Roof Pitch Calculator

A roof pitch calculator turns a rise-and-run measurement into pitch (x/12), the angle in degrees, the slope factor and rafter length. Divide rise by run and multiply by 12: a roof rising 6 inches over 12 inches is a 6/12 pitch, about 26.6°, a 50% grade and a 1.118 slope factor, so the surface is 12% larger than the footprint.

Related home-and-construction tools: the Roofing Calculator takes the pitch and footprint here and counts shingle bundles and squares, the Concrete Calculator prices slabs and footings by volume, the Paint Calculator estimates gallons for the gable wall, and the Mulch Calculator handles landscape beds around the finished job. Use this page to find how steep the roof is; use those to buy the material.

What is roof pitch?

Roof pitch is how steep a roof is, written as the vertical rise over a fixed horizontal run of 12 inches, for example 4/12, 6/12 or 9/12. The bigger the first number, the steeper the roof. Pitch controls almost everything downstream: which roofing materials you can use, how much surface area you have to cover, how well the roof sheds rain and snow, and how much labor and safety equipment the install needs.

The formulas behind the calculator

Every output comes from one right triangle, with rise, run and the rafter as the hypotenuse:

For a symmetrical gable, the run in the rafter formula is half the building span. The slope factor is what you multiply a flat footprint area by to get the true sloped roofing area; it never drops below 1.0 and grows as the roof gets steeper.

A worked example

Say you have a gable building that is 30 feet wide (the span), and the ridge sits 7.5 feet above the wall plates (the total rise). Each rafter runs over half the span, so the run is 15 feet.

• Pitch: (7.5 ÷ 15) × 12 = 6/12.
• Angle: arctangent(7.5 ÷ 15) = arctangent(0.5) ≈ 26.6°.
• Slope factor: √(7.5² + 15²) ÷ 15 = √(56.25 + 225) ÷ 15 ≈ 1.118.
• Rafter length: √(7.5² + 15²) ≈ 16.77 feet (before overhang).

If that 30 × 40 ft building has a 1,200 sq ft flat footprint, the actual roof surface is about 1,200 × 1.118 = 1,342 sq ft for the full roof, and at a 10% waste factor you would buy material for about 1,476 sq ft (14.76 squares). These are the calculator's default inputs, so you can check every step against it.

Rafter length by building span and pitch

One of the most common questions is "how long is my rafter?" Rafter length is √(rise² + run²) where the run is half the building span. The table below gives the finished rafter length (wall plate to ridge, before overhang and birdsmouth) in feet for common spans and pitches:

Add your planned eave overhang to each of these figures before cutting: a 12-inch overhang on a 6/12 roof adds about 1.12 ft of rafter (the overhang follows the same slope factor).

How to measure rise and run

You only need a level and a tape measure. There are two reliable ways:

1. On a rafter (from the attic): hold a level horizontally against the underside of a rafter, mark 12 inches along the level, then measure straight down from that mark to the rafter. That vertical drop is your rise over a 12-inch run.
2. On the roof or gable end: rest one end of a 24-inch level on the roof surface, level it, mark the 12-inch point, and measure down to the shingles. If you measure the drop at the 24-inch end instead, divide the reading by 2 to get the rise per 12 inches.

If you already know the building width and how high the ridge sits, skip the level entirely: switch the calculator to Span & rise mode and enter both numbers in feet.

How to use this calculator

1. Pick a mode. Use Rise & run if you measured inches on the slope; use Span & rise if you know the building width and ridge height in feet.
2. Enter your measurements. The calculator accepts decimals, so a 6.25-inch rise or a 30.5-foot span is fine.
3. Add the footprint (optional). Enter the flat area under the roof, including overhangs, to get the roof surface and squares.
4. Set a waste factor. Start at 10% for a simple gable; bump it to 15% for cut-up roofs with hips and valleys.
5. Read the results. They update as you type: the big x/12 result first, then the angle, slope factor, rafter length, grade and roof surface below it.

Who this calculator is for

• DIY homeowners figuring out whether shingles will work on a porch or shed roof.
• Roofers and estimators converting a footprint into true roofing area and bundle counts.
• Carpenters and framers cutting rafters to length for a new build or addition.
• Solar installers checking the tilt angle a roof gives panels.
• Inspectors and buyers sanity-checking that a roof's pitch matches its material.

