Roof Pitch Calculator

This is an estimate, not professional advice. Check your inputs and verify the result against your plans and local building code before you build or order. See terms and disclaimer.

How this calculator works

Enter your dimensions and the result updates instantly. A waste allowance is included so you order slightly over rather than running short mid-pour, and ready-mix is rounded up to the nearest quarter yard, which is how it is sold.

Worked example

A 6/12 gable roof over a 24 ft × 30 ft building with a 12 in overhang and rafters at 16 in on center. Inputs: Rise 6 in, Run 12 in, Building span (eave to eave) 24 ft, Roof length (along the ridge) 30 ft, Eave overhang 12 in, Roof style gable, Rafter spacing 16 in O.C.. Result: 6 /12.

Common roof pitches: angle, slope and rafter multiplier

Calculated for a 24 × 30 ft gable roof with a 12 in overhang and rafters at 16 in on center. Tap a pitch to load it in the calculator above.

Method & assumptions

Roof pitch is the ratio of the vertical rise to the horizontal run it is measured over, most often expressed in the U.S. as X/12, meaning the roof rises X inches for every 12 inches of horizontal run. Technically, framing carpenters call this ratio the "slope"; the term "pitch" strictly refers to the total rise divided by the full building span. In practice the two are used interchangeably on the job site, and this calculator follows that everyday convention: enter any rise and run and it returns the equivalent X/12 figure, the angle in degrees (the arctangent of the slope), and the slope expressed as a percent grade.

The rafter length multiplier, the square root of the slope squared plus one, comes straight from the Pythagorean theorem: it is the sloped distance covered for every one unit of level horizontal run. Multiply it by the horizontal run, which is half the building span for a gable roof (each side carries half the load to the ridge) or the full span for a single-slope shed roof, plus your eave overhang, and you get the actual line length of a common rafter from the ridge to the tip of the overhang. That figure, multiplied by the roof length and by two for a gable's pair of slopes, gives the covering area you need to buy shingles, underlayment or metal panels for, before adding your own waste allowance.

The rafter count comes from spacing common rafters on-center along the ridge length, the same grid logic used for framing joists or studs: divide the ridge length by the spacing and add one for the rafter at the start. Sixteen and 24 inches on-center are the two spacings used on almost every residential roof. Always confirm rafter size and span against your local building code or an engineer for anything beyond a simple gable or shed.

Pro tips and common mistakes

• Measure rise and run on the level. Hold a torpedo level truly horizontal along the run and measure straight down to the roof surface for the rise, or use a speed square against a rafter. A tilted reference throws off every downstream number.
• Respect the minimum slope for your roofing. Asphalt shingle manufacturers require at least a 2/12 slope, with special low-slope underlayment between 2/12 and 4/12; NRCA recommends 4/12 or steeper as best practice. Below 2/12 you need a low-slope membrane system, not shingles.
• Steeper roofs need more material, not just more slope. The rafter length multiplier shows why: a 9/12 roof needs 25% more rafter and covering material than the flat footprint alone, a 12/12 roof needs over 41% more. Budget material and cost accordingly as pitch increases.
• Add stock beyond the calculated rafter length. Buy rafter lumber a foot or two longer than the calculated length to allow for the plumb cut at the ridge and the birdsmouth notch at the wall plate, the same way stringers are oversized on a staircase.
• Know the walkability threshold. Roofs steeper than about 6/12 to 7/12 (roughly 30 to 33°) generally require fall protection and are considered unsafe to walk without it. Factor that into labor cost and safety planning before you commit to a steep design.

Frequently asked questions

References

• Roof pitch (Wikipedia)
• IRC Section R802: Wood Roof Framing (UpCodes)
• ARMA: Installation of Asphalt Shingles on Lower Sloped Roofs
• Rafter (Wikipedia)

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