Hip rafter calculator: hip rafter length
On a regular hip roof (every plane at the same pitch), the hip sits at 45° in plan, so for every 12 in of common run the hip runs 16.97 in. It rises the same amount as the common rafter over that longer run. Its length per foot of common run is √(288 + pitch²) inches: 18 in at 6/12.
| Pitch | Common rafter | Hip or valley | Hip angle |
|---|---|---|---|
| 3/12 | 12.37 in | 17.23 in | 10° |
| 4/12 | 12.65 in | 17.44 in | 13.3° |
| 5/12 | 13 in | 17.69 in | 16.4° |
| 6/12 | 13.42 in | 18 in | 19.5° |
| 7/12 | 13.89 in | 18.36 in | 22.4° |
| 8/12 | 14.42 in | 18.76 in | 25.2° |
| 9/12 | 15 in | 19.21 in | 27.9° |
| 10/12 | 15.62 in | 19.7 in | 30.5° |
| 12/12 | 16.97 in | 20.78 in | 35.3° |
The tool gives the theoretical line length; deduct half the 45° thickness of the ridge, measured level, where the hip meets it. For a hip rafter the IRC wants at least 2 in nominal thickness and a depth no less than the cut end of the rafters (R802.4.3)[1].
Jack rafters
Jack rafters run from the wall plate to the hip, each one shorter than the last by the spacing times the rafter factor. At 16 in spacing and 6/12 that common difference is 17-7/8″. The list in the results starts at the shortest jack; cut them in pairs, one left and one right, with a 45° side cut where they meet the hip.
- King commons: one at the centre of each end wall, running to the end of the ridge.
- Ridge commons: the regular rafters along the ridge between the hips.
- Jacks: eight per spacing step on a full hip roof, two on each side of each of the four hips.
Ridge length and roof area
The ridge on a regular hip roof is the building length minus its width, because each hip eats half the width at each end. A square building has no ridge at all and becomes a pyramid roof. Roof area is the same as for a gable of the same pitch and footprint, which the roof calculator totals in squares.
Low slopes and loads
Below a 3/12 pitch, the IRC requires ridges, hips and valleys to be designed as beams (R802.4.4)[1]. Asphalt shingles stop at 2/12[2]. Common rafter sizes come from the rafter span tables[3]; the rafter calculator handles a common rafter's overhang and birdsmouth, and the roof pitch calculator converts the pitch to degrees for a saw.
Frequently asked questions
How do you calculate a hip rafter length?
Multiply the common run (half the width) by √(2 + (pitch ÷ 12)²). At 6/12 that is 1.5 × the run.
What is 16.97 on a framing square?
The hip run for 12 in of common run (12 × √2). Set the pitch on the tongue and 17 on the body to lay out hip and valley cuts.
How long is the ridge on a hip roof?
Building length minus building width, when all four sides share one pitch.
How many jack rafters does a hip roof have?
About eight for every spacing step along the common run: two per side on each of the four hips.