How to read the chart
Each row is one pitch, written as inches of rise per 12 inches of level run. The columns give the same steepness as an angle in degrees and as a slope percentage, then two numbers for framing. The rafter multiplier turns level run into sloped length: multiply a common rafter's run by it. Per foot of run is the same multiplier in inches of rafter per 12 inches of run, the figure printed on a framing square's rafter table. Thehip/valley factor does the same job for hip and valley rafters on a regular hip roof.
The small triangles are drawn to scale, so you can hold the printed chart up against a roof from the ground and compare. Use the Print the chart button. The site header, ads and the calculator controls are left off the printout.
Roof pitch chart: 1/12 to 24/12
| Pitch | Shape | Angle | Slope | Rafter multiplier | Per foot of run | Hip/valley factor |
|---|---|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.003 | 12.04 in | 1.417 | |
| 2/12 | 9.46° | 16.7% | 1.014 | 12.17 in | 1.424 | |
| 3/12 | 14.04° | 25% | 1.031 | 12.37 in | 1.436 | |
| 4/12 | 18.43° | 33.3% | 1.054 | 12.65 in | 1.453 | |
| 5/12 | 22.62° | 41.7% | 1.083 | 13 in | 1.474 | |
| 6/12 | 26.57° | 50% | 1.118 | 13.42 in | 1.5 | |
| 7/12 | 30.26° | 58.3% | 1.158 | 13.89 in | 1.53 | |
| 8/12 | 33.69° | 66.7% | 1.202 | 14.42 in | 1.563 | |
| 9/12 | 36.87° | 75% | 1.25 | 15 in | 1.601 | |
| 10/12 | 39.81° | 83.3% | 1.302 | 15.62 in | 1.641 | |
| 11/12 | 42.51° | 91.7% | 1.357 | 16.28 in | 1.685 | |
| 12/12 | 45° | 100% | 1.414 | 16.97 in | 1.732 | |
| 13/12 | 47.29° | 108.3% | 1.474 | 17.69 in | 1.781 | |
| 14/12 | 49.4° | 116.7% | 1.537 | 18.44 in | 1.833 | |
| 15/12 | 51.34° | 125% | 1.601 | 19.21 in | 1.887 | |
| 16/12 | 53.13° | 133.3% | 1.667 | 20 in | 1.944 | |
| 17/12 | 54.78° | 141.7% | 1.734 | 20.81 in | 2.002 | |
| 18/12 | 56.31° | 150% | 1.803 | 21.63 in | 2.062 | |
| 19/12 | 57.72° | 158.3% | 1.873 | 22.47 in | 2.123 | |
| 20/12 | 59.04° | 166.7% | 1.944 | 23.32 in | 2.186 | |
| 21/12 | 60.26° | 175% | 2.016 | 24.19 in | 2.25 | |
| 22/12 | 61.39° | 183.3% | 2.088 | 25.06 in | 2.315 | |
| 23/12 | 62.45° | 191.7% | 2.162 | 25.94 in | 2.382 | |
| 24/12 | 63.43° | 200% | 2.236 | 26.83 in | 2.449 |
Worked example: hip rafter on a 9/12 roof
A 24 ft wide hip roof at 9/12 has a common run of 12 ft. From the 9/12 row, the rafter multiplier is1.25 and the hip/valley factor is 1.601.
- Common rafter (to ridge centre) = 12 × 1.25 = 15 ft. A 9/12 roof is a 3-4-5 triangle: rise 9, run 12, rafter 15.
- Hip rafter (to ridge centre) = 12 × 1.601 = 18.75 ft, from √(9² + 288) ÷ 12 = √369 ÷ 12 = 1.601.
- Roof angle = 36.87°, slope 75%.
Both lengths are before the ridge allowance and overhang. The rafter length calculator handles those for common rafters.
Using the chart without a calculator
On site, the chart answers the common questions by looking along one row. Say a phone inclinometer reads33.7° on a rafter. The nearest angle in the chart is 33.69°, the 8/12 row. Reading across: slope 66.7%, rafter multiplier 1.202, 14.42 in of rafter per foot of run.
To get a rafter length, multiply the run by the per-foot figure. With an 11 ft run at 8/12: 11 × 14.42 in =158.6 in, or about 13 ft 2 5/8 in, to the ridge centre. To get roof area, multiply the footprint by the multiplier. A 1,000 sq ft footprint at 8/12 is about 1,202 sq ft of roof. For readings between rows, type the exact pitch into the lookup above; the chart highlights the nearest row.
Where the numbers come from
Angle = arctan(pitch ÷ 12). Slope = pitch ÷ 12 × 100. Rafter multiplier = √(pitch² + 144) ÷ 12. Hip/valley factor = √(pitch² + 288) ÷ 12. The 288 is 2 × 12²: a hip crosses the corner of a square plan at 45°, so it runs 12√2 ≈ 16.97 inches for every 12 inches of common run. The roof pitch calculator uses the same formulas if you want them with your own numbers filled in.
Pitches worth knowing
- 2/12 — the lowest slope the 2021 IRC allows for asphalt shingles, with double underlayment.
- 4/12 — below this, asphalt shingles need double underlayment under the 2021 IRC.
- 4/12 for slate — the minimum slope the 2021 IRC allows for slate.
- 9/12 — a 3-4-5 triangle, handy for checking a framing square or a measurement.
- 12/12 — 45°, rafter multiplier √2.
For every covering's minimum see the minimum roof pitch guide. To find your own roof's pitch, see how to measure roof pitchor use the roof pitch calculator. To turn pitch into material, use theroofing squares calculator.
Common mistakes
- Using the common multiplier for a hip. The hip runs farther in plan, so it needs the hip/valley factor, not the common rafter multiplier.
- Reading the wrong run. All factors are per unit of common run, which is half the span on a symmetrical roof.
- Treating slope % as degrees. A 100% slope is 45°.
Frequently asked questions
What is the angle of a 6/12 pitch roof?
26.57°. A 6/12 roof rises 6 inches per 12 inches of run, and arctan(6 ÷ 12) = 26.57°. Its slope is 50% and its rafter multiplier is 1.118.
How many degrees is a 4/12 pitch?
18.43°, a 33.3% slope. It is the point below which the 2021 IRC requires double underlayment for asphalt shingles.
What pitch is a 45 degree roof?
12/12. The rise equals the run, so the slope is 100% and the rafter multiplier is √2 = 1.414.
What is a hip/valley factor?
On a regular hip roof (all sides the same pitch), the hip rafter runs diagonally, 16.97 inches for every 12 inches of common run. The factor √(pitch² + 288) ÷ 12 converts the common run into the hip or valley rafter length. For 6/12 it is 1.5, or 18 inches per foot of run.
Sources & last checked
Last checked .