Pyramid Hip Roof Calculator (Tented)
Calculate framing and surface area for square pyramid (tented) roofs. Solves for Jack Rafter decrements, hip lengths, and costs.
About
A pyramid roof (or tented roof) is a subtype of hip roof built on a square base with four triangular sides meeting at a single central peak. There is no ridge board. This structure is common in gazebos, garages, and towers. The framing challenge lies in the Jack Rafters. These rafters become progressively shorter as they approach the corners. Accurate calculation of the "decrease increment" is essential to cut all lumber efficiently without measuring every single piece on the roof.
This tool calculates the precise lengths for the Corner Hip Rafters, the Common Rafter (center of the triangle), and the surface area for sheathing. It includes a cost estimator based on your local price per square foot.
Formulas
For a square base of width W and pitch P (x/12):
Note: The Lateral Area formula simplifies to 2 × Width × Slant Height because there are 4 triangles: 4 × (1/2 × W × S).
Reference Data
| Parameter | Formula / Relation | Notes |
|---|---|---|
| Common Rafter | √Run2 + Rise2 | Also the slant height of the triangular face. |
| Hip Rafter | √Common2 + Run2 | The corner framing member. |
| Lateral Area | 4 × (0.5 × Base × Common) | Total roof surface area (excluding overhangs in formula, but included in tool). |
| Jack Decrease | Spacing × (Common / Run) | The amount to subtract from each subsequent jack rafter. |