Data Source and Methodology
Authoritative Data Source (formula): International Association of Certified Home Inspectors (InterNACHI), “Roof Pitch Multiplier,” 2022. https://www.nachi.org/roof-slope-pitch-multiplier.htm — The multiplier is derived from right-triangle geometry.
Manufacturer references (coverage defaults): GAF Technical Data Sheets (ridge caps and shingles), 2024; CertainTeed Underlayment Data Sheets, 2023. Coverage varies by product—override fields as needed.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formulas Explained
Roof pitch multiplier: \( f = \sqrt{1 + \left(\dfrac{\text{rise}}{\text{run}}\right)^2} = \sec(\theta) \)
Plan dimensions with overhang: \( L' = L + 2e,\quad W' = W + 2e \)
Plan area: \( A_{\text{plan}} = L' \times W' \)
Sloped roof area (no waste): \( A = A_{\text{plan}} \times f \)
With waste factor \( w \) (as a fraction): \( A_w = A \times (1 + w) \)
Roofing squares: \( \text{squares} = \dfrac{A_w}{100\ \text{ft}^2} \)
Bundles: \( \text{bundles} = \left\lceil \text{squares} \times B_{\text{per sq}} \right\rceil \)
Ridge length: for gable \( R = L \); for hip \( R = |L - W| \); for shed \( R = 0 \)
Ridge cap bundles: \( \left\lceil \dfrac{R}{C_{\text{ridge}}} \right\rceil \), where \( C_{\text{ridge}} \) is linear feet per bundle
Drip edge (perimeter): \( P = 2(L' + W') \)
Ice-and-water shield along eaves (courses of ~3 ft): area \( \approx E \times 3\ \text{ft} \times c \), where \( E \) is eave length and \( c \) the number of courses
Glossary of Variables
| Symbol / Field | Meaning |
|---|---|
| L, W | Footprint length and width (without overhang) |
| e | Overhang per side |
| f | Pitch multiplier |
| A_plan | Plan (horizontal) area with overhang |
| A, A_w | Roof sloped area without/with waste |
| w | Waste factor as a fraction (e.g., 0.10) |
| Squares | Roofing area in 100 ft² units |
| B per sq | Bundles per square (default 3) |
| R | Ridge length |
| C_ridge | Linear feet per ridge-cap bundle |
| P | Perimeter for drip edge with overhang |
How It Works: A Step-by-Step Example
- Inputs: units = Imperial; shape = Gable; L = 40 ft, W = 28 ft; overhang e = 1 ft; pitch = 6 per 12; waste = 10%; bundles per square = 3; ridge coverage = 20 ft/bundle; underlayment = 400 ft²/roll.
- Pitch multiplier: f = √(1 + (6/12)²) = √(1 + 0.25) = √1.25 ≈ 1.118.
- Plan dims: L' = 40 + 2(1) = 42 ft; W' = 28 + 2(1) = 30 ft.
- Plan area: A_plan = 42 × 30 = 1260 ft².
- Sloped area: A = 1260 × 1.118 ≈ 1409. ≈ 1409 ft².
- With waste: A_w = 1409 × 1.10 ≈ 1550 ft².
- Squares: 1550/100 = 15.5 sq. Bundles: ceil(15.5 × 3) = ceil(46.5) = 47.
- Ridge length: R = L = 40 ft → ridge bundles = ceil(40/20) = 2.
- Perimeter: P = 2(42 + 30) = 144 ft (drip edge).
- Underlayment rolls: ceil(1550/400) = 4.
Frequently Asked Questions (FAQ)
Does this roofing calculator support metric?
Yes. Switch to Metric to enter meters. Results display in both Imperial and Metric for clarity.
How do you handle hip roofs?
For uniform pitch, surface area is plan area times the pitch multiplier. Ridge length for hips is approximated as |L − W|, which is accurate for symmetrical hips.
Should I include valleys and dormers?
Complex features increase waste and may add material. Increase the waste factor or perform a detailed takeoff for those elements.
How reliable are bundle and roll coverages?
Defaults reflect common products (e.g., 3 bundles/square, ~400 ft² per 15 lb felt roll). Always verify coverage on the product’s technical data sheet and adjust the fields.
What is a roofing square?
One roofing square equals 100 square feet of roof surface area (about 9.29 m²).
Can this estimate drip edge and ice-and-water shield?
Yes. We compute perimeter length for drip edge and rolls for membrane along eaves based on the number of courses you select.
Why does the calculator add overhangs before calculating area?
Shingles and underlayment cover the full roof surface, including overhangs. Adding overhang to the footprint yields a more accurate material estimate.