12/12 Roof Pitch: Degrees, Multiplier and What It Means
A 12/12 roof rises 12 inches for every 12 inches of run. That is 45.00°, a pitch multiplier of 1.414 and a slope of 100%. Here is what those numbers do to your roof area, your materials and your quote.
12/12 at a glance
A-frames, Tudor and Gothic revival houses, and snow country.
Nearby pitches
12 in rise per 12 in run
atan(12 ÷ 12) = 45.00°
√(12² + 12²) ÷ 12 = 1.414
12 ÷ 12 × 100 = 100%
Measured something different? The roof pitch calculator takes any rise and run, or an angle, and gives you all four numbers with the full reference chart.
Turn this pitch into a roof size
Measure the roof surface at this pitch, then price the whole job.
What a 12/12 roof pitch means
A 12/12 roof rises 12 inches for every 12 inches of run, which makes it a perfect 45 degree slope — the only common pitch where rise and run are equal. You see it on A-frames, Tudor and Gothic revival houses, and on houses built where snow needs to slide off rather than sit.
12/12 in degrees
The angle is the arctangent of rise over run:
atan(12 ÷ 12) = atan(1.0000) = 45.00°
That is the angle between the roof surface and horizontal. It is the number a smartphone level app gives you if you hold it flat against the slope, and the number to enter if a supplier asks for degrees rather than a ratio.
The 12/12 pitch multiplier
The pitch multiplier turns the flat footprint of a roof into its real sloped area. It is the hypotenuse of the rise-and-run triangle divided by the run:
√(12² + 12²) ÷ 12 = √288 ÷ 12 = 1.414
So a 2,000 square foot footprint on a 12/12 roof is about 2,830 square feet of actual roof surface, or 28.3 roofing squares before any waste allowance. Use the roof area calculator to do this for a footprint that is not a simple rectangle, and the roofing square calculator to add a waste factor and convert to squares and bundles.
How 12/12 compares with the 6:12 that cost tables assume
Published roofing cost tables are built on a 6:12 roof. The HomeGuide roof replacement cost guide states in the footnote to its cost-by-house-size table that the figures are based on a single-storey home with a 6:12 roof pitch. A 12/12 roof has 26.5% more surface than that, on the same footprint — so a table priced off your house size understates the material your roof actually needs.
| Footprint | Roof at 12:12 | Roof at 6:12 | Difference |
|---|---|---|---|
| 1,200 | 1,695 sq ft | 1,340 sq ft | +26.5% |
| 1,600 | 2,265 sq ft | 1,790 sq ft | +26.5% |
| 2,000 | 2,830 sq ft | 2,235 sq ft | +26.6% |
| 2,400 | 3,395 sq ft | 2,685 sq ft | +26.4% |
Areas are rounded to the nearest 5 square feet. These are surface-area differences only. We do not publish a percentage for the labour surcharge on steep roofs, because none of the sources this site cites puts a number on it.
Walking on a 12/12 roof
A 12/12 roof cannot be walked. At 45 degrees it needs staging, roof jacks or a harness throughout, and it falls well inside the group that the HomeGuide cost guide says requires extra safety precautions and more labour.
Slope is not a constraint at 12/12
No roofing material is excluded at 12/12 by slope. What changes is handling: heavy tile and slate become slow and awkward to set at 45 degrees, and some products call for extra fasteners on steep slopes to stop them creeping. Those are manufacturer instructions rather than code limits.
For what the finished roof costs once you know your square count, see the roof replacement cost guide, or price a specific material with the roof replacement cost calculator.
Sources
- 2024 International Residential Code, Chapter 9 — minimum slopes for asphalt shingles and the underlayment requirement below 4:12 (R905.2.2).
- HomeGuide roof replacement cost guide — the cost-by-house-size table and its 6:12 footnote, and the note that slopes over 6:12 need extra safety precautions and more labour.
- Angle, multiplier and slope percentage are computed from the pitch, not taken from a source. The arithmetic is shown above so you can check it.
Every source on this site is listed on the methodology page. Nobody involved in this site installs roofs.
Related calculators and guides
12/12 roof pitch FAQ
What is a 12/12 pitch in degrees?
Exactly 45 degrees. A 12/12 roof rises as much as it runs, so the angle is atan(1), which is 45 degrees precisely.
Why is the 12/12 pitch multiplier the square root of 2?
Because rise and run are equal. The square root of (12 squared plus 12 squared) divided by 12 simplifies to the square root of 2, or 1.4142. It is the same constant as the diagonal of a square.
Can you walk on a 12/12 roof?
No. A 45 degree slope needs staging, roof jacks or fall-arrest equipment. HomeGuide lists slopes over 6:12 as requiring extra safety precautions and more labour, and 12/12 is double that.
How much more roof is a 12/12 than a 6/12?
About 26.5 percent more surface on the same footprint. A 2,000 square foot footprint gives roughly 2,830 square feet at 12/12 against 2,235 at 6/12.