How to calculate roof pitch (chart: x:12, degrees, multiplier)
Pitch = rise / run. Measure how many inches the roof rises for every 12 in of horizontal run, and that number is the pitch in x:12: a rise of 6 in over 12 in is 6:12, which is 26.6°, a 50% slope, and multiplies the footprint by 1.118 to give the roof surface. In degrees, pitch = arctan(rise / run); 12:12 is 45°. The charts below convert 1:12 to 12:12 into degrees, percent and the area multiplier, turn 10° to 45° (UK and metric roofs) back into x:12, and give the rise and rafter length for 12 ft of run at each pitch.
Open the roof pitch calculator
How do I calculate the pitch of a roof?
Pitch is the rise divided by the run. In the US it is written as the rise for 12 units of run, so a roof that climbs 6 in over 12 in across is 6:12; in the UK, Australia and most metric countries it is quoted in degrees from the horizontal. The three forms convert with school trigonometry: degrees = arctan(rise / run), percent = rise / run x 100, rise per 12 = tan(degrees) x 12. The units cancel, so 1 m of rise over 2 m of run is 6:12 as surely as 6 in over 12 in.
The number the roofing quantities need is the area multiplier, the square root of 1 + (rise / run)²: the length of the slope for one unit of run. Roof surface = footprint (the plan area, overhang included) x multiplier, for a gable and a hip roof alike as long as every slope has the same pitch. At 6:12 the multiplier is 1.118, so a 1,000 sq ft footprint carries 1,118 sq ft of roof; the roof pitch calculator does the conversion from any of the three forms and keeps the pitch for the shingle and tile calculators.
Roof pitch chart: x:12 to degrees, percent and multiplier
Every whole pitch from 1:12 to 12:12, computed. These are geometry, not published figures, so no source is cited for them.
| Pitch | Degrees | Slope | Area multiplier |
|---|---|---|---|
| 1:12 | 4.8° | 8.3% | 1.0035 |
| 2:12 | 9.5° | 16.7% | 1.0138 |
| 3:12 | 14° | 25% | 1.0308 |
| 4:12 | 18.4° | 33.3% | 1.0541 |
| 5:12 | 22.6° | 41.7% | 1.0833 |
| 6:12 | 26.6° | 50% | 1.118 |
| 7:12 | 30.3° | 58.3% | 1.1577 |
| 8:12 | 33.7° | 66.7% | 1.2019 |
| 9:12 | 36.9° | 75% | 1.25 |
| 10:12 | 39.8° | 83.3% | 1.3017 |
| 11:12 | 42.5° | 91.7% | 1.3566 |
| 12:12 | 45° | 100% | 1.4142 |
Degrees to x:12 (UK, metric roofs)
Tile data sheets and UK quotes give the pitch in degrees. The chart turns the common values back into rise per 12 so the same footprint maths works; the multiplier is the same whichever way the pitch is written.
| Degrees | Rise per 12 | Slope | Area multiplier |
|---|---|---|---|
| 10° | 2.12:12 | 17.6% | 1.0154 |
| 15° | 3.22:12 | 26.8% | 1.0353 |
| 20° | 4.37:12 | 36.4% | 1.0642 |
| 22.5° | 4.97:12 | 41.4% | 1.0824 |
| 25° | 5.6:12 | 46.6% | 1.1034 |
| 30° | 6.93:12 | 57.7% | 1.1547 |
| 35° | 8.4:12 | 70% | 1.2208 |
| 40° | 10.07:12 | 83.9% | 1.3054 |
| 45° | 12:12 | 100% | 1.4142 |
Rise and rafter length per 12 ft of run
Half of a 24 ft wide gable is 12 ft of run from the wall to the ridge. The rise is run x rise / 12 and the rafter along the slope is run x multiplier, without the tail past the wall and without the ridge board allowance. For a different run, scale the row: a 15 ft run at 6:12 is 16.77 ft of rafter.