Key terms explained

• Rise: the vertical height the roof gains over the run.
• Run: the horizontal distance: by convention 12 inches, or half the span for a gable.
• Span: the full width of the building the roof covers.
• Slope factor (roof multiplier): the number you multiply a flat footprint area by to get sloped surface area.
• Roofing square: 100 square feet of roof surface, the unit shingles and underlayment are sold and counted in.
• Cubic yard: 27 cubic feet; you will see it on related material calculators (concrete, gravel, mulch) where you convert area and depth into volume to order by the truckload.
• Waste factor: the percentage of extra material added for cuts, overlaps, hips, valleys and breakage.
• Birdsmouth: the notch cut into a rafter where it sits on the wall plate; it slightly shortens the usable rafter span.

Three quick scenarios

• Low-slope porch (2/12): angle ≈ 9.5°, slope factor ≈ 1.014. This is the IRC minimum for asphalt shingles, and it calls for a double layer of underlayment; many builders choose a membrane instead. The added roofing area is tiny, barely above the footprint.
• Standard house (6/12): angle ≈ 26.6°, slope factor ≈ 1.118. A common choice for asphalt shingles: it sheds water well and adds only about 12% more area than the footprint.
• Steep roof (12/12): angle = 45°, slope factor ≈ 1.414. The surface is over 40% larger than the footprint, so material and labor jump, and crews typically need roof jacks or scaffolding.

Common roof pitches at a glance

Most residential roofs cluster into a handful of standard pitches. The list below shows the angle in degrees and the slope (area) factor for each, so you can see at a glance how steeper roofs add surface area:

• 2/12: about 9.5°, slope factor ≈ 1.014. The IRC minimum for asphalt shingles (with double underlayment); just above the footprint.
• 3/12: about 14.0°, slope factor ≈ 1.031. Low slope, common on porches and additions.
• 4/12: about 18.4°, slope factor ≈ 1.054. The point where single-layer underlayment becomes standard for shingles.
• 6/12: about 26.6°, slope factor ≈ 1.118. A common residential pitch in the US.
• 8/12: about 33.7°, slope factor ≈ 1.202. Steeper, sheds snow well; harder to walk.
• 9/12: about 36.9°, slope factor ≈ 1.250. Steep enough that work slows down.
• 12/12: exactly 45°, slope factor ≈ 1.414. Very steep; over 40% more surface than the footprint.

Notice how the slope factor climbs slowly at first and then faster as the roof steepens. The jump from 6/12 to 12/12 more than triples the "extra" area you have to cover (roughly 12% over footprint versus 41%), which is exactly why steep roofs cost more in both material and labor. When you turn the footprint into a flat area to multiply, the Square Footage Calculator handles the rectangle math.

Roof pitch to angle and percent grade chart

To convert a roof pitch to degrees, take arctangent(rise ÷ run); to convert it to a percent grade, take (rise ÷ run) × 100. This chart lists both plus the slope factor for every standard pitch, so you can read off the answer without doing the trig yourself:

How pitch decides your roofing material

Pitch is not just a number for framing: it directly limits which roof coverings you are allowed to use. Water moves more slowly across a shallow roof, so a low slope gives wind-driven rain more chance to creep back under the courses. The International Residential Code therefore sets a minimum slope for each covering:

• Low-slope roof systems (built-up roofing, modified bitumen, single-ply membranes such as TPO and EPDM): allowed down to 1/4 in 12, which makes them the choice below 2/12, where shingles are not permitted. These are fully adhered or seamed systems rather than overlapping pieces.
• Asphalt shingles: 2/12 and steeper, with a double layer of underlayment from 2/12 up to 4/12 and a standard single layer from 4/12 up.
• Metal roof panels: standing-seam panels down to 1/4 in 12; lapped, nonsoldered seams need 3/12 without lap sealant or 1/2 in 12 with it. Metal shingles need 3/12.
• Clay and concrete tile: 2.5/12 minimum, with double underlayment from 2.5/12 up to 4/12.
• Wood shingles and shakes: 3/12 minimum.
• Slate: 4/12 minimum.

Run your measurement through the calculator first; the x/12 result tells you immediately whether the material you have in mind is even an option before you price anything. Manufacturers' installation instructions and your local code can be stricter.

