How it works
A hip rafter runs diagonally from the corner of the building up to the ridge, at 45° in plan. Its run is √2 times the common run, and it rises the same height as the common rafters, so it is longer and less steep. A valley rafter is the same geometry turned inside out.
Jack rafters run from the hip or valley to the wall or the ridge, parallel to the commons. Each successive jack is shorter (or longer) than the last by the common difference: the spacing times the common slope factor. Use that to step off the whole set.
Worked example
A 24 ft wide hip roof (12 ft common run) at 6/12 pitch with jack rafters at 16 inches on center:
- Hip factor = √(2 + (6 ÷ 12)²) = 1.5
- Hip length = 12 ft × 1.5 = 18 ft
- Jack rafter common difference = 16 in × √(1 + (6 ÷ 12)²) = 17.89 in
| Input | Value |
|---|---|
| Roof pitch: rise per 12 in of run | 6 in |
| Common run (half the building span, to the ridge) | 12 ft |
| Jack rafter spacing (on center) | 16 in |
| Result | Value |
|---|---|
| Hip or valley rafter length along the slope (to ridge) | 18 ft |
| Hip/valley length per 12 in of common run | 18 in |
| Hip/valley run in plan (the diagonal) | 16.97 ft |
| Hip/valley slope angle | 19.5 ° |
| Hip/valley pitch, rise per 12 in of its own run | 4.24 in |
| Jack rafter common difference in length | 17.89 in |
| Common rafter length for the same run | 13.42 ft |
Assumptions and limits
- Both roof planes have the same pitch and meet at 90° in plan (a rectangular hip or valley).
- Lengths are theoretical, measured along the centerline of the top edge from the wall corner to the ridge. Deduct half the ridge or hip thickness where the members meet, and add the overhang measured along the same slope.
- This tool does not give the side (cheek) cuts. Use a framing square or a rafter square to lay those out on the actual timber.
Common questions
How long is a hip rafter for a 6/12 roof?
It runs 1.50 ft of rafter for every foot of common run, or 18.00 inches per 12 inches of run. With a 12 ft common run, that is 18.00 ft.
Why is the hip less steep than the commons?
It covers the same rise over a longer horizontal run (the diagonal), so a 6/12 roof rises 6 inches over 16.97 inches of diagonal run, a hip pitch of about 4.24 in 12.
What is the common difference?
It is how much shorter each jack rafter is than its neighbor: the spacing times the common rafter factor. At 16 in on center on a 6/12 roof that is 17.89 in.
Do valleys use the same formula?
Yes, for two equal-pitch roofs meeting at 90°. A valley of unequal pitches needs a different calculation.
Sources
- Right-triangle geometry for hip and valley rafters; unit lengths per 12 in of common run as printed in standard rafter tables (6/12 = 18.00 in, 8/12 = 18.76 in, 12/12 = 20.78 in).
Updated 2026-09-30