Sources & formulas

Every calculator on ExteriorCalcs rests on established construction math from geometry, drainage hydraulics and heat-flow physics. Unlike topics with a time dependency, "verification" here is mathematical: each formula is tested against known values and is therefore correct for good. Here are the technical foundations by area.

Roof pitch & geometry

  • Pitch multiplier: M = √(1 + (rise/12)²); angle = arctan(rise/run); grade = rise/run × 100.
  • Roof area: flat footprint × multiplier. Roofing squares: roof area ÷ 100 (1 square = 100 sq ft).
  • Rafter length: (run + overhang) × multiplier (line length — geometry, not structural sizing).

Shingles & materials

  • Bundles: 3 bundles per square (~33.3 sq ft/bundle). Nails: ~320/square (4-nail) or ~480/square (6-nail high-wind).
  • Coverage typicals: underlayment roll coverage, ridge-cap LF/bundle and metal-panel width are user-adjustable — check your product label.

Roof replacement cost

  • No prices are stored: total = squares × the price per square you enter; $/square = $/sq ft × 100.
  • Tear-off debris (typicals): 3-tab ≈ 250 lb/square, architectural ≈ 400 lb/square, tile ≈ 900 lb/square; tons = squares × layers × lb/square ÷ 2,000.

Gutters & drainage

  • K-style capacity (SMACNA-derived, at 1 in/hr): 5" ≈ 5,520 sq ft, 6" ≈ 7,960 sq ft; downspouts 2×3 ≈ 600, 3×4 ≈ 1,200 sq ft.
  • Sizing: adjusted area = plan area × roof-pitch factor × rainfall intensity (in/hr, from NOAA for your ZIP). Slope: 1/4 in per 10 ft.

Siding

  • Squares: (perimeter × height + gables − openings) ÷ 100, plus waste. Panel coverage: exposure/12 × panel length.

Windows

  • Egress (2021 IRC R310): clear opening ≥ 5.7 sq ft (5.0 at grade), width ≥ 20 in, height ≥ 24 in, sill ≤ 44 in — cited with edition; local code prevails.
  • Energy: heat loss = ΔU × area × HDD × 24; 1 kWh = 3,412 BTU. HDD and rate are your inputs.

Attic insulation & ventilation

  • R-per-inch: fiberglass batt ≈ 3.2, blown fiberglass ≈ 2.5, cellulose ≈ 3.5, open-cell ≈ 3.7, closed-cell ≈ 6.5. Depth: R ÷ R-per-inch.
  • Ventilation (2021 IRC R806): net-free area = attic area ÷ 150 (or ÷ 300 with balanced vents + vapor retarder).
  • Savings: BTU = area × HDD × 24 × (1/R_old − 1/R_new); 1 therm = 100,000 BTU. HDD, fuel rate and efficiency are your inputs.