A 6/12 roof is 11.8% bigger than the house under it.
That percentage is the slope factor, and it is the number that decides whether your order is right. Pitch in — factor, angle, grade, and the real area above any footprint.
6/12 pitch
Under 8/12 — you could walk it
What the code says about this pitch
At 4:12 and above, asphalt shingles go on with single underlayment under IRC R905.2.2.
Now put it on a real roof
The slope factor is the first half of a takeoff. The second half is what to order — bundles, underlayment, starter, cap, nails — and that needs the edges as well as the area.
Run the full takeoff →Every pitch, converted
| Pitch | Slope factor | Angle | Grade | On the roof |
|---|---|---|---|---|
| 1/12 | 1.0035 | 4.8° | 8% | you could walk it |
| 2/12 | 1.0138 | 9.5° | 17% | you could walk it |
| 3/12 | 1.0308 | 14.0° | 25% | you could walk it |
| 4/12 | 1.0541 | 18.4° | 33% | you could walk it |
| 5/12 | 1.0833 | 22.6° | 42% | you could walk it |
| 6/12 | 1.1180 | 26.6° | 50% | you could walk it |
| 7/12 | 1.1577 | 30.3° | 58% | you could walk it |
| 8/12 | 1.2019 | 33.7° | 67% | roof jacks needed |
| 9/12 | 1.2500 | 36.9° | 75% | roof jacks needed |
| 10/12 | 1.3017 | 39.8° | 83% | roof jacks needed |
| 11/12 | 1.3566 | 42.5° | 92% | staging and harnesses |
| 12/12 | 1.4142 | 45.0° | 100% | staging and harnesses |
| 14/12 | 1.5366 | 49.4° | 117% | staging and harnesses |
| 16/12 | 1.6667 | 53.1° | 133% | staging and harnesses |
| 18/12 | 1.8028 | 56.3° | 150% | staging and harnesses |
| 20/12 | 1.9437 | 59.0° | 167% | staging and harnesses |
| 24/12 | 2.2361 | 63.4° | 200% | staging and harnesses |
Pitch inputs
Pitch
- Pitch
- 6/12
- Rise over run
- 6 in 12
- Slope factor
- 1.1180×
- Angle
- 26.57°
- Grade
- 50.0%
The formula
A pitch is written rise in 12: a 6/12 roof climbs 6 inches for every 12 inches it travels horizontally. The slope factor is the hypotenuse of that triangle divided by its run, which is the ratio between the sloped surface and its shadow on the ground. For 6/12 that is √(6² + 12²) ÷ 12 = 13.416 ÷ 12 = 1.1180.
How the slope factor is computed, and why it is one shared function
It is computed with Math.hypot rather than Math.sqrt(rise*rise + run*run). That is not fussiness: squaring first underflows to zero for very small values and overflows to infinity for very large ones, and a slope factor of zero turns a whole roof into no roof. The same factor is used by the takeoff, the bid calculator and the replacement-cost estimator — one function, so no two pages on this site can disagree about what a 6/12 roof measures.
Grade and angle are not the same number, and the confusion is common enough to be worth stating. A 12/12 roof is a 100% grade and a 45° angle. A 6/12 is a 50% grade but 26.6°, not 25. Grade is a ratio; the angle is its arctangent.
A 40 × 30 house at 6/12
- Footprint
- 40 ft × 30 ft = 1,200 sq ft
- Pitch
- 6/12
- Slope factor. √(6² + 12²) ÷ 12 = √180 ÷ 12 = 13.4164 ÷ 12 = 1.1180.
- Angle. arctan(6 ÷ 12) = arctan(0.5) = 26.6°.
- Grade. (6 ÷ 12) × 100 = 50%.
- Roof area. 1,200 sq ft × 1.1180 = 1,341.6 sq ft, which is 13.42 squares.
- What it cost you to skip. Ordering off the 1,200 is 12 squares, not 13.42 — one and a half squares short, which on architectural shingles at 3 bundles a square is four and a half bundles. That is a second trip to the supplier in the middle of a tear-off.
1.1180 slope factor, 26.6°, 50% grade. The roof is 1,342 sq ft over a 1,200 sq ft footprint — 11.8% more roof than house.
Figures from The pitch and area maths, with every factor listed; Turn this into bundles, rolls and nails.