Roof Pitch
Calculator
Roof pitch is the rise over a 12-unit run. Enter the rise and run to get the pitch as x:12, the angle in degrees, percent slope, the roof-area multiplier, and optional rafter length.
Who it's for: architects, builders, roofers, and homeowners who need a quick pitch read — the angle, slope, and how much extra roof area the slope adds — before ordering materials at the pre-construction stage or sizing rafters.
| Pitch | Angle | Multiplier |
|---|---|---|
| 3:12 | 14.0° | 1.031 |
| 4:12 | 18.4° | 1.054 |
| 6:12 | 26.6° | 1.118 |
| 9:12 | 36.9° | 1.250 |
| 12:12 | 45.0° | 1.414 |
How to use this calculator
The formula
Pitch (x:12) = (rise ÷ run) × 12
Angle = arctan(rise ÷ run), in degrees
Percent slope = (rise ÷ run) × 100
Slope multiplier = √((rise ÷ run)² + 1)
Rafter length = horizontal run × slope multiplier
rise = vertical height gained (any unit)
run = horizontal distance over which that rise occurs (same unit as rise)
The slope multiplier converts a plan (footprint) area to the actual sloped roof surface area.
Worked example
When this estimate will be off
- Assumes a simple gable or shed roof — hip, gambrel, and mansard roofs have multiple pitch sections that each need a separate calculation.
- Rise and run must be in the same unit. Mixing feet and inches without converting first gives a wrong pitch and wrong rafter length.
- The rafter result is the straight-line length along the slope only. It does not include overhangs, fascia extension, or ridge board offset — add those before ordering lumber.
- Curved or barrel-vault roofs have no constant pitch. Measure at several points and use the steepest section when sizing waterproofing or ordering materials.
Frequently asked questions
A common mistake: Assumes a simple gable or shed roof — hip, gambrel, and mansard roofs have multiple pitch sections that each need a separate calculation.
Roof pitch is the steepness of a roof, written as rise over run: the vertical rise for every 12 units of horizontal run. A 6:12 pitch climbs 6 inches for every 12 inches across. Rise and run must use the same unit. Pitch drives drainage, material choice, and how much roof area a footprint actually covers.
Take the arctangent of rise divided by run, then read it in degrees. For a 6:12 pitch, arctan(6 / 12) = arctan(0.5) = 26.6°. A 12:12 pitch equals exactly 45°, and 4:12 works out to about 18.4°. This calculator runs that conversion automatically once you enter the rise and run.
The x:12 notation fixes the run at 12 and reports the rise over that span. A 4:12 roof rises 4 units for every 12 units of horizontal travel, and 9:12 rises 9. Twelve is the convention because it matches inches per foot, so framers can read pitch straight off a framing square.
Low-slope roofs sit below about 18°, around 3:12 or shallower, and usually need membrane or sealed systems because shingles can leak at shallow angles. Standard pitched roofs run roughly 18° to 45° (about 4:12 to 12:12). Anything steeper than 45°, above 12:12, is a steep slope. This calculator labels each range.
Sources
- IRC 2021 R905 — minimum slope requirements by roofing material type (e.g. asphalt shingles: 2:12 minimum; low-slope membrane: below 2:12)
This free Roof Pitch Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.