To calculate roof pitch, divide the rise by the run and multiply by 12: the result is inches of rise per 12 inches of horizontal run, written as 6/12, 8/12 and so on. The slope factor, √(rise² + 12²) ÷ 12, turns a footprint into roof area and a run into rafter length. A 6/12 roof is 26.6°, a 50% slope, with a factor of 1.118.
This page is for homeowners checking a roof before ordering shingles, DIY builders laying out shed or garage rafters, and anyone converting between pitch, degrees and percent. Enter a rise and run in any unit, an angle from a phone level, or a percentage. You get the pitch in 12, the angle, the percent grade, the slope and hip factors, and a code check against the asphalt-shingle minimum. Add the building span and overhang for rafter length in feet and inches.
How to use the roof pitch calculator
- Choose what you measured: rise and run, an angle in degrees, or a slope in percent.
- For rise and run, use any unit as long as both are the same. 3 in over 12 in, 1 ft over 4 ft and 50 cm over 200 cm all give 3/12.
- For rafters, enter the building span (outside of wall to outside of wall), the level overhang past the wall, and the ridge board thickness. Enter 0 for a ridge with no board, such as most truss roofs.
- Read the results on the right, then copy the link to share the exact numbers.
How to calculate roof slope (rise over run)
Roof slope is a ratio. Builders in the US always scale it to a 12-inch run because the framing square has a 12-inch tongue and blade, and FM 5-426, the Army carpentry manual, lays rafters out with the square held at the rise on the tongue and 12 on the blade. The conversions are:
- Pitch in 12 = rise ÷ run × 12
- Angle = arctan(rise ÷ 12), in degrees
- Percent = rise ÷ 12 × 100
- Slope factor = √(rise² + 144) ÷ 12
- Rise from an angle = 12 × tan(angle)
Example: you hold a 2-foot level against the roof and measure 7 inches from the far end of the level down to the shingles. 7 in over 24 in is 7 ÷ 24 × 12 = 3.5/12, which is 16.3°. Most roofs are framed to whole or half-inch pitches, so you would call this a 3.5/12 roof and check it against the plans.
How to work out the pitch of a roof without climbing on it
You have three safe options. From the attic, use a level and tape on a rafter as the FAQ explains. From the gable end, measure the building width and the height of the ridge above the top of the wall; the pitch is height ÷ (width ÷ 2) × 12. From the ground, a phone angle app held on a rafter tail or the rake board gives degrees, which the calculator converts. A gable 24 ft wide whose ridge sits 6 ft above the wall plate has a 6 ÷ 12 × 12 = 6/12 pitch.
Roof pitch factor (slope factor) and what it is used for
The slope factor is the length of the sloped line over one foot of level run. Because every square foot of footprint is stretched by the same factor in the direction of the slope, it also converts footprint area to roof surface area. That is why a roofer measures the house from the ground, adds the overhangs, and multiplies by the factor. Hip roofs and gable roofs with the same pitch have the same factor; only the edges (eaves, rakes, hips and ridges) differ. Our roofing shingles calculator uses exactly this to turn a footprint into squares and bundles.
Worked example: a 30 × 40 ft house with 1 ft overhangs on all sides has a 32 × 42 = 1,344 ft² footprint. At 6/12 the roof is 1,344 × 1.118 = 1,503 ft²; at 9/12 it is 1,344 × 1.25 = 1,680 ft². The steeper roof needs about 12% more shingles.
Roof pitch chart: 1/12 to 24/12
Every pitch from 1/12 to 24/12 with its angle, percent grade, slope factor, hip/valley factor and the old “fraction of span” name. The factors are rounded to four decimals.
