Gable Roof Calculator
Calculate rafter lengths, ridge height, and material requirements for gable roofs. Includes cut lists and truss diagrams for carpenters.
About
Professional carpentry requires precise trigonometry to ensure structural stability and material efficiency. A gable roof consists of two sloping planes meeting at a central ridge. Builders must calculate the common rafter length based on the run and pitch. Incorrect calculations lead to open ridges or unstable bird's mouth cuts. This tool computes the exact geometry including the hypotenuse for the rafter and the vertical rise. It adjusts for the ridge board thickness which reduces the theoretical run. Material estimation helps contractors order the correct amount of sheathing and lumber. Accuracy prevents costly waste during the framing phase.
Formulas
The theoretical rafter length L is derived from the span S and the pitch P using the Pythagorean theorem. The run r is half the span minus half the ridge thickness.
The rise h is calculated using the pitch ratio.
Reference Data
| Pitch Ratio | Angle (°) | Multiplier (Secant) | Valley Multiplier | Common Application |
|---|---|---|---|---|
| 1:12 | 4.76° | 1.0035 | 1.416 | Industrial / Sheds |
| 3:12 | 14.04° | 1.0308 | 1.436 | Low Slope Residential |
| 4:12 | 18.43° | 1.0541 | 1.453 | Standard Ranch |
| 5:12 | 22.62° | 1.0833 | 1.474 | Conventional Housing |
| 6:12 | 26.57° | 1.1180 | 1.500 | Common Residential |
| 8:12 | 33.69° | 1.2019 | 1.563 | Tudor / Cape Cod |
| 9:12 | 36.87° | 1.2500 | 1.601 | Steep Residential |
| 10:12 | 39.81° | 1.3017 | 1.641 | Attic Conversions |
| 12:12 | 45.00° | 1.4142 | 1.732 | Cathedral / A-Frame |