Pitch, drainage and climate

Beyond material rules, pitch affects how a roof performs in your weather. A steeper roof sheds water and snow faster, which reduces the time moisture sits on the surface and lowers the chance of ice dams and leaks, one reason steep roofs are popular in snowy regions. A shallower roof catches less wind and is cheaper to build and safer to work on, but it relies more heavily on a flawless underlayment and good flashing because water lingers longer. In high-snow regions, the steeper pitch also matters structurally: it sheds snow load instead of accumulating it, though the actual live-load design is an engineering question, not something a pitch calculator answers. If you are also estimating attic or living space under the roof, remember that a steeper pitch creates more headroom for a given span but a larger, more expensive roof surface overall.

From pitch to a materials order

Knowing the pitch is step one; turning it into a shopping list is step two. The workflow most estimators follow is: measure the building footprint, convert that footprint to a flat area, multiply by the slope factor to get true roof surface, divide by 100 to get roofing squares, then add a waste factor and round up to whole bundles.

The table below runs that math for a 1,500 sq ft flat roof footprint at each common pitch, showing the true surface area and the material to buy at a 10% waste factor (1 roofing square = 100 sq ft):

The same 1,500 sq ft footprint needs about 16.7 squares of shingles on a low 2/12 roof but 23.3 squares on a steep 12/12, a 39% jump driven entirely by the slope factor. For ground-level companion projects on the same job (a new concrete apron, a gravel drip line, or fresh mulch around the foundation) you switch from area to volume. The Concrete Calculator and Gravel Calculator turn length, width and depth into the cubic yards you order by the truckload, and the Mulch Calculator does the same for landscape beds. If the gable wall or soffits need fresh paint while the scaffolding is up, the Paint Calculator estimates the gallons.

What changes the result the most

• The rise: for a fixed run, more rise means a steeper pitch, a bigger angle and a larger slope factor; this is the dominant lever.
• The span: in span-and-rise mode, a wider building lengthens the rafters even when the pitch is unchanged.
• The waste factor: it does not change the geometry but directly scales how much material you buy; the difference between 10% and 15% on a big roof is real money.
• Roof complexity: hips, valleys, dormers and skylights all add cuts and waste that a single pitch number cannot capture.

Tips for ordering material

• Always buy about 10% extra. It covers cuts, starter and ridge courses, and gives you spares for future repairs that match your current color lot.
• Round up to whole bundles or squares. Shingles come in bundles (usually 3 per square); you cannot buy a fraction.
• Measure twice. A wrong pitch by one number in 12 can throw off your area by several percent on a large roof.
• Account for the overhang. The rafter length here stops at the wall plate; add your planned eave overhang before cutting lumber.

Limitations and assumptions

• It assumes a simple, symmetrical gable when converting span to rafter length; complex roofs need per-plane calculations.
• It does not add overhang, ridge thickness, birdsmouth depth or fascia; these are framing details you add yourself.
• It is a geometry and estimating tool, not a structural design. Rafter sizing, load and span tables are an engineering question.
• Material counts depend on the specific product's coverage; always confirm against the manufacturer's coverage per bundle or square.

How it compares to related calculators

This page answers "how steep is my roof, and how much surface does that create?" If your question is a little different, a sister tool fits better:

• To turn a roof or room footprint into a flat area, use the Square Footage Calculator.
• To price a slab, footing or driveway by volume, use the Concrete Calculator.
• To order base rock or a drip line, use the Gravel Calculator, and for landscape beds the Mulch Calculator.
• To convert any area-and-depth job into truckloads, use the Cubic Yard Calculator.
• To estimate gallons for the gable wall, soffits or fascia, use the Paint Calculator.

Sources and standards

• Roof pitch, angle, percent grade and rafter length come from standard right-triangle trigonometry (rise, run and the rafter as the hypotenuse).
• International Code Council: International Residential Code, Chapter 9, Roof Assemblies (R905.1.1 underlayment, R905.2.2 asphalt shingles at 2/12 or steeper, R905.3.2 clay and concrete tile, R905.4.2 metal roof shingles, R905.6.2 slate, R905.7.2 and R905.8.2 wood shingles and shakes, R905.10.2 metal roof panels, and the Section R905 provisions for built-up, modified bitumen and single-ply roofs).
• Waste-factor and roofing-square conventions (100 sq ft per square) are standard roofing-trade estimating practice; complex roofs with hips and valleys warrant higher allowances.