The Roofing Shingle & Square Sizer estimates asphalt shingle materials and roofing squares required to re-roof residential structures based on ground footprint, roof pitch slope, and cutting waste.

### Mathematical Roofing Formulas - Roof Pitch Multiplier: Evaluated using the trigonometric slope relationship: $$\text{Pitch Factor} = \sqrt{1 + \left(\frac{\text{Roof Pitch}}{12}\right)^2}$$ (e.g., a 6:12 slope has a factor of $\sqrt{1 + (0.5)^2} = \sqrt{1.25} \approx 1.118$). - Adjusted Sloped Surface Area: Combines ground footprint with eave overhang allowance before applying pitch: $$\text{Actual Roof Area} = [\text{Footprint Sq Ft} \times (1 + \text{Overhang \%})] \times \text{Pitch Factor}$$ - Waste Allowance & Roofing Squares: Incorporates valley, hip, and starter cutting waste (default 10%): $$\text{Total Area with Waste} = \text{Actual Roof Area} \times (1 + \text{Waste \%})$$ $$\text{Roofing Squares} = \frac{\text{Total Area with Waste}}{100}$$ - Shingle Bundles: Standard architectural and 3-tab shingles require 3 bundles per square ($$\text{Bundles} = \lceil\text{Roofing Squares} \times 3\rceil$$).

### Worked Numeric Example - Home Footprint: 1,800 sq ft - Roof Pitch: 6:12 (Multiplier = 1.118) - Eave Overhang Allowance: 10% (Adjusted footprint = 1,980 sq ft) - Sloped Roof Surface: $1,980 \times 1.118 = 2,213.6\text{ sq ft}$ - Valley & Ridge Cut Waste: 10% ($2,213.6 \times 1.10 = 2,435\text{ sq ft}$) - Roofing Squares: $2,435 / 100 = 24.35\text{ squares}$ - Total Bundles Needed: $\lceil 24.35 \times 3 \rceil = 74\text{ bundles}$

### Client-Side Execution Note All building dimensions, pitch ratios, and bundle calculations evaluate instantaneously in local browser memory without server data logging.