The Roof Pitch Slope (X/12), Common Rafter Length & Overhang Sizer provides a three-variable mathematical modeling interface for exploring comparative architectural framing ratios in timber roof construction.

### Algebraic Ratio Formulation The component evaluates user parameters using three generalized algebraic equations: - Primary Metric: $(val_1 \times val_2) / \max(0.01, val_3)$. In structural roof framing models, this represents proportional rafter span load relative to pitch slope or lumber thickness. - Geometric Mean (Secondary Index): $\sqrt{\max(0, val_1 \times val_2)}$, modeling transitional hypotenuse rafter lengths. - Efficiency Ratio (%): $\min(100, \max(0, (val_1 / (val_1 + val_2)) \times 100))$, expressing relative load weighting.

### Note on Architectural Timber Framing Calculations This calculator computes a generalized three-parameter algebraic ratio. It does not replace trigonometric right-triangle rafter formulas ($L = \sqrt{\text{run}^2 + \text{rise}^2}$), IRC building code live/dead load span tables, birdsmouth heel cut deductions, or ridge board thickness adjustments. Framers and carpenters should consult architectural plans and speed square tables for production cutting.

### Worked Numeric Example Using default inputs: - Primary Dimension / Load ($val_1$): 100 - Secondary Factor / Velocity ($val_2$): 20 - Tuning / Geometric Modifier ($val_3$): 5 - Results: - Primary Ratio: $(100 \times 20) / 5 = 400.00$ - Geometric Mean: $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$ - Efficiency Ratio: $(100 / (100 + 20)) \times 100 = 83.33\%$

### In-Browser Processing All equations evaluate directly within your client browser session using local JavaScript. No building dimensions or framing specifications are transmitted to external servers.