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Roof Pitch Calculator · https://calcnaut.com/roof-pitch-calculator/

Roof Pitch Calculator

Enter your roof rise and run to get the pitch, angle, slope percent and rafter length multiplier. Add the span, ridge length, overhang and maximum on-center spacing to estimate a simple gable or shed layout. The count does not select the structural rafter size or spacing.

Inputs

Enter your measurements

Rise

Vertical rise for every "Run" of horizontal distance. This is the 6 in a 6/12 pitch.

Run

12 in is the U.S. standard reference, the "12" in X/12. Change it only if you measured the rise over a different horizontal distance.

Building span (eave to eave)

ft / in

The full horizontal width of the roof footprint, outside wall to outside wall.

Roof length (along the ridge)

ft / in

The other building dimension, running parallel to the ridge.

Eave overhang

Horizontal projection of the rafter tail past the wall. 12 to 24 in is typical.

Roof style

Rafter spacing

Maximum on-center spacing from your approved design. The calculator adds positions so the actual spacing never exceeds this value; it does not select a safe spacing.

Resultlive

6/12

A roof with a 6.0/12 pitch has an angle of 26.6° (a 50% slope). Each rafter runs about 14' 6 7/16", so buy 16 ft stock, and the roof needs roughly 872 ft² of covering.

rise 6 in over run 12 in = a 6.0/12 pitch (26.6 degrees)
multiplier = square root of (slope squared + 1) = 1.12, so every 1 ft of horizontal run is 1.12 ft of rafter
half span 12.00 ft + 1.00 ft overhang = 13.00 ft of run, x 1.12 = 14' 6 7/16" of rafter
48 rafters create intervals no wider than the entered maximum; actual spacing is 15.65 in on center
buy 16 ft stock: dimension lumber comes in 2 ft lengths (PS 20, 5.3.1)

Round to

Roof angle26.57 °

Slope (grade)50 %

Rafter length multiplier1.12 ×

Rafter length (with overhang)14' 6 7/16"

Buy rafter stock16'

Roof covering area872 ft²

Rafters needed (total boards)48

Actual layout spacing15.65 in O.C.

Total rafter lumber697' 7 13/16"

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

Roof pitch = Rise ÷ Run × 12 (the x-in-12 figure)Slope = Rise ÷ RunAngle (°) = arctan(Rise ÷ Run) × 180 ÷ πRafter length multiplier = √(Slope² + 1)Rafter length (ft) = (Half-span + Overhang) × Multiplier (shed: full span, not half-span)Roof area (ft²) = Rafter length × Roof length × (2 for gable, 1 for shed)

Enter the rise and run and the result updates instantly. There is no waste allowance in these figures: this is roof geometry, not a materials count. Add your own margin when you order shingles, and remember that rafters need extra length for the birdsmouth and ridge cuts.

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, 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.

Pitch	Roof angle (°)	Slope (grade) (%)	Rafter length multiplier (×)
2/12	9.46	16.7	1.01	Use →
3/12	14.04	25	1.03	Use →
4/12	18.43	33.3	1.05	Use →
5/12	22.62	41.7	1.08	Use →
6/12	26.57	50	1.12	Use →
7/12	30.26	58.3	1.16	Use →
8/12	33.69	66.7	1.2	Use →
9/12	36.87	75	1.25	Use →
10/12	39.81	83.3	1.3	Use →
12/12	45	100	1.41	Use →

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. To turn that area straight into squares, shingle bundles, underlayment rolls and a material cost, run the numbers through our roofing calculator.

The entered spacing is treated as a maximum. We divide the ridge length by it, round the number of intervals up, and add one end position. The displayed actual spacing is therefore equal to or less than the requested maximum. This is a quantity layout for a simple gable or shed, not structural design: rafter size and permitted spacing depend on species, grade, loads, span, connections and the adopted code.

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.

By Calcnaut

Formula and declared-case checks run during the build; sources are listed for readers to review. Read our method and editorial policy.

Frequently asked questions

What does a 6/12 roof pitch mean?

A 6/12 roof pitch means the roof rises 6 inches for every 12 inches of horizontal run. That works out to a 26.57° angle and a 50% slope, the most common pitch on U.S. residential roofs.

How do I calculate roof pitch from rise and run?

Divide the rise by the run to get the slope, then multiply by 12 to express it as X/12. For the angle, take the arctangent of rise ÷ run and convert to degrees. A 4 in rise over a 12 in run, for example, is arctan(4/12) = 18.43°.

What is the minimum roof pitch for shingles?

Asphalt shingle manufacturers set 2/12 as the code minimum, and only with special low-slope underlayment between 2/12 and 4/12. The National Roofing Contractors Association recommends 4/12 or steeper as best practice; below 2/12 you need a low-slope membrane roof instead of shingles.

How much longer is a rafter than the roof’s horizontal run?

Multiply the horizontal run by the rafter length multiplier, the square root of the slope squared plus one. A 6/12 roof has a multiplier of about 1.118, so the rafter is roughly 11.8% longer than the flat horizontal distance it covers; a 12/12 roof is about 41.4% longer.

How much roofing material do I need for a pitched roof?

Multiply the flat footprint area by the same rafter length multiplier to get the actual sloped covering area, then add your own waste allowance for cuts and hips. A 6/12 roof needs about 11.8% more shingles or metal panels than the building’s footprint alone.

Sources and references

These references and structured source records support the method and material data used on this page.

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Roof pitch
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