Hip, Valley, and Jack Rafter Principles

Hip, Valley, and Jack Rafter Principles

Understanding how hip, valley, and jack rafters work together is essential to framing any roof that has more than two planes. Unlike a simple gable roof, a hip or valley roof requires rafters that travel at angles across the plate and meet a ridge or a hip/valley rafter at compound cuts. Getting the math right before you cut saves lumber and prevents costly structural errors.

The Three Rafter Types

Hip rafters run from a corner of the wall plate up to the end of the ridge board at a 45-degree plan angle on a square-cornered building. Because they travel diagonally across the plan, they are always longer than a common rafter of the same run and carry a different unit rise per unit of run.

Valley rafters follow the same 45-degree diagonal path as hip rafters but run into an inside corner rather than an outside corner. They span the junction where two roof planes meet and slope downward toward the eave. Valley rafters share the same unit-diagonal math as hip rafters.

Jack rafters are shortened common rafters that frame into a hip or valley rafter rather than into a ridge. Hip jacks get shorter as they approach the corner; valley jacks get longer as they approach the ridge. Each successive jack in a regular layout differs from the next by a constant amount called the common difference.

Unit Rise, Unit Run, and the Unit Diagonal

For common rafters the unit run is always 12 inches. For hip and valley rafters the unit run is 16.97 inches (the diagonal of a 12×12 square, calculated as √(12² + 12²) = √288 ≈ 16.97). This value appears directly in the second line of the rafter tables stamped on a standard framing square, labeled "Length of Hip or Valley Rafter per Foot Run."

The unit length for a hip or valley rafter is:

> Unit length = √(unit rise² + 16.97²)

For a 6-in-12 pitch, the framing square rafter table gives the common unit length as 13.42 in. The hip/valley unit length for the same pitch is √(6² + 16.97²) = √(36 + 287.98) = √323.98 ≈ 18.00 in.

Calculating Total Rafter Length: The Unit-Diagonal Method

1. Find the total run of the common rafter (half the span, or the horizontal distance from the plate to directly below the ridge).

2. Look up the hip/valley unit length for your pitch from the rafter table on the framing square.

3. Multiply: Total rafter length = (unit length ÷ 12) × total run (in feet).

4. Apply the ridge reduction. The hip rafter must be shortened by half the diagonal thickness of the ridge board. For a 1½-in. ridge, the diagonal is 1½ × √2 ≈ 2.12 in.; subtract half of that (≈ 1.06 in.) measured perpendicular to the plumb cut.

5. Apply the tail length for the overhang using the same unit-diagonal ratio.

Always measure rafter length along the measuring line (top edge), not along the bottom edge.

Cheek Cuts (Side Cuts)

Hip, valley, and jack rafters all require cheek cuts (also called side cuts or compound cuts) where they meet at an angle. The framing square rafter table provides side-cut values on the fifth and sixth lines of the table.

• Hip and valley cheek cuts are made at the same angle because both travel at 45 degrees in plan. The cut is a compound angle: one component is the plumb cut angle (determined by pitch), and the other is the plan angle (45 degrees for a square building).
• Jack rafter cheek cuts are cut at the same plumb angle as a common rafter but with a 45-degree side bevel, because jacks meet the hip or valley at 45 degrees in plan.
• The key difference: hip/valley cheek cuts are symmetrical (both sides of the rafter receive the bevel); jack cheek cuts are on one side only and mirror for opposite jacks.

To lay out a cheek cut, use the side-cut number from the rafter table. Hold that number on the tongue and 12 on the blade; the tongue gives the cheek cut line.

Ridge Reduction and Common Errors

The most frequent layout error is forgetting the ridge reduction, which causes the hip rafter to push the ridge out of position. A second common mistake is measuring rafter length along the bottom edge rather than the measuring line, introducing error equal to the rafter depth. A third error is using the common-rafter unit length (second line) instead of the hip/valley unit length when calculating hip or valley length.

Safety Notes

When working with a framing square, keep it flat on the material and clamp a fence (stair gauges) to prevent slipping and marking errors. When cutting compound angles on a miter saw or circular saw, secure the workpiece firmly—compound cuts create asymmetrical feed forces. Always wear safety glasses and hearing protection when cutting. On the roof, use fall protection (harness, anchor, lanyard rated for your weight) any time you are at or above 6 feet per OSHA standards for construction. Keep the work area clear of offcuts to prevent trip hazards.

Putting It Together

Mastering the unit-diagonal method lets you calculate hip and valley rafter lengths from the framing square alone, without trigonometry tables. Combine that with the correct ridge reduction and the proper cheek-cut layout and your rafters will fit accurately the first time.