Calculation Methodology and Validation
How every number on this site is produced: the formulas, the unit conventions, the assumptions and the tests that check them.
All calculators share one engine of pure functions, separated from the interface. Lengths are held internally in feet at full precision and rounded only for display. Pitch is normalized to a single slope ratio p = X/12 = tan(angle), so a pitch entered anywhere behaves identically everywhere.
Core formulas
Surface area is footprint × √(1 + p²). A common rafter line is run × √(1 + p²). A regular hip rafter line is run × √(2 + p²), with a diagonal plan run of run × √2. The ridge of a rectangular hip is the long side minus the short side. Order area is net area × (1 + waste%), and bundles are the order area divided by the bundle coverage, rounded up. Cap is a separate linear total divided by its own coverage.
Units and conventions
Exact constants: 1 ft = 12 in, 1 in = 0.0254 m, 1 ft = 0.3048 m, and 1 roofing square = 100 sq ft. Areas are reported in square feet and squares; ridge and cap in linear feet. Degrees and percent slope are treated as distinct units. Overhang and waste may be zero; physical dimensions must be positive.
Validation status
The engine is checked by an automated fixture suite covering the worked scenarios published across the site, plus invariants: swapping length and width preserves area and hip length, the four faces sum to the total area, imperial and metric round-trip within tolerance, and invalid inputs (negatives, blanks, division by zero, bad fractions) are rejected rather than producing misleading numbers. These checks are numeric; this page does not claim engineer review or code compliance.
Reporting an issue
If a result looks wrong, use the contact page to send the page, the inputs, the result you saw and the result you expected. Reproducible reports let the geometry be checked and corrected quickly.
Sources consulted for packaging and platform behavior are linked near the relevant explanations where applicable; geometry is derived from first principles rather than copied from another estimator.