How to Calculate Roof Pitch
Measuring rise and run, and reading the result as X-in-12
The roof pitch formula
Roof pitch = rise ÷ run × 12, written as X-in-12 (or X/12). Measure the vertical rise and the horizontal run in the same unit, divide, and multiply by 12: a roof that rises 4 ft over an 8 ft run is 4 ÷ 8 × 12 = 6, a 6-in-12 pitch. The Roof Pitch Calculator does the same conversion and also gives the angle and slope factor.
Rise and run
Roof pitch compares vertical rise to horizontal run. In the US convention, run is standardized to 12 units, so a roof that rises 6 units for every 12 units of horizontal run is a '6-in-12' pitch. The units of rise and run cancel out, so a 6-in-12 pitch is 6-in-12 whether you measured in inches, feet, or centimetres — as long as rise and run use the same unit.
How to measure it
There are three practical ways to get rise and run. Measuring in the attic is the safest, measuring on the roof surface carries the most fall risk, and the gable-end method works from the ground or from drawings.
From the attic
Set a level against the underside of a rafter and hold it horizontal. Mark the level 12 in from where it meets the rafter, then measure vertically from that mark up to the rafter with a tape measure or rafter square. That measurement in inches is the rise per 12 — the pitch. A digital angle finder or a smartphone level app laid on the rafter gives the angle faster, though sometimes less precisely; convert it with rise = 12 × tan(angle), so a reading of 26.6° is a 6-in-12 roof.
On the roof surface
The same level-and-tape method works on top of the roofing: rest the upslope end of the level on the roof, hold it horizontal, and measure straight down from the 12 in mark to the roof surface. Only do this if you are trained and equipped for roof work. Under OSHA's construction rules, any roof steeper than 4-in-12 is a steep roof, and workers on a steep roof with an unprotected edge 6 ft or more above a lower level must be protected by guardrails with toeboards, safety nets or personal fall-arrest systems. Measuring from the attic or the gable end avoids the climb.
From the gable end or plans
On a symmetrical gable, the run is approximately half the building's span and the rise is approximately the height of the ridge above the top of the wall plates; both can be measured from the ground or read from drawings. A 28 ft wide building with the ridge 7 ft above the plates has a 14 ft run, so the pitch is 7 ÷ 14 × 12 = 6-in-12.
The same numbers give the rafter's line length: 14 ft × the 6-in-12 slope factor of 1.118 = 15.65 ft from plate to ridge, before the overhang. The Rafter Length Calculator works this out, and the birdsmouth cut is the notch where that rafter seats on the wall plate.
Pitch as an angle, and the slope factor
Pitch converts to an angle in degrees using arctan(rise/run) — a 6-in-12 pitch is arctan(6/12) ≈ 26.6°. It also produces the slope factor, √(1 + (rise/run)²), used to convert a flat footprint area into the true sloped roof area. Angle and slope factor are two different numbers derived from the same rise/run ratio — pitch itself never changes with the units you measured in.
Pitch also converts to a percent slope, or grade: percent = rise ÷ run × 100, so 6-in-12 is 50% and 12-in-12 is 100%. The table gives each conversion and its reverse. For the values of each common pitch from 2/12 to 12/12, see the roof pitch chart.
| You have | You want | Formula | Example (6-in-12) |
|---|---|---|---|
| Rise and run | Pitch (X-in-12) | X = rise ÷ run × 12 | 7 ÷ 14 × 12 = 6 |
| Pitch X | Angle | arctan(X ÷ 12) | arctan(0.5) ≈ 26.57° |
| Angle | Pitch X | X = 12 × tan(angle) | 12 × tan 26.57° ≈ 6 |
| Pitch X | Percent slope | X ÷ 12 × 100 | 50% |
| Percent slope | Pitch X | X = percent × 12 ÷ 100 | 50 × 12 ÷ 100 = 6 |
| Pitch X | Slope factor | √(X² + 144) ÷ 12 | ≈ 1.118 |
Worked Example
A roof rises 8 inches over a 12-inch run.
Pitch = 8-in-12
Angle = arctan(8/12) ≈ 33.7°
Slope factor = √(1 + (8/12)²) ≈ 1.202
Percent slope = 8 ÷ 12 × 100 ≈ 66.7%
FAQ
- Is a steeper pitch always a bigger number?
- Yes — a higher rise-per-12 number means a steeper roof. A 3-in-12 is a shallow, walkable slope; a 12-in-12 (a 45° angle) is a steep roof requiring fall-protection for most work.
- Does roof pitch change if I measure in metric units?
- No. Pitch is a ratio of rise to run, so as long as both are measured in the same unit, the ratio — and the angle and slope factor derived from it — comes out identical whether you used inches, feet, or metres.
- How do I convert roof pitch to a percentage?
- Divide the rise by the run and multiply by 100. A 6-in-12 roof is 6 ÷ 12 × 100 = 50%, and a 4-in-12 roof is about 33.3%.
- Can I find roof pitch without going on the roof?
- Yes. Measure along a rafter in the attic, or measure the building's span and the ridge height above the wall plates from the gable end and use half the span as the run. Both avoid the fall risk of working on the roof surface.
Related Calculators
Related Guides
From the Blog
Sources
Trigonometry
Pitch = rise ÷ run × 12; angle = arctan(rise ÷ run); percent slope = rise ÷ run × 100; slope factor = √(rise² + run²) ÷ run.
OSHA 29 CFR 1926.500(b)
Definitions: a low-slope roof is 4 in 12 or less; a steep roof is more than 4 in 12.
OSHA 29 CFR 1926.501(b)(11)
Fall protection for employees on steep roofs with unprotected sides and edges 6 ft or more above lower levels.