Hip and Valley Rafter Calculator
What size hip or valley rafter does your roof need? Enter the slope, the common rafters' run and the roof load, and see which built-up 2x hip works, the longest run each size can serve, and how much load its top end puts on the post or brace under it.
A 2-2x12 hip works for a 12′ run, using 95% of its capacity (limited by bending).
The roof corner from above. Jack rafters frame into the hip from both sides.
The hip on its supports, with the load from the jacks rising to the ridge.
Longest run, Douglas Fir-Larch No.2
| Hip | 1 ply | 2 plies | 3 plies |
|---|---|---|---|
| 2x6 | – | – | – |
| 2x8 | – | – | – |
| 2x10 | 8′ 10″ | 11′ | 12′ 7″ |
| 2x12 | 9′ 9″ | 12′ 2″ | 13′ 10″ |
The common rafters' run, level from the wall to the ridge. Runs in bold reach 12′.
At a 12′ run, 2 plies
| 2-2x6Fails bending | 297% |
| 2-2x8Fails bending | 187% |
| 2-2x10Fails bending | 127% |
| 2-2x12Works | 95% |
Every check for the 2-2x12
| Bending | 95% PASS |
| Shear | 34% PASS |
| Bending under dead load alone | 48% PASS |
| Deflection under the roof load (span/180) | 25% PASS |
| Depth for the rafters’ cut ends (8.11 in for 2x8 rafters) | 72% PASS |
The hip spans 17′ level and is 18′ long along its slope, before the cuts. It puts 824 lb on the wall corner and 1,573 lb on its support at the ridge: a post or a brace down to a bearing wall, or a ridge beam sized for it (IRC R802.4.3).
Both roofs at 6 in 12, 10 psf dead load along the roof and 20 psf snow, on Douglas Fir-Larch No.2, with no ceiling attached. The plies are nailed together.
Hip and valley rafter tables
The longest common rafter run each Douglas Fir-Larch No.2 hip or valley serves, on a 6 in 12 roof with 10 psf dead load, no ceiling attached and 2x6 common rafters. The run is level, from the wall to the ridge: half the building's width. A hip and a valley at the same run carry the same load, so one table serves both. Snow is at allowable stress level, as on the ASCE 7-16 maps and the 2024 IRC map; for an ASCE 7-22 snow load, read the table at 0.7 times it. Worked out by the calculator, not copied from a code table: the IRC has none for hips.
20 psf roof live load
| Hip | 1 ply | 2 plies | 3 plies |
|---|---|---|---|
| 2x6 | – | – | – |
| 2x8 | 7′ 11″ | 9′ 11″ | 11′ 4″ |
| 2x10 | 9′ 1″ | 11′ 4″ | 12′ 11″ |
| 2x12 | 10′ | 12′ 6″ | 14′ 3″ |
30 psf snow
| Hip | 1 ply | 2 plies | 3 plies |
|---|---|---|---|
| 2x6 | – | – | – |
| 2x8 | 7′ | 8′ 10″ | 10′ 1″ |
| 2x10 | 8′ | 10′ 1″ | 11′ 6″ |
| 2x12 | 8′ 10″ | 11′ 1″ | 12′ 8″ |
50 psf snow
| Hip | 1 ply | 2 plies | 3 plies |
|---|---|---|---|
| 2x6 | – | – | – |
| 2x8 | 6′ 2″ | 7′ 9″ | 8′ 10″ |
| 2x10 | 7′ 1″ | 8′ 10″ | 10′ 1″ |
| 2x12 | 7′ 9″ | 9′ 9″ | 11′ 2″ |
For other species, slopes and loads, use the calculator above.
How the calculator checks a hip or valley
A hip runs from an outside corner of the walls up to the end of the ridge; a valley from an inside corner up to where two ridges meet. With both roofs at the same slope, either one runs at 45° in plan, so its level span is 1.41 times the common rafters' run. Jack rafters frame into it from both sides and hand it half their load:
- Hip: the jacks get longer toward the ridge, so the load grows from nothing at the wall corner to its most at the ridge end, which carries two thirds of it.
- Valley: the jacks run up to the ridges, so they're longest at the wall corner. The load is the most there, and the wall end carries two thirds of it.
- In all, either carries half the roof in the square at the corner: the roof load times the run squared, over 2, plus its own weight.
Each is a simple span from the wall corner to a support at the ridge, checked to the 2024 National Design Specification (NDS) for wood with allowable stress design (ASD), as dry lumber. The plies are nailed together and don't take the repetitive member factor that rafters 24 in apart do. The checks:
- Bending and shear under the dead and roof load, with the load duration factor for the roof load: 1.15 for snow and 1.25 for roof live load.
- Snow: pick where the snow load comes from. The ASCE 7-16 maps and the 2024 IRC's ground snow map give it at allowable stress level, and it's used in full. ASCE 7-22 and the ASCE Hazard Tool give it at strength level, so the checks take 0.7 times it, as the ASCE 7-22 allowable stress combinations do, and the 2024 IBC allows for deflection (Table 1604.3, note j).
- Bending under dead load alone, with the load duration factor of 0.9.
- Deflection under the roof load, up to the span over 180, or over 240 with a ceiling attached, the limits in IRC Table R301.7.
- Depth: the International Residential Code (IRC R802.4.3) asks for hips and valleys at least 2 in thick and no shallower than the cut end of the rafters, which is deeper than the rafter itself on a slope: a 2x8 cut at 6 in 12 is 8.1 in deep, so it needs a 2x10 hip.
The same IRC section asks for the top end to be held up by a brace to a bearing wall, unless the hip is designed to carry and spread that load. The calculator gives that load, so the post, brace or ridge beam under it can be sized too.
Hip and valley questions
What size hip rafter do I need?
Under 20 psf roof live load on a 6 in 12 roof, a Douglas Fir-Larch No.2 2-2x10 hip serves a run up to 11′ 4″, a 2-2x12 up to 12′ 6″ and a 3-2x12 up to 14′ 3″. Under 30 psf of snow, a 2-2x12 serves 11′ 1″.
Why is the hip bigger than the rafters?
It spans 1.41 times as far as the common rafters and carries the jack rafters from both sides, much more load than any one rafter. The IRC also asks for it to be at least as deep as the rafters' cut ends.
What if no 2x hip works?
Put a post under the hip partway up, down to a bearing wall or beam, to split its span, or use a deeper engineered beam such as an LVL, sized in the beam designer.
Is a valley sized like a hip?
The same way and for the same load, so the tables above work for both, but the heavy end is at the wall instead of the ridge. The ridge end of a valley carries a third of its load, against two thirds for a hip.
What about the common and jack rafters?
Size them with the rafter span calculator. A jack rafter is never longer than a common rafter, so jacks the same size and spacing as the commons work.