| Pitch | Degrees | Rise (ft) | Rafter length (ft) |
|---|---|---|---|
| 1:12 | 4.8° | 1 | 12.04 |
| 2:12 | 9.5° | 2 | 12.17 |
| 3:12 | 14° | 3 | 12.37 |
| 4:12 | 18.4° | 4 | 12.65 |
| 5:12 | 22.6° | 5 | 13 |
| 6:12 | 26.6° | 6 | 13.42 |
| 7:12 | 30.3° | 7 | 13.89 |
| 8:12 | 33.7° | 8 | 14.42 |
| 9:12 | 36.9° | 9 | 15 |
| 10:12 | 39.8° | 10 | 15.62 |
| 11:12 | 42.5° | 11 | 16.28 |
| 12:12 | 45° | 12 | 16.97 |
What the pitch does to the roof area
The steeper the roof, the more surface sits over the same footprint, and the more shingles or tiles it takes. On a 1,000 sq ft footprint the roof is 1,054 sq ft at 4:12 and 1,414 sq ft at 12:12, 35 against 47 bundles at 3 per square with 10% waste. The bundles per square guide has the chart for 1,000 to 3,000 sq ft at four pitches, and the roof shingle calculator runs your own footprint, overhang and pitch.
| Pitch | Multiplier | Roof area (sq ft) | Squares | Bundles |
|---|---|---|---|---|
| 4:12 | 1.054 | 1,054 | 10.5 | 35 |
| 6:12 | 1.118 | 1,118 | 11.2 | 37 |
| 8:12 | 1.202 | 1,202 | 12 | 40 |
| 12:12 | 1.414 | 1,414 | 14.1 | 47 |
Frequently asked questions
- What is a 4:12 pitch in degrees?
- 18.4°: arctan(4 / 12). It is a 33.3% slope and multiplies the footprint by 1.054. 6:12 is 26.6°, 8:12 is 33.7° and 12:12 is 45°; the first chart has every whole pitch from 1:12.
- What is a 30 degree roof pitch in x:12?
- 6.93:12: rise per 12 = tan(30°) x 12. So a UK roof at 30° sits between 6:12 and 7:12 in US terms, with a multiplier of 1.155. The second chart converts 10°, 15°, 20°, 22.5°, 25°, 30°, 35°, 40°, 45°; the calculator takes any value.
- How do I measure the pitch of a roof?
- In the attic, hold a spirit level horizontally against the underside of a rafter, mark 12 in from the point where it touches, and measure straight up from that mark to the rafter: that measurement in inches is the pitch in x:12. On the roof surface, do the same with the level on the shingles, or read the degrees from a phone inclinometer laid flat on the slope. From the ground, count the courses of siding on a gable end to get the rise and the run. Type whichever you have into the calculator.
- How do I work out the pitch of a lean-to roof?
- Rise and run in the same unit, then rise / run x 12. A lean-to that rises 2.5 ft over a 10 ft run is 3:12, 14°, a 25% slope; the rafter along that slope is 10.31 ft long for the 10 ft of run. Metres work the same: 0.75 m over 3 m is the same 3:12.
- Why is 12:12 exactly 45 degrees?
- Because rise equals run: tan(45°) = 1, so 12 in of rise per 12 in of run. The rafter is then 1.4142 times the run (the square root of 2), so a 12 ft run needs 16.97 ft of rafter against 13.42 ft at 6:12.
- Does the pitch change how many shingles I need?
- Yes: roof area = footprint x multiplier. A 1,000 sq ft footprint is 1,054 sq ft of roof at 4:12 and 1,414 sq ft at 12:12, so 35 bundles against 47 at 3 per square with 10% waste. The bundles guide has the full chart by footprint and pitch.
More guides
- How much does a new roof cost for a 1,500 square foot house?
Installed cost for a 1,500 sq ft footprint at 6:12 by material, from the HomeAdvisor 2026 ranges per square; charts for 1,000 to 3,000 sq ft and UK cost per m².
- How much does it cost to tile a roof in the UK? (per m² and per roof)
Supplied-and-fitted cost per m² for concrete, clay and slate (MyJobQuote 2026) for 50 to 150 m² of roof; tiles, battens and tile cost per type at 10% waste.
- How many bundles of shingles per square? (with roof size chart)
Three bundles per square for standard shingles (Owens Corning, IKO); squares and bundles for 1,000 to 3,000 sq ft footprints at 4:12 to 10:12; UK tiles per m2.
Last updated 2026-09-21. Planning quantities from manufacturer coverage figures and published cost ranges, each with its source and date: measure the roof and follow the product data sheet. Not a structural assessment.