Roof pitch, rafter length, and what each slope may carry
Pitch is a ratio — rise over a 12-inch run — and the ratio alone gives you the angle and the length of rafter each foot of run takes. What it will not tell you is how far that rafter is allowed to reach, or whether the covering you had in mind may be laid on that slope. Both of those are in the 2021 International Residential Code, and both are on these pages, cited to the section.
Every whole-inch pitch
The angle, the grade, and the rafter length each foot of run takes — all three follow from the rise-over-12 ratio, so they hold on any roof at that pitch. The last column is how many of the 13 roof covering entries in 2021 IRC R905 clear their own minimum slope at that pitch.
| Pitch | Angle | Grade | Rafter per ft of run | Rafter over a 12 ft run | Coverings permitted |
|---|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.0035 | 12’0½” | 5 of 13 |
| 2/12 | 9.46° | 16.7% | 1.0138 | 12’2” | 7 of 13 |
| 3/12 | 14.04° | 25% | 1.0308 | 12’4⅜” | 12 of 13 |
| 4/12 | 18.43° | 33.3% | 1.0541 | 12’7¾” | 13 of 13 |
| 5/12 | 22.62° | 41.7% | 1.0833 | 13’0” | 13 of 13 |
| 6/12 | 26.57° | 50% | 1.1180 | 13’5” | 13 of 13 |
| 7/12 | 30.26° | 58.3% | 1.1577 | 13’10¾” | 13 of 13 |
| 8/12 | 33.69° | 66.7% | 1.2019 | 14’5⅛” | 13 of 13 |
| 9/12 | 36.87° | 75% | 1.2500 | 15’0” | 13 of 13 |
| 10/12 | 39.81° | 83.3% | 1.3017 | 15’7½” | 13 of 13 |
| 11/12 | 42.51° | 91.7% | 1.3566 | 16’3⅜” | 13 of 13 |
| 12/12 | 45.00° | 100% | 1.4142 | 16’11⅝” | 13 of 13 |
Angles are to the nearest hundredth of a degree, rafter lengths to the nearest eighth of an inch. A rafter length is the sloping distance over that run and nothing more: no overhang, and no allowance for how the rafter meets the ridge.
Minimum slope by roof covering
Chapter 9 of the 2021 IRC gives every roof covering a minimum slope, stated the same way a pitch is — a rise over 12 units of run. Membranes and standing-seam metal go nearly flat; slate shingles want the steepest roof in the chapter. The right-hand column is the shallowest whole-inch pitch that clears each minimum.
| Roof covering | Minimum slope | Section | Clears at |
|---|---|---|---|
| Built-up roofs | ¼:12 | R905.9.1 | 1/12 |
| Metal roof panels — standing seam | ¼:12 | R905.10.2 | 1/12 |
| Membrane roofs — modified bitumen, thermoset and thermoplastic single-ply, sprayed polyurethane foam, liquid-applied | ¼:12 | R905.11.1, R905.12.1, R905.13.1, R905.14.1 and R905.15.1 | 1/12 |
| Metal roof panels — lapped, nonsoldered seam with lap sealant | ½:12 | R905.10.2 | 1/12 |
| Mineral-surfaced roll roofing | 1:12 | R905.5.2 | 1/12 |
| Asphalt shingles | 2:12 | R905.2.2 | 2/12 |
| Photovoltaic shingles | 2:12 | R905.16.2 | 2/12 |
| Clay and concrete roof tile | 2½:12 | R905.3.2 | 3/12 |
| Metal roof shingles | 3:12 | R905.4.2 | 3/12 |
| Metal roof panels — lapped, nonsoldered seam without lap sealant | 3:12 | R905.10.2 | 3/12 |
| Wood shingles | 3:12 | R905.7.2 | 3/12 |
| Wood shakes | 3:12 | R905.8.2 | 3/12 |
| Slate shingles | 4:12 | R905.6.2 | 4/12 |
Minimum slopes as stated in the 2021 IRC R905 sections named on each row. chapter source
Two of those sections carry a second slope rule as well: R905.2.2 puts asphalt shingles from 2:12 through 4:12 under a double-underlayment requirement (R905.1.1), and R905.3.2 puts clay and concrete roof tile from 2½:12 through 4:12 under a double-underlayment requirement (R905.3.3). Each pitch page says whether that band takes in the pitch you are standing on.
The R802 rules that turn on pitch
R802.4.1 rafter size. Rafters are sized on the spans in the R802.4.1 tables, and a rafter span is measured along the horizontal projection of the rafter — the run, not the sloping stick.
R802.4.4 rafter supports. Below a 3:12 pitch, the members carrying rafters — ridges, hips and valleys — are designed as beams rather than sized off a table, with bearing provided for the rafters per R802.6.
The first of those is why this site's rafter pages and these pitch pages fit together: a span in the R802.4.1 tables is a horizontal distance, and the pitch multiplier is what turns it into the length of the stick. Every species, grade, and spacing in both tables the site carries is on the rafter span pages. Point loads, cantilevers beyond the table footnotes, unusual snow loads, or anything else outside the table's stated conditions — that's an engineer's question. chapter source
Ordering the roof off the same multiplier
The multiplier in the table above is also what turns a footprint into a quantity of roofing: how much surface is up there, how many panels cross the eave, and how long each one has to be. That arithmetic, plus the minimum slope R905 gives each kind of metal roof, is on figuring metal roofing.
Every pitch, page by page
Each page carries the pitch drawn to scale, rafter lengths for runs from 4 to 24 feet, the rafter spans the two 2021 IRC tables list at 16-inch centers with the stick length each one works out to, and the R905 coverings split into what that slope may carry and what it may not.
1/12 pitch · 2/12 pitch · 3/12 pitch · 4/12 pitch · 5/12 pitch · 6/12 pitch · 7/12 pitch · 8/12 pitch · 9/12 pitch · 10/12 pitch · 11/12 pitch · 12/12 pitch
Common questions
What is a roof pitch?
The rise of the roof over a fixed 12 inches of run, written as a ratio: a 6/12 roof climbs 6 inches for every 12 inches it travels horizontally. Everything else about the slope follows from that one ratio — the angle (26.57° at 6/12), the grade (50%), and the rafter length (1.1180 feet of rafter per foot of run).
How do you work out rafter length from a roof pitch?
Multiply the horizontal run by the pitch multiplier — the hypotenuse of the rise-and-12 triangle. At 6/12 that multiplier is 1.1180, so a 12-foot run carries 13’5” of rafter. The multiplier for every whole-inch pitch is in the table on this page, and each pitch page runs it out to a length for runs from 4 to 24 feet.
Does roof pitch change how far a rafter can span?
Not in the tables. R802.4.1 measures a rafter span along the horizontal projection of the rafter, so the 14’2” 2021 IRC Table R802.4.1(3) lists for a 2×8 Southern pine No. 2 at 16-inch centers is 14’2” of run at any pitch. What the pitch changes is how much stick that run takes: 15’10⅛” at 6/12. Pitch does change which structural members need designing rather than sizing — see R802.4.4 below.
What is the lowest slope a roof covering can go on?
It depends entirely on the covering, and the 2021 IRC states a minimum for each one. Built-up roofs go as low as ¼:12 (R905.9.1); slate shingles are the steepest ask in R905 at 4:12 (R905.6.2). The full list is on this page, and each pitch page splits it into what that slope may carry and what it may not.