Roof pitch describes how steep a roof is. This free calculator converts between all three ways of writing it — pitch as rise over 12, angle in degrees, and slope as a percentage — and works out the rafter length for your span. Everything runs in your browser: nothing is uploaded, and there is no sign-up.
Roof Pitch Calculator
Enter any one value — rise and run, angle in degrees, or slope in percent. Everything else is calculated instantly in your browser.
| Pitch | Angle | Slope | Multiplier |
|---|
How to calculate a roof pitch
Roof pitch is the vertical rise divided by the horizontal run, expressed per 12 units of run: pitch = (rise ÷ run) × 12. Measure the run horizontally from the ridge out to the wall, and the rise vertically from the top of the wall plate to the underside of the ridge. If a roof climbs 4 inches for every 12 inches of run, that is a 4:12 pitch — usually spoken as “four twelve”.
The easiest field method: hold a level horizontally against the rafter, mark 12 inches along it, then measure straight down from that mark to the rafter. That measurement is the rise, and the number you read is the pitch. Because the ratio is dimensionless, the same formula works in metric — a roof rising 100 mm over 300 mm of run is 1:3, which is the same as 4:12.
What is a 4/12 roof pitch formula?
A 4/12 roof rises 4 units for every 12 units of run. From that single ratio everything else follows:
- Angle: arctan(4 ÷ 12) = 18.43°
- Slope: 4 ÷ 12 × 100 = 33.3 %
- Rafter multiplier: √(1 + (4÷12)²) = 1.0541
The multiplier is the useful one on site. Multiply it by the run and you get the rafter length directly — for a 24 ft span the run is 12 ft, so the common rafter is 12 × 1.0541 = 12.65 ft, or 12 ft 7¾ in before any overhang. 4:12 is the most common residential pitch in North America: it sheds water well, takes standard asphalt shingles, and is still walkable for most roofers.
Roof pitch chart
| Pitch | Angle | Slope | Multiplier |
|---|---|---|---|
| 1:12 | 4.76° | 8.3 % | 1.0035 |
| 2:12 | 9.46° | 16.7 % | 1.0138 |
| 3:12 | 14.04° | 25.0 % | 1.0308 |
| 4:12 | 18.43° | 33.3 % | 1.0541 |
| 5:12 | 22.62° | 41.7 % | 1.0833 |
| 6:12 | 26.57° | 50.0 % | 1.1180 |
| 7:12 | 30.26° | 58.3 % | 1.1577 |
| 8:12 | 33.69° | 66.7 % | 1.2019 |
| 9:12 | 36.87° | 75.0 % | 1.2500 |
| 10:12 | 39.81° | 83.3 % | 1.3017 |
| 11:12 | 42.51° | 91.7 % | 1.3566 |
| 12:12 | 45.00° | 100.0 % | 1.4142 |
How to calculate roof pitch in degrees
Degrees come from the arctangent of the ratio: angle = arctan(rise ÷ run). For 6:12 that is arctan(0.5) = 26.57°. Going the other way, multiply the tangent of the angle by 12 — a 30° roof is tan(30°) × 12 = 6.93, so roughly 7:12.
Degrees are what you will see on architectural drawings and in most of Europe; the x:12 notation is a North American carpentry convention. The calculator above accepts either — switch the input mode and the rest updates.
What pitch is a 22.5 degree roof?
tan(22.5°) = 0.4142, and 0.4142 × 12 = 4.97, so a 22.5° roof is almost exactly 5:12. Its slope is 41.4 %, and the rafter multiplier is 1.0824. In practice a roofer would simply call this a 5:12 roof — the 0.03 difference is far below normal framing tolerance.
What is a 25% roof slope?
A 25 % slope means the roof rises 25 units for every 100 units of run — a ratio of 0.25. In pitch notation that is 0.25 × 12 = 3:12, and the angle is arctan(0.25) = 14.04°.
Watch out for a common mix-up: 25 % is not a 25° roof. A 25° roof has a slope of 46.6 % and a pitch of about 5.6:12 — significantly steeper.
Roof pitch calculator in metric
Switch the calculator to metric and enter rise and run in millimetres, with the span in metres. The ratio itself does not change — pitch, degrees and percent are all dimensionless. Metric practice usually skips the x:12 notation and states the angle in degrees or the slope as a ratio like 1:3, so a drawing marked 1:3 converts to 4:12 without arithmetic.
Lean-to, shed, flat and single-slope roofs
These all describe a roof with one slope rather than two, and the pitch maths is identical — what changes is the run.
- Shed and lean-to roofs run the full width of the structure, not half of it. Enter the full width as the span and remember the rafter covers all of it.
- Flat roofs are never truly flat. Codes generally require a minimum fall — commonly 1:80 to 1:40, about ¼ in per foot or 1–2 % — so water drains. A “flat” roof here is a very low pitch, not zero.
- Single-slope (monopitch) roofs are the same geometry as a shed roof, just the architectural name.
For a gable roof, the calculator halves the span automatically, since each rafter only covers half the width.
Rafter length from roof pitch
Rafter length is the hypotenuse of the rise-and-run triangle: rafter = √(rise² + run²), or more conveniently rafter = run × multiplier. The result is the common rafter from the wall plate to the ridge, measured along the top edge. It does not include the overhang (add it to the run first), the ridge board thickness (subtract half of it from the run), or the birdsmouth and plumb cuts at either end.
For a 24 ft gable roof at 6:12: run = 12 ft, multiplier = 1.1180, rafter = 13.42 ft = 13 ft 5 in. If you need bending moments, shear or deflection for that rafter rather than just its length, use the free Beam & Frame Calculator.
These figures are geometry, not a structural design. Rafter sizing depends on span, spacing, species, grade and the snow and wind loads at your site — check your local building code, and have anything structural reviewed by a qualified engineer. For the underlying theory see our guide to beam load calculations.