Roof Pitch Calculator

Convert roof rise and run into pitch as a percent grade, degrees, or ratio, plus rafter length.

Roof Pitch Calculator: Convert Rise, Run, Angle & Ratio

Roof pitch is the single number that drives almost every other decision on a re-roof or new build: which materials you are allowed to use, how fast water and snow shed off the surface, whether it is safe to walk on, and how much rafter and covering material you actually need to order. The trouble is that pitch gets expressed four completely different ways depending on who you are talking to — a carpenter will quote it as "6-in-12", an engineer or a European supplier will quote it in degrees, and a drainage spec will quote it as a percentage grade. This calculator converts between all of them instantly, and also works out the rafter length (including any overhang) from the same rise and run figures.

If you already know your rise (the vertical height the roof climbs) and run (the horizontal distance it covers, usually half the building width for a simple gable), enter both and the calculator gives you the pitch as a ratio, in degrees, and as a percentage, plus the rafter length via the Pythagorean theorem. If you only know a target pitch — because a shingle manufacturer specifies a 4-in-12 minimum, or your local building code specifies a maximum in degrees — you can work backwards from that instead.

The four notations are not interchangeable in a simple linear way, which is exactly why a calculator (rather than a rule of thumb) is worth using. A 6-in-12 pitch is not "twice as steep" as a 3-in-12 pitch in any way that matters for drainage or walkability — the underlying relationship is a tangent function, not a straight ratio, so pitch steepens quickly at first and then flattens out its rate of change as you approach vertical. Understanding that curve, not just memorizing one conversion, is what lets you sanity-check a number a supplier or contractor gives you.

This guide walks through exactly how the conversions work, gives a full worked example you can check by hand, includes a quick-reference table of common pitches, and covers the practical side too: why pitch limits your material choice, when a roof is safely walkable, and the mistakes people most often make when reading a pitch spec off a set of plans.

How to use the roof pitch calculator

  1. Enter the rise — the vertical height the roof gains over the run. This is usually measured at the ridge relative to the top of the wall plate, in your chosen unit (feet/inches, meters, or millimeters).
  2. Enter the run — the horizontal distance the roof covers to reach that rise. For a simple gable roof this is normally half the building width, from the outer wall to the centerline of the ridge.
  3. Optionally, add an overhang — the horizontal distance the rafter extends past the wall line — if you want the rafter-length figure to include the eave overhang rather than just the distance to the wall.
  4. Read off the results: pitch as an x-in-12 ratio, pitch in degrees, pitch as a percentage grade, and the rafter length (hypotenuse) both with and without the overhang included.
  5. If you are working the other way — you have a target pitch in degrees or as a ratio and need to find a matching rise for a fixed run (or vice versa) — use the pitch and run figures to back-solve the rise using the formulas in the next section.
  6. Compare your result against the reference table below to sanity-check it against common named pitches, and check the tips section for material-specific minimum-pitch guidance before finalizing a design.

The roof pitch formulas, explained

Every pitch notation comes from the same right triangle: rise (vertical), run (horizontal), and rafter length (the hypotenuse). Once you have rise and run, everything else follows from basic trigonometry.

Pitch angle in degrees: angle = arctan(rise / run). This is the true geometric slope angle measured from horizontal — the number an engineer, an inclinometer, or a European building code will use.

Pitch as a percentage grade: percent = (rise / run) × 100. A 100% grade is a 45-degree angle (rise equals run) — this trips people up because a 45-degree roof is not "100% steep" in any intuitive sense, it is just where the ratio and the percentage happen to both read as clean numbers.

Pitch as an x-in-12 ratio (the carpenter's notation, standard in the US, Canada, and Australia): x = (rise / run) × 12. This tells you how many inches (or any consistent unit) the roof rises for every 12 units of run — a "6-in-12" roof rises 6 inches for every 12 inches (1 foot) of horizontal run.

Rafter length (hypotenuse): rafter = √(rise² + run²), by the Pythagorean theorem. If you are including the eave overhang, add the overhang distance to the run before taking the square root, since the overhang extends the horizontal distance the rafter has to span at the same rise-per-run slope.

