Pitch & Span

Methodology

This page lists where every non-obvious number on Pitch & Span comes from. Pure geometry (Pythagorean theorem, trigonometric slope factor) is implemented directly from the formula and verified with an automated test suite — those numbers aren't "sourced" from a third party because they're derived, not looked up. Material coefficients, cost ranges, and span tables are different: those are real-world data that must trace to a named, dated source, or they don't get published.

Geometry (derived, not sourced)

Rafter length, run, rise, roof area, pitch/angle/percent conversion, birdsmouth notch geometry, and board footage all come directly from the Pythagorean theorem and standard trigonometric identities. Every one of these has a Vitest suite checking known reference cases (for example: a 24 ft span at 6/12 pitch must produce a 13.416 ft rafter length) before it ships. See each calculator's own "How we checked this page" block for the specific cases verified.

Asphalt shingle coefficients

Bundles per square (3), exposure (5.625"), and shingle width (39.375") come from GAF Timberline HDZ product specifications, cross-corroborated against CertainTeed Landmark's technical data sheet. Nailing pattern (4 nails standard, 6 nails high-wind) comes from 2018/2021 IRC §R905.2.6 and ARMA nailing guidance.

Explicitly not published: starter strip and ridge cap coverage per bundle. We found conflicting figures across manufacturer sources and could not verify a single reliable number, so the Shingle Calculator reports linear feet needed instead of a bundle count for those two items — see its FAQ for the full explanation.

Source: GAF Timberline HDZ product specifications; CertainTeed Landmark technical data sheet; 2018/2021 IRC §R905.2.6; ARMA nailing guidance (checked July 2026).

Metal roofing coefficients

Panel coverage (36"), field fastener spacing (12" o.c.), side-lap fastener spacing (12" o.c.), and end-lap overlap (6") come from a manufacturer installation manual read in full, including its UL 580 Wind Uplift listing.

Source: Metal Sales Manufacturing Corp., R-Panel Installation Manual (4/04) and PBR-Panel Installation Manual (12/11), incl. UL 580 Wind Uplift listing Construction No. 161 (checked July 2026).

Roof replacement cost ranges

Material cost per square, tear-off cost per square, and permit fee ranges come from two live, dated cost guides. These are planning-grade ranges, explicitly not a substitute for a contractor quote — cost is the fastest-moving data category on this site and gets the shortest re-check interval.

Joist span tables

Allowable floor joist spans (Douglas Fir-Larch No.2 and Southern Pine No.2, 2x8-2x12, 16"/24" o.c., 40 psf live load, 10 psf dead load, L/360 deflection) are looked up directly from published span tables, not computed. The Joist Span Calculator carries an explicit, highlighted disclaimer: this is reference information, not an engineered design.

Our hard rule

If we can't trace a material coefficient or span value to a named, dated source, we don't publish it as a default — we either derive it from geometry we can verify, or we say so plainly and ask you to check the specific product's spec sheet instead of guessing on your behalf.

Last reviewed: 2026-07-28. See Editorial Standards for our review process and correction policy.