Methodology
Every calculator on this site uses published trigonometry and code minimums, computes in a single canonical unit, and rounds only at display time. The formulas below are the complete set — you can reproduce any result on paper.
| Quantity | Formula | Note |
|---|---|---|
| Roof pitch | pitch = (rise ÷ run) × 12 | Stated as rise per 12 units of run. |
| Roof angle | angle = arctan(rise ÷ run) × 180 ÷ π | Degrees, unrounded until output. |
| Slope percentage | slope% = (rise ÷ run) × 100 | Used for drainage checks. |
| Pitch multiplier | m = √(rise² + run²) ÷ run | Footprint area × m = sloped area. |
| Hip / valley factor | h = √(rise² + 2 × run²) ÷ run | Length per unit of common run. |
| Rafter length | rafter = √(rise² + run²) | Add overhang separately. |
| Roof squares | squares = sloped area ÷ 100 | One square = 100 ft² of roof surface. |
| Shingle bundles | bundles = squares × 3 × (1 + waste) | Three bundles per square for 3-tab and most architectural shingles. |
Units and rounding
Inputs are converted to one canonical unit per quantity before any maths runs, so mixing metres with inches cannot introduce an error. Intermediate values are kept at full double precision; rounding happens once, at the moment a value is displayed.
Testing
Each calculator has unit tests that pin its outputs against hand-worked examples, and the registry is audited automatically for duplicate titles, over-length metadata and orphaned pages.