Hip, Valley and Jack Rafter Layout

A gable roof forgives a lot. A hip roof does not. Every jack rafter takes its length from the hip, and the hip takes its line from the plates and the ridge. A small mistake at the corner shows up as a wave in the sheathing, or a run of jacks that all come up short.

You can already lay out a common rafter, cut a bird's mouth and read a pitch. This guide adds the rafters that run on a diagonal. It works in straight numbers, so you can check them on any calculator. It also tells you where your layout ends. Sizes, spans and supports come from the plans, the adopted code and the engineer of record. You lay out what they specify. You do not decide that a hip is big enough.

What You Will Be Able to Do

• Find hip and valley lengths for any regular roof.
• Mark the plumb cuts, the ridge deduction and the drop.
• Set a hip seat so it matches the commons.
• Step off jack rafters and cut their cheek cuts.
• Work out an irregular hip where the two pitches differ.

Why the Diagonal Changes the Math

On a regular hip, two roofs of the same pitch meet over a corner, so the hip runs at 45 degrees in plan. For every 12 inches a common rafter runs, the hip has to run the diagonal of a 12-inch square. That is the square root of (12 x 12 + 12 x 12), or 16.97 inches. This is the hip unit run. On the framing square, you round it to 17.

The rise does not change. A hip climbs the same height as the commons, over a longer run, so its slope is flatter. That is why you mark the hip's plumb cut with 17 and the rise on the square, not 12 and the rise.

The hip number is the square root of (16.97 x 16.97 + rise x rise). Your rafter square lists the same numbers.

Laying Out a Regular Hip

Worked example. A building is 28 feet wide and 44 feet long, at 6/12.

1. Common run: 28 / 2 = 14 feet.
2. Total rise: 14 x 6 = 84 inches.
3. Theoretical hip length: 14 x 18.00 = 252 inches, or 21 feet 0 inches.
4. Check it: the hip's run is 14 x 16.97 = 237.6 inches. The square root of (237.6 x 237.6 + 84 x 84) is 252.0. It matches.
5. Theoretical ridge length: 44 - 28 = 16 feet. Adjust this for how your commons and hips meet at the ridge end, and confirm it with a dry layout on the plates.

The Ridge Deduction

That 21 feet runs to the center of the ridge. The real hip stops short, against the ridge or the commons at the ridge end. When a hip meets a 1-1/2-inch ridge at 45 degrees, take off half the ridge's thickness as measured on the 45.

• Half the ridge: 0.75 inch.
• On the 45: 0.75 x 1.414 = 1.06 inches, or about 1-1/16 inches.

Measure this level, square to the plumb line, not along the top edge of the rafter. Then mark a new plumb line. On a regular hip the two faces at the top get a 45-degree cheek cut, so the hip's point seats into the corner.

The Drop

Think of the roof plane passing over the hip. The plane meets the hip's center line, but the top outside corners of a square-edged hip poke up through it. Sheathing laid over them will hump. You fix that one of two ways: bevel the top edges, which is called backing, or lower the whole hip, which is called dropping. Dropping is more common, because it is only a deeper seat.

Drop = half the hip's thickness x rise / 16.97

For a 1-1/2-inch hip at 6/12: 0.75 x 6 / 16.97 = 0.27 inch, or about 1/4 inch. At 12/12 it is about 1/2 inch.

A valley needs no drop. Its top edges sit low, not high, so they do not push the sheathing up. Follow the plan's detail for how the sheathing is carried there.

Matching the Seat

Height above plate (HAP) is how far the top of a rafter sits above the wall plate, measured at the outside wall line. The commons set this height. The hip has to land at the same height, less its drop, or the roof plane breaks at the corner.

Worked example. Commons are 2x10 (9-1/4 inches deep) at 6/12, with a 3-1/2-inch seat.

1. Plumb depth of the common: 9.25 x 13.42 / 12 = 10.34 inches.
2. Depth of the bird's mouth: 3.5 x 6 / 12 = 1.75 inches.
3. HAP: 10.34 - 1.75 = 8.59 inches.

The hip is a 2x12 (11-1/4 inches deep).

1. Plumb depth of the hip: 11.25 x 18.00 / 16.97 = 11.93 inches.
2. HAP the hip needs: 8.59 - 0.27 = 8.32 inches.
3. Plumb cut at the seat: 11.93 - 8.32 = 3.61 inches, or about 3-5/8 inches.

Note that the deeper hip does not change the HAP. It only changes how much wood is left under the seat.

What a Hip or Valley Has to Do

A ridge board is mostly something for rafters to land on. A hip or valley is different, because it carries the jacks on both sides of it. Treat it as a beam.

Under the model residential code (IRC, the International Residential Code), hips and valleys on roofs of 3/12 or steeper must be at least 2-inch nominal thickness, and no less in depth than the cut end of the rafter. They also need support at the ridge, by a brace down to a bearing partition, or else a design that carries that load. Your adopted edition and local changes may differ.

Those are minimums, not a size. Many hips and valleys need more, so size and support come from the plans or the engineer. If you find a hip with nothing under its top end, or a brace that lands on a wall that is not bearing, stop and ask before you load it.

