Hip, Valley & Jack Rafter Guide

Hip rafter length is calculated using the diagonal formula: L = √(Run² + Ridge² + Rise²), where Run is the horizontal distance from wall to center, Ridge is the horizontal distance perpendicular to the run (the hip setback), and Rise is the vertical height. For a standard hip roof (45° hip), the hip rafter length = Common Rafter Run × √2, and the hip drop (vertical distance from common rafter line to hip rafter) = Common Rafter Run × (1 − 1/√2).

The hip rafter has two critical angles: the hip angle (the angle between the hip rafter and the common rafter run, typically 45° for equal-pitch hip roofs) and the plumb/seat angles. The hip rafter's top cut angle (where it meets the ridge) = 90° − Pitch Angle, and the bottom cut (where it meets the wall) = Pitch Angle. For a 6/12 pitch hip roof, the hip angle is 45°, the top cut is 63.43°, and the bottom cut is 26.57°.

Valley rafter length uses the same 3D diagonal formula as hip rafter: L = √(Run² + ValleySetback² + Rise²). The valley setback is the horizontal distance from the main ridge to the valley ridge, measured perpendicular to the main run. For a standard valley at 45° intersection: Valley Length = Main Run × √2. The valley rafter also has compound angles where it meets the main ridge and the valley ridge.

Hip rafters run from the corner of a building up to the ridge, forming the hip of a hip roof (external angle). Valley rafters run from an interior corner upward to the ridge intersection, forming the valley where two roof slopes meet at an internal angle. Both use the same 3D geometry formula, but hip rafters typically extend from outside corners while valley rafters extend from inside corners where roofs intersect.

Jack rafters are the short rafters that run from the wall plate to the hip or valley rafter. Each jack rafter has a different length, calculated by proportional geometry: Jack Length = Common Rafter Length × (Jack Setback / Total Hip Setback). The first jack rafter is adjacent to the common rafter (longest), and each successive jack gets shorter until reaching a zero-length common rafter position at the hip/valley intersection.

Hip rafter drop is the vertical distance from the common rafter's top edge to the hip rafter's top edge at the wall plate. This occurs because the hip rafter is rotated 45° in plan view, so its effective rise per foot of horizontal run is less than the common rafter's. For a 6/12 pitch hip roof: Hip Drop = Run × (1 − 1/√2) × tan(26.57°) ≈ Run × 0.293 × 0.5 = Run × 0.1465 ft/ft of run.

Hip rafters are typically sized the same or one size larger than common rafters in the same roof. The hip rafter carries more load per linear foot because it collects the loads from two rafter planes. Check local building codes: the hip rafter's required size depends on span, species, spacing, and load. As a rule of thumb, if common rafters are 2x8 at 16" OC, the hip rafter should be 2x10 at maximum.

A bastard hip rafter (also called an unequal hip) occurs when the two roof pitches are different (e.g., main roof at 6/12 pitch, hip roof at 4/12 pitch). In this case, the hip angle is not 45° and the calculation requires resolving the compound angle. The hip length formula becomes: L = √(Run² + (RidgeOffset × cos(PitchDifference))² + Rise²), where RidgeOffset is adjusted for the unequal pitches.

Intersecting roofs (L-shaped or T-shaped) produce both hip and valley rafters at the intersection. First, identify the ridge intersection point. The valley rafter runs from the interior wall corner to the ridge intersection. The hip rafter runs from the exterior corner to the same intersection. Calculate each using the 3D diagonal formula: L = √(a² + b² + c²), where a = wall-to-intersection run, b = ridge perpendicular distance, c = rise at intersection.

The core hip rafter formula for a standard 45° hip roof: Hip Rafter Length = Common Rafter Run × √2. For a 10-foot run: Hip Length = 10 × 1.4142 = 14.14 ft = 14' 1-3/4". For non-standard hips, use the general 3D diagonal: L = √(Run² + Ridge² + Rise²) where Ridge = Run × tan(Hip Angle in plan).

