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A valley rafter carries the jacks where a wing roof runs into a main roof. When both roofs share one pitch the valley runs at 45° in plan and is exactly as long as a hip over the same run: √(288 + rise²) inches per foot of common run, 18.76 in at 8/12 — the figure stamped in the rafter table of a steel framing square. When the pitches differ, the valley swings toward the shallower roof: the wing ridge climbs its run × pitch ÷ 12, the main roof needs height × 12 ÷ its pitch of run to reach the same height, and the valley is the diagonal of those two runs lifted by the height. Enter the wing width, both pitches, the jack spacing and the overhang and the Valley Rafter Calculator returns the valley length and tail, its pitch and plan angle, every valley jack length and, for equal pitches, the side cuts. A 24 ft wide wing at 8/12 needs an 18 ft 9 1/8 in valley and jacks that step 19 1/4 in at 16 in centres; a 20 ft wing at 12/12 on a 6/12 roof needs a 24.49 ft valley.
Where a wing roof meets a main roof, the valley rafter runs from the inside corner of the walls up to the point where the wing ridge meets the main roof. With both roofs at one pitch it runs at 45° in plan and uses the same figure as a hip: √(288 + rise²) inches per foot of common run, the "hip or valley per foot run" row of a steel framing square. With unequal pitches the valley swings toward the shallower roof, and its length follows from the two runs that climb to the wing ridge height.
| Pitch | Valley / ft | Valley angle | Jacks 16 in | Jacks 24 in | Side cut jacks | Side cut valley |
|---|---|---|---|---|---|---|
| 3/12 | 17.23 in | 10.02° | 16 1/2 in | 24 3/4 in | 11 5/8 | 11 13/16 |
| 4/12 | 17.44 in | 13.26° | 16 7/8 in | 25 5/16 in | 11 3/8 | 11 11/16 |
| 5/12 | 17.69 in | 16.42° | 17 5/16 in | 26 in | 11 1/16 | 11 1/2 |
| 6/12 | 18.00 in | 19.47° | 17 7/8 in | 26 13/16 in | 10 3/4 | 11 5/16 |
| 7/12 | 18.36 in | 22.42° | 18 1/2 in | 27 13/16 in | 10 3/8 | 11 1/16 |
| 8/12 | 18.76 in | 25.24° | 19 1/4 in | 28 7/8 in | 10 | 10 7/8 |
| 9/12 | 19.21 in | 27.94° | 20 in | 30 in | 9 5/8 | 10 5/8 |
| 10/12 | 19.70 in | 30.51° | 20 13/16 in | 31 1/4 in | 9 3/16 | 10 5/16 |
| 12/12 | 20.78 in | 35.26° | 22 5/8 in | 33 15/16 in | 8 1/2 | 9 13/16 |
When both roofs share one pitch, multiply the wing's common run in feet by √(288 + rise²) and divide by 12 — exactly like a hip. At 8/12 that is 18.76 in per foot, so a 24 ft wide wing (12 ft run) needs a valley 12 × 18.76 ÷ 12 = 18.76 ft long, plus the tail for the overhang.
Yes, for equal pitches over the same run. Both run at 45° in plan and use the same framing-square figure (18.00 in per foot at 6/12, 20.78 at 12/12). The difference is in the cuts: a valley is pushed down into the roof, so its birdsmouth and ridge end are cut the opposite way, and valley jacks sit on it from above.
Find how high the wing ridge climbs (wing run × wing pitch ÷ 12), then how far up the main roof you travel to reach that height (height × 12 ÷ main pitch). The valley's plan length is the diagonal of those two runs and its true length adds the height: a 20 ft wing at 12/12 on a 6/12 main roof climbs 10 ft, travels 20 ft up the main roof, and needs a 24.49 ft valley.
The same as hip jacks when the pitches match: spacing × √(144 + rise²) ÷ 12, which is 19 1/4 in at 16 in centres on an 8/12 roof. With unequal pitches each side has its own figure, because the valley is no longer at 45° — the calculator gives both.
The same framing-square figure as a hip: at 8/12 the valley side cut is 10 7/8 and the jack side cut 10, each used with 12 on the other arm. Unequal-pitch valleys need the cut worked from the plan angle, so lay one out full size or cut a test piece.
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