Roof Pitch Converter
Convert roof pitch between rise-per-12, degrees, percent and rafter multiplier, and get rafter length for any run.
Pitch, angle, percent and rafter length are four ways of saying the same thing. Change any one and the rest follow. Pure geometry, so it is the same in every jurisdiction.
Quick answer: roof pitch to degrees, percent and rafter multiplier
| Pitch | Angle | Percent | Rafter multiplier |
|---|---|---|---|
| 1:12 | 4.76° | 8.33% | 1.0035 |
| 2:12 | 9.46° | 16.67% | 1.0138 |
| 2.5:12 | 11.77° | 20.83% | 1.0215 |
| 3:12 | 14.04° | 25% | 1.0308 |
| 4:12 | 18.43° | 33.33% | 1.0541 |
| 5:12 | 22.62° | 41.67% | 1.0833 |
| 6:12 | 26.57° | 50% | 1.118 |
| 7:12 | 30.26° | 58.33% | 1.1577 |
| 8:12 | 33.69° | 66.67% | 1.2019 |
| 9:12 | 36.87° | 75% | 1.25 |
| 10:12 | 39.81° | 83.33% | 1.3017 |
| 12:12 | 45° | 100% | 1.4142 |
Percent = rise ÷ 12 × 100; angle = arctan(rise ÷ 12); rafter length = run × multiplier. 2½:12 is 20.83 %, whatever the code's parenthetical says; 3:12 is 25 %.
| Pitch | — |
|---|---|
| Angle | — |
| Slope | — |
| Rafter multiplier | — |
| Rafter length (for the run above) | — |
| Vertical rise over that run | — |
The IRC prints the wrong percent beside its own tile threshold. R905.3.2 sets clay and concrete tile at 2½:12 and calls it a 25-percent slope. 2.5 ÷ 12 is 20.83%. Not a rounding convention: the same sentence prints 4:12 as 33-percent, R905.2.2 prints 2:12 as 17-percent, and other sections of the same chapter (R905.4.2, R905.7.2, R905.8.2, R905.3.8, R905.10.2) print 25-percent against 3:12, which is what 25% is. The IBC's parallel provision, 1507.3.2, prints 21-percent. The error survives in both the 2018 and 2021 editions. Trust the parenthetical and you build a 3:12 roof to clear a 2½:12 minimum: half an inch of extra ridge per foot of run, 7½ inches on a 15‑foot run, for nothing. Where the two columns disagree, the ratio governs.
The cliff is at 4:12. R905.2.2 allows asphalt shingles down to 2:12, but from 2:12 up to 4:12 the deck takes two layers of underlayment. Table R905.1.1(2) spells it out: a 19‑inch strip of felt at the eave, then 36‑inch sheets lapped 19 inches, which is felt over the whole deck twice. Dropping a design from 4:12 to 3½:12 to shave ridge height buys that second layer over every square foot. Where wind design is required (Figure R301.2.1.1), two layers apply at every slope. 4:12 is also the floor for slate, R905.6.2.
Why the material order comes up short. The slope multiplier is √(rise² + 144) ÷ 12, or 1.1180 at 6:12, so the surface is 11.8% larger than the plan beneath it. That is the smaller of the two things estimators miss. Two feet of overhang on all four sides of a 40 × 30 house takes the plan from 1,200 sq ft to 44 × 34 = 1,496, up 24.7% before any pitch is applied. They compound: 1,496 × 1.1180 = 1,673 sq ft. Order against the footprint and you are 4.7 squares short.
What I check on a job
Which run I typed in, and why. Before I trust the rafter length on a real job, I check which run went in. The converter wants horizontal run, the plan dimension, and the number people reach for is often something else: a length taped along an existing roof, which is already the sloped length, or the full span of a symmetrical gable, which is twice the run of one rafter. Either mistake passes straight through the math and comes out looking reasonable. Then I check where that run starts and stops. The rafter length is for the run you entered, so the overhang is not in it unless you put it there, and a run started at the outside face of the wall is not the same run as one started at the inside face. Last, I check which column the drawing actually committed to. Sections often label a roof in rounded degrees, and a rounded angle converted back into rise per 12 can land on a pitch nobody specified.
Definitions: a 6:12 pitch rises 6 units for every 12 of horizontal run. Angle = arctan(rise / 12). Slope % = rise / 12 × 100. Rafter multiplier = √(rise² + 12²) / 12; multiply the horizontal run by it to get the sloped length. No building code is involved in the arithmetic; roofing material minimum slopes are a separate, manufacturer- and code-specific question.
Worked example
What is a 6:12 roof in degrees and percent, and how much longer is the rafter than the run?
- 6:12 is a rise of 6 for every 12 of run: 6 ÷ 12 = 0.5 = 50%.
- Angle = atan(0.5) = 26.6°.
- Rafter multiplier = √(1 + 0.5²) = 1.118: a 12 ft run needs a 13.42 ft rafter before overhangs.
26.6°, 50%, and a rafter 11.8% longer than its run. The multiplier is the number that makes a roof larger than the house beneath it.
6 values on this page were driven in a browser and compared with independently derived figures on 2026-10-29 (2808 values across 228 calculators site-wide).
Questions
What angle is a 6:12 pitch?
26.6 degrees, a 50% slope. The rafter multiplier is 1.118, so a rafter is about 12% longer than its run.
What is a 4:12 roof in degrees?
18.4 degrees, 33% slope, with a multiplier of 1.054.
Is 2½:12 a 25 percent slope?
No, 20.83%. IRC R905.3.2 prints "25-percent slope" beside its 2½:12 tile minimum, an error that survives the 2018 and 2021 editions; the IBC's 1507.3.2 prints 21-percent. Where the ratio and the percent disagree, the ratio governs.
What changes below 4:12?
The underlayment. IRC R905.2.2 allows asphalt shingles down to 2:12, but from 2:12 up to 4:12 the deck takes two layers (Table R905.1.1(2)). 4:12 is also the floor for slate, R905.6.2.