About

Roof pitch defines the steepness of a roof, a critical factor in structural engineering and architectural design. It determines how effectively a roof sheds water, snow, and debris. Builders in North America typically express pitch as a ratio of vertical rise to a 12-inch horizontal run (e.g., 4/12). In contrast, engineering plans often utilize degrees or percentage grades.

Accuracy in these calculations prevents costly material waste and structural failures. Specific roofing materials require minimum slopes to function correctly. Asphalt shingles, for instance, generally require a minimum pitch of 2/12 to prevent water backup under the tabs. Metal roofing can often accommodate lower slopes. This tool standardizes the conversion between these units, providing the necessary data for cutting rafters and estimating material coverage.

Formulas

The geometry of a gable roof relies on right-angle trigonometry. The slope is the ratio of vertical rise to horizontal run.

1. Pitch Angle (θ):

θ = arctanriserun

2. Rafter Length (L):

L = √rise² + run²

3. Grade Percentage (G):

G = riserun × 100

4. Pitch Ratio (x/12):

x = 12 × riserun

Note: The run in these formulas refers to the horizontal distance covered by the rafter, which is typically half the total building span for a symmetrical gable roof.

Reference Data

Pitch (x/12)	Angle (°)	Grade (%)	Rafter Multiplier	Common Application
1/12	4.76°	8.3%	1.003	Industrial / Built-up Roofing
2/12	9.46°	16.7%	1.014	Minimum for Asphalt Shingles (Low Slope)
3/12	14.04°	25.0%	1.031	Sheds / Carports
4/12	18.43°	33.3%	1.054	Standard Residential Minimum
5/12	22.62°	41.7%	1.083	Moderate Residential
6/12	26.57°	50.0%	1.118	Common Residential
7/12	30.26°	58.3%	1.158	Steeper Residential / Snow Areas
8/12	33.69°	66.7%	1.202	Traditional Gable
9/12	36.87°	75.0%	1.250	Architectural Style
10/12	39.81°	83.3%	1.302	Attic Space Maximization
12/12	45.00°	100.0%	1.414	Tudor / Gothic Styles
18/12	56.31°	150.0%	1.803	A-Frame Structures

Frequently Asked Questions

While there is no single standard, pitches between 4/12 and 9/12 are most common in North America. A 4/12 pitch is considered the minimum for standard asphalt shingles without special underlayment. Steeper pitches like 10/12 or 12/12 are used to increase attic space or shed snow more effectively in colder climates.

For a symmetrical gable roof (equal slopes on both sides), the Run is exactly half of the total Span. If the building is 24 feet wide, the Run is 12 feet. If the roof is asymmetrical (saltbox style), you must measure the run for each side independently relative to the ridge board location.

The mathematical hypotenuse is the line from the top of the top plate to the center of the ridge. However, actual rafter cutting requires adjustments. You must deduct half the thickness of the ridge board from the top of the rafter. You also need to add length for the overhang (eave) at the bottom. This tool calculates the theoretical hypotenuse (triangle line length).

Material specifications and local building codes dictate minimum pitch. Asphalt shingles generally fail below 2/12 because water moves too slowly and can wick under the shingles. Metal standing seam roofs can often go as low as 1/4 per 12. Flat roofs (low slope) require continuous membranes like TPO or EPDM rather than overlapping units.

Yes. A 12/12 pitch means the roof rises 12 inches for every 12 inches of run. This creates a ratio of 1, and the arctangent of 1 is 45 degrees. This is the only pitch where the Rise equals the Run.