Roof Pitch Calculator
Determine roof pitch, slope angle, and rafter length from rise and run
Results
Step-by-Step Calculation
Understanding Roof Pitch
Roof pitch describes how steep a roof is. It is the ratio between the vertical rise and the horizontal run. In the United States, pitch is conventionally expressed as the number of inches of rise per 12 inches of run, written as "x:12" or "x/12". A 6:12 roof, for example, rises 6 inches for every 12 inches of horizontal distance.
Key Formulas:
- Pitch ratio: (Rise x 12 / Run) : 12
- Slope angle: arctan(Rise / Run) in degrees
- Rafter multiplier: sqrt(Rise^2 + Run^2) / Run
- Grade percentage: (Rise / Run) x 100
Common Pitch Categories:
- Flat / Low slope: below 2:12 (under ~9.5 degrees)
- Conventional: 4:12 to 9:12 (~18 to 37 degrees)
- Steep slope: above 9:12 (over ~37 degrees)
Roof Pitch Reference Table
| Pitch (x:12) | Angle (degrees) | Grade (%) | Rafter Multiplier |
|---|---|---|---|
| 2:12 | 9.46 | 16.7% | 1.014 |
| 4:12 | 18.43 | 33.3% | 1.054 |
| 6:12 | 26.57 | 50.0% | 1.118 |
| 8:12 | 33.69 | 66.7% | 1.202 |
| 10:12 | 39.81 | 83.3% | 1.302 |
| 12:12 | 45.00 | 100.0% | 1.414 |
Tip: Multiply the horizontal run by the rafter multiplier to estimate the rafter length along the slope. This is the length of material needed per unit of horizontal distance, before adding overhang.
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Note: This calculator provides estimates based on standard geometric formulas. Rafter multipliers give the slope length per unit of horizontal run and do not include overhang, ridge thickness, or framing allowances. For actual construction, consult a structural engineer or local building code.