To calculate the length of a valley rafter, use the same 3D diagonal formula as a hip rafter but with the valley setback replacing the ridge offset: Valley Rafter Length = √(Run² + ValleySetback² + Rise²). The step-by-step procedure: (1) identify the interior corner where the two roof planes meet and mark the ridge intersection point; (2) measure the run from that corner to the ridge intersection (horizontal, in the main roof plane); (3) measure the valley setback — the perpendicular horizontal distance from the main ridge to the valley ridge; (4) compute the rise at the intersection, Rise = Run × (Pitch ÷ 12); (5) solve the 3D diagonal. For a standard 45° valley where the setback equals the run, this simplifies to Valley Length = Run × √(2 + tan²(Pitch)). The valley rafter also carries compound cheek cuts where it meets both the main ridge and the intersecting ridge, unlike a common rafter's single plumb cut.

Board length for a hip roof rafter = hip line length + overhang (along the rafter) + cheek-cut waste + plumb setback − ridge deduction. The hip line length comes from the 3D diagonal formula √(Run² + Setback² + Rise²); the overhang is the horizontal overhang divided by cos(pitch); cheek-cut waste equals roughly the hip depth at each beveled end for a 45° hip; the plumb setback is hip depth × tan(hip plumb angle); and the ridge deduction is half the ridge board thickness parallel to the plumb cut. For an 8' run at 6/12 with a 12" overhang on a 2x8 hip, the board length works out to about 13' 5-1/2" — always round up to the next even lumber length when ordering.

Jack rafter angles need three cuts: a plumb cut (90° − pitch angle) at the ridge, a seat cut (pitch angle) at the birdsmouth — both identical to a common rafter — plus a cheek cut where the jack meets the hip or valley. For a standard 45° hip, the cheek cut angle is 45°. For a bastard hip on a non-45° plan angle, Cheek Angle = arctan(tan(pitch) × cos(plan angle)). Set the circular saw bevel to the cheek angle and cut along the plumb line so the jack's beveled face bears flush against the side of the hip. Valley jacks use the same three angles but reverse the bevel direction because the valley sits in a trough.

Yes. The hip rafter calculator embedded above takes your common run, roof pitch, and hip plan angle (45° for a standard hip roof) and returns the hip rafter line length, hip drop, cheek-cut angle, and jack rafter progression — all from the 3D diagonal formula L = √(Run² + Setback² + Rise²). Enter your run, pitch, and hip angle, and the hip rafter calculator outputs every cut needed for a hip or valley roof in feet-inches-fraction format.

This page focuses on hip and valley rafter geometry — the diagonal rafters that appear when a roof has hips or valleys instead of a simple gable. A gable roof has only common rafters (no hips or valleys), so a gable roof calculator is really just a common rafter calculator plus a truss count — use the main Rafter Calculator for the rafter length and cuts, and the Roof Truss Calculator for the truss count and package cost. If you are comparing a gable vs a hip roof for the same building footprint, a hip roof has four sloped planes (versus two for a gable), needs hip rafters at the corners, and adds roughly 25–40% more roof area and rafter material — the Hip vs. Valley vs. Common Rafter section above breaks down which rafters each roof type needs.

A hip roof framing calculator produces the complete cut list for an entire hip roof in one pass — the four king common rafters, hip rafter lengths with drop and cheek bevels, ridge length and height, and the full jack rafter progression for every bay. This guide works as that calculator: the embedded tool above returns the hip and jack numbers, and the Hip Roof Framing Calculator section walks the five-step sequence (king commons → ridge → hips → jacks → plane check) that turns those numbers into a framed roof.

A valley rafter calculator applies the same 3D diagonal as the hip formula — Valley Length = √(Run² + ValleySetback² + Rise²) — but at the 45° internal intersection the valley's effective pitch is 17-in-12, so a regular valley simplifies to Valley Run × 1.4736. It also returns the two opposite-direction cheek bevels, the valley drop that lets jack birdsmouths plane flush on both faces, and the valley jack setbacks measured from the valley centerline. Set the embedded tool above to valley mode, enter each plane's run and pitch, and the report lists all of these values in feet-inches-fraction.