| Pitch | Angle | Percent | Slope factor | Rafter in per ft of run | Hip/valley factor | Fraction of span |
|---|---|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.0035 | 12.04 | 1.4167 | 1/24 |
| 2/12 | 9.46° | 16.7% | 1.0138 | 12.17 | 1.424 | 1/12 |
| 3/12 | 14.04° | 25% | 1.0308 | 12.37 | 1.4361 | 1/8 |
| 4/12 | 18.43° | 33.3% | 1.0541 | 12.65 | 1.453 | 1/6 |
| 5/12 | 22.62° | 41.7% | 1.0833 | 13 | 1.4743 | 1/4.8 |
| 6/12 | 26.57° | 50% | 1.118 | 13.42 | 1.5 | 1/4 |
| 7/12 | 30.26° | 58.3% | 1.1577 | 13.89 | 1.5298 | 1/3.43 |
| 8/12 | 33.69° | 66.7% | 1.2019 | 14.42 | 1.5635 | 1/3 |
| 9/12 | 36.87° | 75% | 1.25 | 15 | 1.6008 | 1/2.67 |
| 10/12 | 39.81° | 83.3% | 1.3017 | 15.62 | 1.6415 | 1/2.4 |
| 11/12 | 42.51° | 91.7% | 1.3566 | 16.28 | 1.6853 | 1/2.18 |
| 12/12 | 45° | 100% | 1.4142 | 16.97 | 1.7321 | 1/2 |
| 13/12 | 47.29° | 108.3% | 1.4743 | 17.69 | 1.7815 | 1/1.85 |
| 14/12 | 49.4° | 116.7% | 1.5366 | 18.44 | 1.8333 | 1/1.71 |
| 15/12 | 51.34° | 125% | 1.6008 | 19.21 | 1.8875 | 1/1.6 |
| 16/12 | 53.13° | 133.3% | 1.6667 | 20 | 1.9437 | 1/1.5 |
| 17/12 | 54.78° | 141.7% | 1.7341 | 20.81 | 2.0017 | 1/1.41 |
| 18/12 | 56.31° | 150% | 1.8028 | 21.63 | 2.0616 | 1/1.33 |
| 19/12 | 57.72° | 158.3% | 1.8727 | 22.47 | 2.123 | 1/1.26 |
| 20/12 | 59.04° | 166.7% | 1.9437 | 23.32 | 2.1858 | 1/1.2 |
| 21/12 | 60.26° | 175% | 2.0156 | 24.19 | 2.25 | 1/1.14 |
| 22/12 | 61.39° | 183.3% | 2.0883 | 25.06 | 2.3154 | 1/1.09 |
| 23/12 | 62.45° | 191.7% | 2.1619 | 25.94 | 2.3819 | 1/1.04 |
| 24/12 | 63.43° | 200% | 2.2361 | 26.83 | 2.4495 | 1/1 |
The “rafter in per ft of run” column is what the first line of a framing-square rafter table shows; FM 5-426 quotes 17.69 in for a 13-in rise and 20.00 in for a 16-in rise, both of which the formula reproduces.
Common roof angles converted to pitch
| Angle | Pitch (rise in 12) | Percent | Slope factor |
|---|---|---|---|
| 5° | 1.05/12 | 8.7% | 1.0038 |
| 10° | 2.12/12 | 17.6% | 1.0154 |
| 15° | 3.22/12 | 26.8% | 1.0353 |
| 18.43° | 4/12 | 33.3% | 1.0541 |
| 20° | 4.37/12 | 36.4% | 1.0642 |
| 22.5° | 4.97/12 | 41.4% | 1.0824 |
| 25° | 5.6/12 | 46.6% | 1.1034 |
| 26.57° | 6/12 | 50% | 1.1181 |
| 30° | 6.93/12 | 57.7% | 1.1547 |
| 33.69° | 8/12 | 66.7% | 1.2018 |
| 35° | 8.4/12 | 70% | 1.2208 |
| 40° | 10.07/12 | 83.9% | 1.3054 |
| 45° | 12/12 | 100% | 1.4142 |
| 50° | 14.3/12 | 119.2% | 1.5557 |
| 60° | 20.78/12 | 173.2% | 2 |
How to calculate rafter length
FM 5-426 starts every rafter with the run: half the horizontal span of the building. Multiply the run by the slope factor to get the line length from the ridge to the outside of the wall plate, then add the overhang the same way. If the rafters butt into a ridge board, shorten each run by half the board's thickness. Under PS 20, the American Softwood Lumber Standard, nominal 2-inch dry lumber dresses to 1-1/2 in, so a 2x ridge takes 3/4 in off each run.
- Run = span ÷ 2 − ridge thickness ÷ 2.
- Line length = run × slope factor.
- Tail = level overhang × slope factor.
- Total = line length + tail. Add stock for the plumb cut at the ridge and for trimming.
Example: 24 ft span, 6/12, 1 ft overhang, 2x ridge
Run = 12 ft − 3/4 in = 11′ 11 1/4″. Line length = 11.9375 × 1.118 = 13′ 4 3/16″. Tail = 1 × 1.118 = 1′ 1 7/16″. Total = 14′ 5 9/16″, so a 16 ft board. The ridge sits 6′ 0″ above the plates (measured at the building line).
Example: 30 ft span, 8/12, 18 in overhang, 2x ridge
Run = 14′ 11 1/4″; line length = 17′ 11 7/16″; tail = 1′ 9 5/8″; total = 19′ 9 1/16″. That needs at least a 20 ft board.
| Span | 4/12 rafter (no overhang, 2x ridge) | 6/12 rafter (no overhang, 2x ridge) | 8/12 rafter (no overhang, 2x ridge) | 10/12 rafter (no overhang, 2x ridge) | 12/12 rafter (no overhang, 2x ridge) |
|---|---|---|---|---|---|
| 12 ft | 6′ 3 1/8″ | 6′ 7 11/16″ | 7′ 1 5/8″ | 7′ 8 3/4″ | 8′ 4 3/4″ |
| 16 ft | 8′ 4 3/8″ | 8′ 10 1/2″ | 9′ 6 1/2″ | 10′ 4″ | 11′ 2 11/16″ |
| 20 ft | 10′ 5 11/16″ | 11′ 1 5/16″ | 11′ 11 5/16″ | 12′ 11 1/4″ | 14′ 0 5/8″ |
| 24 ft | 12′ 7″ | 13′ 4 3/16″ | 14′ 4 3/16″ | 15′ 6 1/2″ | 16′ 10 9/16″ |
| 28 ft | 14′ 8 5/16″ | 15′ 7″ | 16′ 9″ | 18′ 1 11/16″ | 19′ 8 1/2″ |
| 32 ft | 16′ 9 5/8″ | 17′ 9 13/16″ | 19′ 1 7/8″ | 20′ 8 15/16″ | 22′ 6 7/16″ |
Minimum slope for asphalt shingles (IRC R905.2.2)
The 2024 International Residential Code, Section R905.2.2, says asphalt shingles “shall be used only on roof slopes of 2 units vertical in 12 units horizontal (17-percent slope) or greater,” and that from 2:12 up to 4:12 (33%) “double underlayment application is required.” Table R905.1.1(2) describes that double layer: a half-width strip at the eave, then full-width sheets each lapped half a sheet plus 2 in. At 4:12 and steeper, one layer lapped 2 in is enough (in areas where wind design is not required). Check which IRC edition your town has adopted and any local amendments; the calculator flags which band your pitch falls in.
