a self-adhered membrane over the whole deck, and 4:12 as the pitch above which normal installation applies. Those are the common published figures rather than a universal rule. What governs your roof is the code edition your jurisdiction has adopted and the installation instructions for the specific product, which is also what the warranty is written against. Below 2:12, shingles are the wrong covering regardless of what anyone allows.
How do I convert percent slope to roof pitch?
Multiply the percent by 12 and divide by 100. A 33 percent slope is 33 x 12 / 100, which is 3.96, so effectively 4/12. Going the other way, divide the rise by 12 and multiply by 100: a 9/12 roof is 75 percent. The confusion comes from percent slope being borrowed from road and drainage work, where a 6 percent grade is steep. On a roof, 6 percent is barely more than 3/4 in 12 and is not a roof pitch at all.
Does the slope multiplier apply to underlayment and sheathing too?
Yes, to anything measured on the plane of the roof. Sheathing, underlayment, ice barrier, shingles and the labour to install them all scale with the sloped area, so they all take the multiplier. What does not take it is anything measured horizontally, such as the ridge length, the eave length, or the plan area of a dormer opening. Rake length does take it, because the rake runs up the slope. Getting the eave and the rake the right way round is worth checking, since on a steep roof the rake is meaningfully longer than the horizontal distance it covers.