Roof Pitch Calculator
Calculate roof pitch ratio, angle in degrees, and rafter length from rise and run measurements.
Formulas
Pitch Ratio = (Rise ÷ Run) × 12 → expressed as X:12
Roof Angle = arctan(Rise ÷ Run) × (180 ÷ π)
Rafter Length = √(Rise² + Run²) (Pythagorean theorem)
Rafter Length per 12″ Run = √(Pitch² + 12²)
If Span is provided: Run = Span ÷ 2 (span is the full width; run is half-span).
Assumptions & References
- Rise and Run must be in the same units (inches by default).
- Pitch is expressed as the number of inches of rise per 12 inches of run (X:12 notation), per standard US building practice.
- Rafter length does not include overhang (eave extension); add overhang separately.
- Roof categories follow general construction guidelines: Flat/Low-Slope < 2:12, Low-Slope 2–4:12, Conventional 4–9:12, Steep 9–18:12, Very Steep ≥ 18:12.
- Reference: IRC (International Residential Code) Section R802 — Roof-Ceiling Construction.
- Trigonometric identity: tan(θ) = Rise / Run, therefore θ = arctan(Rise / Run).