Roof pitch calculator
Enter a rise and run, an angle, or a pitch. You get it back in every form a roofer or framer uses, the rafter length for your span, and the roofing materials the code allows at that slope.
Inputs
Rafter length (optional)
Result
Roofing allowed at 6/12
Minimum slopes from the 2021 International Residential Code, Section R905. The manufacturer's instructions can ask for more, and they govern when they do.
| Roofing | Minimum pitch | At this pitch | IRC |
|---|
Roof pitch chart
Every whole pitch from 1/12 to 24/12. The rafter factor is the length of a common rafter per foot of run; the hip factor is the length of a hip or valley rafter per foot of common run.
| Pitch | Angle | Slope | Rafter factor | Hip / valley factor |
|---|
How to measure roof pitch
- On the roof. Hold a level flat against the roof surface, then measure straight down from its 12 in mark to the shingles. That gap in inches is the pitch: 6 in means 6/12.
- From the attic. Do the same against the underside of a rafter. It is safer and gives the framing pitch directly.
- From the ground. At a gable end, measure the height from the wall plate to the peak and half the building's width. Enter them as rise and run, in the same unit.
- With a digital level or phone. Read the angle off a rafter or the roof deck and use the angle mode.
The formulas
Pitch is a right triangle: rise over a run of 12. Everything else is trigonometry on that triangle, so there is nothing to look up and nothing rounded.
The hip factor is bigger because a hip runs diagonally across the corner. For every 12 in the common rafters run, a regular hip runs 16.97 in (12 times the square root of 2), which is why framing squares print hip figures against a 17 in run.
How the rafter length is worked out
The run of each common rafter is half the span, less half the ridge board's thickness, since the rafters butt into the ridge's faces rather than meeting at its centre. Multiplying that run by the rafter factor gives the line length along the rafter's measuring line, from the plumb cut at the ridge to the plate line at the birdsmouth. The tail is the level overhang times the same factor.
A 24 ft span at 6/12 with a 2x ridge has a run of 143.25 in, so the rafter is 143.25 x 1.118 = 160.16 in, or 13' 4-3/16", to the plate. A 12 in overhang adds 13-7/16" of tail, and the board to buy is a 16 footer.
These are line lengths. Lay them out along the measuring line, and allow for the fascia, any plumb or square tail cut, and the birdsmouth seat when you mark the board.
What pitch means for the job
Pitch decides which roofing you can use. Asphalt shingles need at least 2/12, and between 2/12 and 4/12 the code requires two layers of underlayment. Below 2/12 you are into metal panels or a membrane. The table above checks every material in IRC Section R905 against your pitch.
Questions
What is a 6/12 roof pitch in degrees?
26.57°. The angle is the arctangent of 6 divided by 12. A 4/12 roof is 18.43°, 8/12 is 33.69°, 12/12 is exactly 45°.
How do I calculate roof pitch?
Divide the rise by the run and multiply by 12. A roof that climbs 30 in over a level 60 in has a pitch of 30 / 60 x 12 = 6, written 6/12 or 6:12.
What is the minimum pitch for asphalt shingles?
2/12 under IRC R905.2.2, with two layers of underlayment required from 2/12 up to 4/12. At 4/12 and above a single layer is enough. Some manufacturers ask for more, and their instructions govern.
What is the rafter factor or pitch multiplier?
The length of rafter per unit of run. At 6/12 it is 1.118, so a rafter that runs 10 ft level is 11.18 ft long. Roofers use the same number to turn a flat footprint into true roof area.
What does 4/12 pitch mean?
The roof rises 4 in for every 12 in it runs level. That is 18.43° or a 33.3% slope, and the bottom of what most people call a conventional roof.
Is a 7/12 roof walkable?
Most roofers walk 7/12 in dry conditions with good footwear, but it is over the 4/12 line where OSHA treats a roof as steep, so fall protection rules apply on a job site. Above about 8/12, plan on roof jacks and a harness.
More Roofing calculators
Roof sheathing calculator
Sheets of OSB or plywood roof decking from the house size and pitch, with H-clips where the panel needs them, nails and weight.
Roofing calculator
Roof area, squares and shingle bundles from the house size and pitch, with underlayment, drip edge, starter, ridge cap and ice barrier.
Attic ventilation calculator
Net free vent area for an attic by the IRC 1/150 and 1/300 rules, split between ridge and soffit vents.
Siding calculator
Squares of siding and the number of lap planks, Hardie or wood, for walls and gables, net of openings.