5/12 Roof Pitch: Degrees, Multiplier and What It Means
A 5/12 roof rises 5 inches for every 12 inches of run. That is 22.62°, a pitch multiplier of 1.083 and a slope of 41.7%. Here is what those numbers do to your roof area, your materials and your quote.
5/12 at a glance
Modern subdivisions, two-storey colonials and most builder-grade housing.
Nearby pitches
5 in rise per 12 in run
atan(5 ÷ 12) = 22.62°
√(5² + 12²) ÷ 12 = 1.083
5 ÷ 12 × 100 = 41.7%
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 5/12 roof pitch means
A 5/12 roof rises 5 inches for every 12 inches of run. It is one of the most common pitches on American housing built in the last forty years, sitting just below the 6:12 that cost tables use as their reference. It is also the only common pitch whose numbers come out exactly.
5/12 in degrees
The angle is the arctangent of rise over run:
atan(5 ÷ 12) = atan(0.4167) = 22.62°
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 5/12 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:
√(5² + 12²) ÷ 12 = √169 ÷ 12 = 1.083
So a 2,000 square foot footprint on a 5/12 roof is about 2,165 square feet of actual roof surface, or 21.6 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 5/12 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 5/12 roof has 3.1% less surface than that, on the same footprint — so a table priced off your house size slightly overstates the material your roof needs.
| Footprint | Roof at 5:12 | Roof at 6:12 | Difference |
|---|---|---|---|
| 1,200 | 1,300 sq ft | 1,340 sq ft | -3.0% |
| 1,600 | 1,735 sq ft | 1,790 sq ft | -3.1% |
| 2,000 | 2,165 sq ft | 2,235 sq ft | -3.1% |
| 2,400 | 2,600 sq ft | 2,685 sq ft | -3.2% |
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 5/12 roof
A 5/12 roof is comfortably walkable. At 22.62 degrees it is below the slope at which the HomeGuide cost guide says extra safety precautions and extra labour begin.
Everything is rated for 5/12
5/12 is above the IRC’s 4:12 line, so standard single-layer underlayment applies and there are no slope-driven restrictions on any mainstream product. Asphalt shingles, metal panels, synthetic slate and concrete tile are all rated well below this pitch. If a material is ruled out on a 5/12 roof it will be for weight or for cost, not for slope.
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
5/12 roof pitch FAQ
What is a 5/12 pitch in degrees?
22.62 degrees. The arithmetic is atan(5 divided by 12), which is atan(0.4167).
Why is the 5/12 pitch multiplier exactly 13/12?
Because 5, 12 and 13 form a Pythagorean triple. The square root of (5 squared plus 12 squared) is the square root of 169, which is exactly 13. So the multiplier is 13 divided by 12, or 1.0833 recurring. No other common roof pitch works out to a whole number like this.
Is a 5/12 roof steep?
No. It is a moderate pitch, just under the 6:12 that published cost tables assume and well under the slope where roofers add staging and fall protection.
How much roof surface does a 5/12 pitch add?
About 8.3 percent over the flat footprint. A 2,000 square foot footprint gives roughly 2,165 square feet of roof.