Common mistakes
- Measuring the run along the roof. Run is level distance. Measuring along the shingles gives the rafter length, not the run, and understates the pitch.
- Using the full span as the run. On a gable, each rafter covers half the span.
- Mixing units. Rise in inches with run in feet gives a pitch twelve times too high. Use one unit for both.
- Forgetting the overhang. Overhangs add both rafter length and roof area.
- Confusing pitch fraction with rise in 12. A “1/4 pitch” roof is 6/12, not 3/12.
Next steps: count materials with the roof shingle calculator, price the job with the roof replacement cost calculator, and add feet-inch-fraction lengths with the construction calculator.
Frequently asked questions
How do I calculate roof pitch?
Divide the rise by the run and multiply by 12 to express it as inches of rise per 12 inches of run. A rise of 30 in over a run of 60 in is 30 ÷ 60 × 12 = 6, so a 6/12 pitch (26.6°).
What is the roof pitch factor?
It is the number you multiply a building's footprint (plan) area by to get the sloped roof area: √(rise² + 12²) ÷ 12. A 4/12 roof has a factor of 1.054, 6/12 is 1.118, 8/12 is 1.202 and 12/12 is 1.414. A 1,200 ft² footprint at 6/12 has about 1,342 ft² of roof before overhangs.
Is roof slope factor the same as pitch factor?
Yes. Both names describe the same multiplier: the length of the rafter for each foot of horizontal run, which is also the ratio of roof surface area to the area it covers. Framing squares print it in inches as the common rafter length per foot of run.
How many degrees is a 6/12 pitch?
A 6/12 pitch is 26.57°, a 50% slope. For comparison 4/12 is 18.43°, 8/12 is 33.69° and 12/12 is exactly 45°.
What pitch is a 30 degree roof?
A 30° roof rises 12 × tan 30° = 6.93 in per foot, so it is about a 6.9/12 pitch, with a slope factor of 1.155.
How do you calculate rafter length?
Take the run (half the building span, less half the ridge board thickness if there is one), multiply by the slope factor, then add the overhang along the slope. For a 24 ft span at 6/12 with a 1-1/2 in ridge board and a 1 ft overhang: run 11′ 11 1/4″ × 1.118 = 13′ 4 3/16″, plus 1′ 1 7/16″ of tail = 14′ 5 9/16″.
What is the minimum pitch for asphalt shingles?
The 2024 IRC (R905.2.2) allows asphalt shingles only on slopes of 2:12 (17%) or steeper. From 2:12 up to 4:12 (33%) the code requires double underlayment applied as Section R905.1.1 describes. Below 2:12 use a low-slope roof covering.
What does a 1/4 pitch or 1/3 pitch mean?
Older carpentry texts state pitch as rise divided by the full span. FM 5-426 gives 4 in rise per 12 in run as a 1/6 pitch, 6 in 12 as 1/4 pitch and 12 in 12 as 1/2 pitch. A 1/3 pitch is therefore 8/12 (33.7°). The calculator shows this fraction too.
How do I measure roof pitch from inside the attic?
Hold a level horizontally against the underside of a rafter, mark 12 in along the level from the rafter, and measure straight up (or down) from that mark to the rafter. That vertical distance in inches is the rise per 12; enter it as the rise with a run of 12.
What is the hip or valley factor?
On a regular hip roof (all planes at the same pitch) the hip runs diagonally, so its plan length is √2 times the common run. The hip factor per foot of common run is √(rise² + 288) ÷ 12: 1.5 at 6/12 and 1.732 at 12/12.
Sources & method
- ICC, 2024 International Residential Code, Chapter 9 Roof Assemblies — R905.2.2 slope for asphalt shingles (2:12 minimum; double underlayment from 2:12 up to 4:12), R905.1.1 and Table R905.1.1(2)
- US Army FM 5-426 Carpentry (1995), Chapter 7 Roof Framing — run is half the span; rafter table gives length per foot of run (13 in rise = 17.69 in, 16 in rise = 20.00 in); pitch as rise ÷ span
- NIST, Voluntary Product Standard PS 20-20 American Softwood Lumber Standard, Table 3 — nominal 2 in dry dimension lumber dresses to 1-1/2 in
Results are estimates for general information. Found an error? It helps everyone — see our methodology.