Roof Pitch Calculator, Degrees and Rise/Run

The formula

• Pitch = (rise ÷ run) × 12, written as x/12
• Angle = arctan(rise ÷ run), in degrees
• Percentage grade = (rise ÷ run) × 100
• Slope factor = √(rise² + run²) ÷ run

A worked example

A roof that rises 4 in over a 12 in run is a 4/12 pitch. That is an angle of 18.43°, a grade of 33.3% and a slope factor of 1.0541, so 2,000 sq ft of floor plan becomes 2,108 sq ft of roof surface.

More about the Roof Pitch Calculator

Rise over run: reading roof pitch

Let us walk it through once with real numbers. You measure 4 inches of rise over a 12 inch run. That is a 4/12 pitch. The calculator reads that as 18.43°, a 33.3% grade, and a slope factor of 1.0541. Apply it: 2,000 sq ft of floor plan × 1.0541 = 2,108 sq ft of actual roof. That extra 108 sq ft is a full square of shingles, the difference between finishing the ridge and making a second trip to the supplier.

Worth memorising a few slope factors, because estimators think in them: 4/12 → 1.054, 6/12 → 1.118, 8/12 → 1.202, 12/12 → 1.414. Underneath sits √(X² + 144) ÷ 12 for a pitch of X/12, simply the sloped rafter length compared to the horizontal run. And here is a handy trick: when a quote looks high, ask which factor they used. It is the easiest number in roofing to fudge, deliberately or not.

Pitch, materials and safe measuring

A few measuring tips. Do it in the attic on a calm day, wind and wobble are the enemies of the 12 inch level trick. If the roof has sections at different pitches, measure each one on its own; averaging pitches gives you a wrong factor. Carry the slope factor straight into the roof square footage and roofing calculators. They are designed to chain together. In Australia, where pitch is usually quoted in degrees, just enter the angle and read off the x/12 equivalent everyone else uses.

What this will not do: it converts geometry, nothing more. It cannot tell you whether your pitch suits a given material, below 4/12, check the shingle manufacturer's warranty before committing, and it does not account for hips, valleys or dormers, which add waste rather than area. It also assumes a straight slope per section. When you are ready to order materials, pair the true area with a waste allowance in the roofing calculator.

A 7/12 roof, worked from tape measure to order sheet

Suppose your attic measurement gives 7 inches of rise over a 12 inch run. That is a 7/12 pitch, and the calculator turns it into an angle of arctan(7 ÷ 12) = 30.26 degrees and a grade of 7 ÷ 12 = 58.3 percent. The figure that drives ordering is the slope factor: the square root of (7² + 144), divided by 12, which is the square root of 193 divided by 12, giving a factor of about 1.1577 for this pitch.

Apply that factor twice and the whole job takes shape. A house with a 1,600 square foot footprint has a true roof surface of 1,600 × 1.1577 = about 1,852 square feet, roughly 18.5 roofing squares before any waste allowance. And for a rafter spanning a 14 foot horizontal run, the sloped length is 14 × 1.1577 = about 16.21 feet, before you add anything for the eaves overhang the design calls for at the wall line.

Notice what the example never did: it never measured the sloped surface directly. Everything came from one vertical and one horizontal measurement taken safely, converted by the geometry of a right triangle. That is the practical value of the calculator on a real job, a tape measure and a level in the attic become an angle for cutting, a factor for ordering and a length for rafters, with no ladder work on the roof itself.

Pitch, slope and angle: three languages for the same roof

Confusion between the three ways of describing steepness causes real ordering errors, because the same roof wears three very different numbers. Our 7/12 roof is a slope of 7 in 12 to a carpenter, an angle of 30.26 degrees to an architect working in degrees, and a grade of 58.3 percent in the language used for ramps and drainage. All three describe one identical triangle; none of the numbers can be swapped for another without converting it first.

The classic mistake is treating degrees and the x/12 figure as interchangeable. An 8/12 pitch is arctan(8 ÷ 12) = 33.69 degrees, which is a properly steep roof. A roof built at 8 degrees, by contrast, rises only tan(8°) × 12 = about 1.69 inches per 12 inches of run, roughly a 1.7/12, nearly flat, and a completely different materials conversation. If a plan, a quote and a supplier ever seem to disagree about steepness, check the units before checking the arithmetic.

Old books add one more trap: they sometimes define pitch as the rise divided by the whole span of a gable, which makes their pitch exactly half of the slope figure everyone uses today. A historical 1/4 pitch is therefore the same roof as a modern 6/12 slope. When you are matching an existing older roof or reading a vintage plan, ask which convention the number follows before you order a single bundle of anything.

Reading pitch from plans and photographs instead of the attic

Sometimes the roof already exists only on paper. On an elevation drawing, pitch can be recovered with a ruler: measure the vertical rise and the horizontal run of the drawn slope in any units, then divide. A slope that rises 35 millimetres over a 100-millimetre run on the page has a ratio of 0.35, equivalent to 4.2 inches of rise per 12 inches of run, so you can enter a rise of 4.2 with a run of 12 and read the angle and slope factor as usual.

Photographs are the unreliable shortcut. A picture taken from ground level at an angle foreshortens the slope, and lens perspective makes the far end of a roof read differently from the near end, so angles measured off an estate agent’s photo can be wrong by several degrees. Use a photo only as a rough cross check against a figure from the attic or from plans, never as the measurement you order materials from, because the slope factor multiplies every error across the whole roof area.

How to use the Roof Pitch Calculator

1. Pick your starting point: rise and run, or an angle you already know.
2. Measure the rise, hold a level 12 in out from the roof surface and measure straight down to the roof.
3. Enter that rise with a run of 12 to read your pitch in the x/12 form used on plans.
4. Note the slope factor, you will need it for the roofing and roof area calculators.