Worked example: a roof with a 4-foot rise over a 12-foot run. Pitch ratio = (4/12) × 12 = 4, i.e. "4-in-12". Angle = arctan(4/12) = arctan(0.333) ≈ 18.4 degrees. Percent grade = (4/12) × 100 ≈ 33.3%. Rafter length = √(4² + 12²) = √(16 + 144) = √160 ≈ 12.65 feet. Add a 1.5-foot overhang: rafter with overhang = √(4² + 13.5²) = √(16 + 182.25) = √198.25 ≈ 14.08 feet.

Notice the relationship is not linear: doubling the rise from 4-in-12 to 8-in-12 does not double the angle — it takes you from 18.4 degrees to 33.7 degrees, less than double, because arctan flattens out as the ratio grows. This is why you cannot reliably "eyeball" a pitch conversion and should always run the actual trig.

Common roof pitches: ratio, degrees and percent (quick reference)

These are standard trigonometric conversions (angle = arctan(rise/12), percent = rise/12 × 100) for the most commonly specified x-in-12 pitches, so you can sanity-check any figure this calculator gives you without re-deriving it.

  • 2-in-12 ≈ 9.5° ≈ 16.7% grade — very low slope, minimum for most standard shingles
  • 3-in-12 ≈ 14.0° ≈ 25.0% grade — minimum for most three-tab and architectural shingles
  • 4-in-12 ≈ 18.4° ≈ 33.3% grade — common "standard" residential pitch
  • 5-in-12 ≈ 22.6° ≈ 41.7% grade
  • 6-in-12 ≈ 26.6° ≈ 50.0% grade — widely cited as the practical walkability threshold
  • 8-in-12 ≈ 33.7° ≈ 66.7% grade — steep, common on traditional/period-style homes
  • 9-in-12 ≈ 36.9° ≈ 75.0% grade
  • 12-in-12 = 45.0° = 100% grade — rise equals run exactly
  • 16-in-12 ≈ 53.1° ≈ 133.3% grade — very steep, typical of some Gothic/A-frame designs

How roof pitch is expressed in Gibraltar

Gibraltar follows UK-derived building practice, so roof pitch is conventionally expressed in degrees rather than the American "x-in-12" ratio. Building control and most roofing material technical datasheets used locally quote minimum pitch as a degree figure, in line with UK Building Regulations Approved Document C conventions.

Pro tips and common mistakes

Pitch is the first thing that limits your material choice, not the last. Most standard asphalt shingles require a minimum of around 2-in-12 to 3-in-12 with special low-slope installation methods (double underlayment, different overlap), and a "normal" installation minimum closer to 4-in-12. Metal panel systems and membrane roofing can go much lower, sometimes near-flat, which is exactly why flat and low-slope roofs are almost always metal or membrane rather than shingle. Always check the minimum pitch rating on the specific product's installation instructions rather than assuming a generic figure — manufacturers vary.

The "walkable roof" threshold most trades use is around 6-in-12 (≈26.6°). Below that, most roofers can walk the surface with normal care and footwear. Above it, and especially above 9-in-12, work typically requires roof jacks, harnesses, and toe boards, which adds labor cost and safety-planning time to any job — factor this into quotes if you are estimating, not just materials.

Steeper pitches shed water and snow faster, which matters more in wet or heavy-snow climates and less in dry ones — this is why you will see much steeper traditional roof pitches in snowy regions (to stop snow load building up) and much flatter ones in arid climates. Do not assume a flat regional average is "correct" for your specific site; check your local building code's minimum pitch requirement, which is often tied to your material choice and local snow/rain design loads.

The single most common mistake is reading rise and run off a drawing at the wrong points. Rise should be measured from the top of the wall plate (where the rafter starts climbing) to the ridge, not from the ground or floor level. Run should be measured horizontally from the outside face of the wall (or the birdsmouth cut point) to the centerline of the ridge — including or excluding the overhang inconsistently is the most common source of a rafter-length figure that does not match what gets cut on site.

Do not confuse pitch (rise:run, or the angle/percent derived from it) with "slope" used loosely to mean overall roof shape — a single building can have multiple different pitches on different roof planes (a gambrel or mansard roof, for example, deliberately uses two), so always specify which plane a pitch figure refers to.

When converting a pitch you have been given in degrees back into an x-in-12 ratio for construction (framing squares and speed squares are marked in the x-in-12 system), remember the conversion is x = 12 × tan(angle) — do not just scale the degree figure directly, since the relationship is not linear.

A typical roofer's callout to survey and confirm roof pitch before quoting for re-roofing work runs about £130-£500 in Gibraltar, depending on access and the size of the property.