Methodology
Last updated November 12, 2026.
Every calculator and table on FreeRoofingCalculators.com uses the same small, tested math library. This page lists the formulas, the defaults and where each manufacturer figure comes from. Sources last checked November 12, 2026.
Geometry
Multiplier = √(12² + rise²) ÷ 12
Diagonal (rise over run page) = run × multiplier = √(rise² + run²) · Ratio = 1 : (run ÷ rise)
Hip/valley factor = √(2 × 12² + rise²) ÷ 12
Roof area = (length + 2 × overhang) × (width + 2 × overhang) × multiplier
Squares = roof area ÷ 100
Gable: ridge = length + 2 × overhang, starter = eaves + 4 slope lengths · Hip: ridge = length − width, cap = ridge + 4 hips, starter = eaves
Common rafter: run = width ÷ 2 + overhang; length = run × multiplier; cut = length − (ridge thickness ÷ 2) × multiplier
The model is a simple rectangle with the same pitch on every plane and the same overhang on every side. Complex roofs should be measured plane by plane. Metric inputs are converted exactly (1 m = 3.28084 ft, 1 in = 2.54 cm, 1 m² = 10.7639 sq ft) before the same math runs.
Roof truss geometry
Top chord, heel to peak = (span ÷ 2) × multiplier · Overhang tail = overhang × multiplier (measured along the slope)
Bottom chord = span · Web length = √(horizontal distance² + height difference²)
King post: one post at mid-span · Queen post: two posts at ⅓ span with a horizontal strut · Fink: webs from the ⅓ points of the bottom chord to the ¼ point of each top chord and to the peak · Howe: posts at ¼ span and mid-span plus a diagonal from each ¼-span post foot to the peak
The truss calculator gives layout dimensions only, measured node to node on the outer lines of the truss (underside of the bottom chord, top edge of the top chord). It does not size members or check loads: trusses must be engineered for your loads, span and local code, and are normally built by truss manufacturers from stamped drawings. The king post and queen post arrangements follow the descriptions in Wikipedia: Truss (king post and queen post trusses). That page does not give member lengths or define the Fink and Howe layouts, so the web layouts here are this site's own typical arrangements; real manufacturers place panel points to suit the design.
Manufacturer figures
| Figure | Value | Source |
|---|---|---|
| Bundles per square | 3 | GAF: How many bundles of shingles are in a square?: "For most standard asphalt shingles (3-tab and architectural), there are three bundles per square." Some specialty shingles need up to five. |
| Waste and trim allowance | 10% default | GAF: How many bundles of shingles are in a square?: add 10 to 15%. |
| Architectural shingles per square | 64 | GAF Timberline HDZ, from GAF: How many bundles of shingles are in a square?. |
| 3-tab shingles per square | 79 | GAF: Royal Sovereign technical data sheet (3 bundles, 79 pieces per square). |
| Starter strip per bundle | 120.33 ft | GAF: Pro-Start starter strip shingles: "approximately 120.33 linear feet"; installed at eaves and rakes. |
| Ridge cap per bundle | 25 ft | GAF Seal-A-Ridge listing (25 lineal ft per bundle, 45 pieces): at 6⅔-inch exposure, 25 lineal feet and 45 pieces per bundle (retailer listing of GAF Seal-A-Ridge). |
| Synthetic underlayment roll | 1,000 sq ft | GAF: FeltBuster data sheet (10 squares per roll, excludes laps): 48 in × 250 ft, 10 squares, "excludes laps". |
| Ice-and-water barrier roll | 200 sq ft | GAF: StormGuard technical data sheet (3 ft x 66.8 ft, 200 sq ft roll): 36 in × 66.8 ft, 2.0 squares. |
| Nails per shingle | 4 (or 6) | GAF: Shingle nails, four nails per shingle: four is the industry standard; six for some higher wind ratings. |
| Nails per pound | 196 | Grip-Rite 1-1/4 in. electro-galvanized roofing nails, 5 lb box, approx. 978 count: 5-lb box, 1¼ in, 11 gauge, approx. 978 nails (978 ÷ 5 = 195.6). Other nails differ; the field is editable. |
| Metal panel coverage | 36 in default | MBCI: PBR panel (36 in coverage, minimum slope 1/2:12, lengths 5 to 50 ft); Metal Sales: Residential metal roofing brochure (panel profiles and minimum slopes) shows coverage widths from 12 to 36 in. |
| Minimum slopes quoted | 2:12 shingles | GAF: Minimum slope for shingles; MBCI PBR ½:12; Metal Sales residential profiles 3:12. |
| Low-slope and steep roofs | 4 in 12 | OSHA 29 CFR 1926.500: definitions of low-slope and steep roofs: low-slope is 4 in 12 or less; steep is more than 4 in 12. |
The defaults the site chose itself, not manufacturer figures: 10% waste, a 10% laps allowance on underlayment (GAF lists 1,000 sq ft per roll excluding laps), 5% extra on metal panels, a 3-ft ice-and-water course, 1½-inch ridge board and 16-inch rafter spacing. All are editable. Pieces per bundle for shingles are calculated by dividing the published pieces per square by three; manufacturers do not list a per-bundle count for those products.
Rounding
Bundles, rolls, panels and boxes are always rounded up. Roll and bundle counts are computed from the unrounded area, with a tiny allowance for floating-point noise so that an exact fit does not round up by one. Rafter lengths are shown to the nearest ⅛ inch.
Prices
The site contains no price data. Every cost shown is a product of numbers you type. Installed estimates use measured squares (before extra); material estimates use bundles and rolls including extra.
Testing
The math has automated tests. Roof pitch multipliers and angles are checked against the rafter-length-per-foot-of-run table published by Swanson Tool (Swanson Tool: Roof pitch reference (rafter length per foot of run)): 12.65, 13.42, 14.42 and 16.97 inches for 4/12, 6/12, 8/12 and 12/12 and hip/valley lengths of 17.44, 18.00, 18.76 and 20.78 inches. The slope factor, hip/valley factor and angle for 4/12, 6/12, 8/12 and 12/12 are also checked against Spike VM: Slope, roof, hip/valley, height and width factors (1.054093, 1.118034, 1.201850 and 1.414214; hip/valley 1.452966, 1.5, 1.563472 and 1.732051). The truss top chord is checked against the same Swanson table (a 24 ft span at 4/12, 6/12, 8/12 and 12/12 gives 12.65, 13.42, 14.42 and 16.97 ft per side), and truss heights and web lengths against exact trigonometry and hand-checked 3-4-5 triangles (24 ft span at 9/12: 9 ft rise, 15 ft chord). The rise over run calculator uses the same functions: its diagonal for a 12 inch run is the Swanson rafter-per-foot figure (13.42 in at 6/12, 16.97 in at 12/12), and its angle, percent and ratio conversions are tested round-trip, including a zero rise, a 89.9° angle and rejected inputs (a zero run, 90°). No published source gives web member lengths for these layouts, so web lengths rest on the trigonometry alone. Angles are checked against exact trigonometry (45° at 12/12, 26.565° at 6/12), and the bundles and squares logic against GAF's three-bundles-per-square figure.
Questions or a correction? Contact us.