Warning: Hip and valley work puts you on open plates and rafters at heights where fall protection is required. Set your anchors and plan your access before you start, and do not walk unsheathed rafters to save a trip. Lift long hips with enough people, or with equipment, and keep them tied off until both ends are fastened.

Jack Rafters

A jack rafter is a shortened common. Three kinds show up on most cut-up roofs:

Common Difference

Each jack on a run is shorter than the next by the same amount.

Common difference = spacing x common inches per foot / 12

Worked example. Jacks at 16 inches on center, at 6/12, measured from the corner of the building.

Each one still needs a deduction for the hip's thickness: half the thickness measured on the 45, about 1-1/16 inches for a 1-1/2-inch hip. Measure it level from the plumb line, as you did at the ridge.

Cheek cut. On a regular hip, set your saw to a 45-degree bevel and follow the plumb line. Jacks on opposite sides of a hip are mirror images, so cut them as lefts and rights. Stack and label them before anyone carries them up.

Valleys on an L-Shaped Roof

When a wing meets a main roof at the same pitch, one valley runs all the way to the main ridge. That is the supporting valley. A second, shorter valley dies into it.

Worked example. The main roof is 28 feet wide. The wing is 20 feet wide. Both are 6/12.

1. Main ridge height above the plate: 14 x 6 = 84 inches.
2. Wing ridge height: 10 x 6 = 60 inches.
3. Supporting valley: 14 feet of common run x 18.00 = 252 inches, to the center of the main ridge.
4. Shorter valley: 10 feet of common run x 18.00 = 180 inches, to the center of the supporting valley.

Each one gets a deduction for what it lands against. Then the valley jacks step off the same common difference as the hip jacks. For a cripple jack, work out its run first. A cripple with a 4-foot run at 6/12 is 4 x 13.42 = 53.68 inches, less a deduction at each end.

When the Two Pitches Differ

Sometimes a hip joins roofs of two different pitches, often to keep a wall or a window line. This is an irregular hip. It does not run at 45 degrees, and neither the 17 nor the 45-degree cheek cut applies. Go back to the triangles.

Worked example. The main roof is 6/12 with a 14-foot run. The end roof is 8/12. Both must reach the same 84-inch height.

1. End roof run: 84 / 8 x 12 = 126 inches, or 10 feet 6 inches.
2. Hip run in plan: the square root of (168 x 168 + 126 x 126) = 210 inches.
3. Hip length: the square root of (210 x 210 + 84 x 84) = 226.2 inches, or about 18 feet 10-3/16 inches.
4. Hip plumb cut: rise 84 over run 210, which is 4.8 in 12. Mark it on the square with 12 and 4.8.
5. Plan angle: the angle whose tangent is 126 / 168 = 0.75, which is about 36.9 degrees off the line of the main roof's commons.

The jacks on each side now have different pitches, different common differences and different cheek cuts. A full-size chalk drawing on the deck is worth the half hour it takes. Confirm the end run on the plan first, because that one number sets where the ridge ends.

Setting the Roof

1. Check the plates. Square and level are your starting point. A plate out of square moves every hip.
2. Set the ridge at the correct height, and brace it plumb.
3. Set the commons that hold the ridge, including the ones at the hip ends.
4. Set the hips and valleys. Check each one with a string along the top before you load it.
5. Add the bracing that the plans call for under the hips.
6. Set jacks in opposite pairs. A jack on one side only pushes the hip out of line. Nail each pair before you move on.
7. Sight the hip again. Fix any bow now, because the sheathing will lock it in.

Common Mistakes

Check Your Understanding

1. A carpenter pulls a hip's length from the common column of the rafter table. What happens when it goes up?

It comes up far short. The common column assumes 12 inches of run per foot, but a hip runs 16.97. At 6/12, that is 13.42 inches per foot against the 18.00 the hip needs.

2. What is the drop on a 1-1/2-inch hip at 10/12?

0.75 x 10 / 16.97 = 0.44 inch, or about 7/16 inch.

3. A cut list for 6/12 jacks at 16 inches on center reads 17.89, 35.78 and 52.67. What do you check before anyone cuts?

The third number. Each step should be 17.89, so it should read 53.67. Fix the list first, or that piece will miss the hip by an inch.

4. A helper marks a hip's plumb cut with 12 and 6 on the square. What is wrong?

A 12 is for commons. The hip runs 16.97 for each 12 of common run, so it is marked with 17 and 6.

5. The owner wants the end of the building steeper than the main slope, to keep a window line. How does that change where the ridge ends?

A steeper end needs less run to reach the same height, so the ridge runs closer to the end wall. The hip no longer sits at 45 degrees, so work it out from the triangles.

Key Takeaways

• A regular hip runs 16.97 for each 12 of common run, so mark it with 17 and the rise.
• Take deductions level, on the 45, and not along the top edge.
• Drop or back a hip, or the sheathing will hump over it.
• The hip must land at the commons' height above the plate, less its drop.
• Set jacks in opposite pairs to keep the hip straight.
• A hip or valley is a beam. Its size and support come from the plans or the engineer.