Roof Pitch Calculator
Enter rise and run (or any two values) to instantly convert roof pitch between x/12 ratio, degrees, percentage slope, and pitch multiplier.
| Pitch | Degrees | Percent | Multiplier | Rafter/ft |
|---|---|---|---|---|
| 3:12 | 14.0° | 25.0% | 1.031 | 1.031 ft |
| 4:12 | 18.4° | 33.3% | 1.054 | 1.054 ft |
| 5:12 | 22.6° | 41.7% | 1.083 | 1.083 ft |
| 6:12 | 26.6° | 50.0% | 1.118 | 1.118 ft |
| 7:12 | 30.3° | 58.3% | 1.158 | 1.158 ft |
| 8:12 | 33.7° | 66.7% | 1.202 | 1.202 ft |
| 9:12 | 36.9° | 75.0% | 1.250 | 1.250 ft |
| 10:12 | 39.8° | 83.3% | 1.302 | 1.302 ft |
| 12:12 | 45.0° | 100.0% | 1.414 | 1.414 ft |
How to Use This Calculator
Enter any two values and the calculator converts to all other formats automatically:
- Rise — The vertical height your roof gains, typically measured in inches over a 12-inch horizontal run
- Run — The horizontal distance, almost always 12 inches for standard pitch notation
- Degrees — The angle of the roof slope from horizontal (0° = flat, 45° = 12/12 pitch)
- Percent slope — Rise divided by run, expressed as a percentage (useful for drainage design)
The calculator also outputs the pitch multiplier — the factor you multiply your footprint area by to get actual roof area. Use this with the Roof Area Calculator.
The Formula
Degrees = arctan(Rise / Run) × (180 / π)
Percent Slope = (Rise / Run) × 100
Pitch Multiplier = √(Run² + Rise²) / Run
For a 6/12 pitch:
Degrees = arctan(6/12) = 26.57°
Percent = (6/12) × 100 = 50%
Multiplier = √(144 + 36) / 12 = √180 / 12 = 1.118
Example: Converting a 7/12 Pitch
Example: 7/12 Roof Pitch Conversion
A 7/12 pitch adds 15.8% more area compared to the footprint. A 30×40 ft house with this pitch has 1,200 × 1.158 = 1,390 sq ft of roof area.
Roof Pitch Quick Reference
| Pitch | Degrees | % Slope | Multiplier | Category |
|---|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.003 | Flat |
| 2/12 | 9.5° | 16.7% | 1.014 | Low slope |
| 3/12 | 14.0° | 25% | 1.031 | Low slope |
| 4/12 | 18.4° | 33.3% | 1.054 | Moderate |
| 5/12 | 22.6° | 41.7% | 1.083 | Moderate |
| 6/12 | 26.6° | 50% | 1.118 | Moderate |
| 7/12 | 30.3° | 58.3% | 1.158 | Steep |
| 8/12 | 33.7° | 66.7% | 1.202 | Steep |
| 9/12 | 36.9° | 75% | 1.250 | Steep |
| 12/12 | 45.0° | 100% | 1.414 | Very steep |
Frequently Asked Questions
Related Calculators
Sources & References
The formulas, code requirements, and reference data used in this calculator are sourced from the following authoritative organizations and publications. Local codes vary — always verify with your jurisdiction's building department.
- International Residential Code (IRC) 2024 — Chapter 9: Roof Assemblies — ICC
- NRCA Roofing Manual (Steep-Slope & Low-Slope) — National Roofing Contractors Association
- Asphalt Shingle Installation Manual — ARMA (Asphalt Roofing Manufacturers Association)
- IRC R905.2.2 — Slope Requirements for Asphalt Shingles — ICC
- ASTM D3161 / D7158 — Wind Resistance of Roof Coverings — ASTM International
Disclaimer: Calculator results are estimates intended for planning and educational purposes only. They do not replace professional engineering analysis, building permit review, or contractor estimates. Always consult a licensed roofing contractor or structural engineer for final specifications.