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RooferMath

Roof Pitch Calculator: Any Rise, Run, or Angle

Solve roof pitch, angle, slope factor, and grade for any rise and run, including non-integer pitches like 5.5/12, or work backwards from an angle in degrees. Live redrawing diagram.

Pitch geometry is arithmetic. Rafter spans and structural load are a different question. Size structural members with a licensed professional and your local code.
Try:

angle = atan(rise ÷ run) × 180 ÷ π
rise ÷ 12 = tan(angle × π ÷ 180) × 12

Angle

18.43°

Slope factor

1.054

Grade

33.33%

Pitch

4/12

Live roof diagram

Roof pitch triangle diagram, redraws with the calculator 4/12 18.43° rafter 12.649 / 12 run

Run drawn horizontal, rise vertical, rafter as the hypotenuse. Redraws live for both pitch and angle input.

How to use the roof pitch calculator

Pick a mode at the top of the calculator. In pitch to results mode, enter a rise and a run and every other value, angle, slope factor, grade, and the equivalent x/12 pitch, updates immediately. In angle to pitch mode, enter an angle in degrees instead and the calculator solves backward for the rise per 12 inches of run, along with slope factor and grade. Both modes share the same live diagram underneath, so you can see the triangle change shape as you type, not just read a new number.

Unlike a printed pitch chart, which only lists whole-number rises from 1/12 through 24/12, this calculator accepts any value. Type 5.5, 7.25, or any decimal rise and it solves exactly, with no need to round to the nearest table row. The run field is editable too, so a measurement that was not taken over exactly 12 inches, for example a 9 inch rise over a 17 inch run, still gets an exact answer instead of an approximation.

Pitch, angle, slope factor, and grade: what each one is for

Pitch (rise over run, written as x/12) is the number roofers, material spec sheets, and permits use in everyday conversation, because it maps directly to how a roof is physically framed. Angle in degrees is what a saw, a speed square, or a framing calculation needs when the input has to be a degree setting rather than a ratio. Slope factor is the multiplier that converts a flat footprint area into the true sloped roof area, the number that actually drives how much material a job needs. Grade, the same ratio expressed as a percentage instead of a fraction, shows up mostly in drainage and civil contexts and on some manufacturer minimum-slope specifications. All four describe the same slope; which one you reach for depends on which document or tool you are talking to.

Why non-integer pitches happen

A pitch chart assumes clean, whole-number rises because that is how lumber, rafter tables, and most reference material are organized for convenience. Real roofs do not always land on a round number. A house that has settled slightly over decades can have a roof plane that reads a few tenths of an inch off what it was framed at. An addition tied into an existing roofline often has to match whatever angle the original roof happens to be, which is rarely a clean integer. Custom or architect-designed roofs sometimes specify an exact angle in degrees rather than a pitch at all. In every one of these cases the trigonometry does not care whether the rise is a whole number, so a calculator that accepts decimals gives an exact answer instead of forcing a rounding error onto the job.

Worked examples

A rise of 5.5 over a run of 12 works out to a 24.62 degree angle, a 1.100 slope factor, and a 45.83 percent grade, a fraction between the common 5/12 and 6/12 pitches on a standard chart. Working the other direction, an angle of 30 degrees solves back to a rise of about 6.93 over 12, a 1.155 slope factor, and a 57.74 percent grade, right between a 6/12 and 7/12 pitch. Feeding that resulting rise and run back through the forward formulas returns 30.00 degrees exactly, confirming the two directions agree.

Measuring on site for this calculator

Hold a level horizontal against the underside of a rafter or the roof deck, extend it out a known distance, and measure straight down to the roof surface at that mark with a tape measure. That vertical distance is your rise, and the horizontal distance you measured out is your run: enter both here exactly as measured, rather than rounding either one to match a chart. If you only have an angle reading from a digital angle finder or a speed square's degree scale, use angle to pitch mode instead and skip the rise and run measurement entirely.

For the full standard whole-number reference from 1/12 through 24/12, see the Roof Pitch Chart. A rafter length calculator for full board lengths, not just the per-run ratio shown here, is planned as a future addition to this hub.

Frequently asked questions

What is the difference between roof pitch and roof angle?

Pitch is a ratio, rise over run, usually written as a fraction of 12 like 6/12. Angle is that same ratio converted into degrees from horizontal using the arctangent function. They describe the same slope, just in two different units: roofers and material spec sheets tend to use pitch, while framing squares, saw settings, and some structural calculations use degrees.

How do you convert roof angle to pitch?

Take the tangent of the angle in degrees, then multiply by 12 to express it as rise per 12 inches of run. A 30 degree angle gives tan(30) times 12, which is about 6.93, so a 30 degree roof is roughly a 6.93/12 pitch. This calculator does that conversion automatically in angle to pitch mode.

Can a roof have a non-standard pitch like 5.5/12?

Yes. Published pitch charts only list whole-number rises because that is how lumber and rafter tables are organized, but real roofs are not required to land on a whole number. Settled or slightly out-of-level older framing, additions tied into an existing roof at a forced angle, and custom architectural work all commonly produce a fractional pitch such as 5.5/12 or 7.25/12, and the underlying trigonometry works identically either way.

What is roof slope factor used for?

Slope factor is the multiplier that converts a flat, top-down footprint area into the true sloped roof surface area, since a tilted plane is always longer than the flat area it covers. Multiply your footprint square footage by the slope factor for a given pitch to get the actual roof area for ordering shingles, underlayment, or decking.

How accurate do rise and run measurements need to be?

For a material estimate, measuring to the nearest quarter inch is generally more than enough, since the resulting angle and slope factor change only fractionally over that range. For cut angles on rafters or fascia, more precision helps, which is exactly why entering a non-integer rise here, rather than rounding to the nearest whole pitch, produces a more exact result.

Does this calculator work for a run other than 12 inches?

Yes, the run field is fully editable. Pitch is conventionally expressed per 12 inches of run, but the geometry works for any run length: enter your actual measured run and rise and the calculator solves the true angle, slope factor, and grade for that pair, then also expresses the equivalent standard x/12 pitch for reference.

Related tools

Roof Pitch ChartRafter Length CalculatorRoof Area CalculatorHip & Valley Rafter CalculatorShingle Squares & Bundles Calculator