Work out a full sequence of jack rafters for a regular hip or valley: the first length, the common difference between successive jacks, hip shortening and the cheek-cut angle for your pitch and spacing.
| Jack | Run | Cut length |
|---|---|---|
| Jack 1 | 1 ft 4 in | 1 ft 4 11/16 in |
| Jack 2 | 2 ft 8 in | 2 ft 10 9/16 in |
| Jack 3 | 4 ft 0 in | 4 ft 4 1/2 in |
| Jack 4 | 5 ft 4 in | 5 ft 10 3/8 in |
| Jack 5 | 6 ft 8 in | 7 ft 4 1/4 in |
| Jack 6 | 8 ft 0 in | 8 ft 10 1/8 in |
Jack rafters fill the triangular part of a hip roof between the wall plate and a hip or valley. Unlike the diagonal member, a jack lies in the same roof plane as a common rafter and has the same pitch. Its length therefore depends on where it stands: as its horizontal run position increases in equal steps, its line length increases by an equal amount. For the full-size commons, use the full-length common rafter calculator; for the diagonal that receives these jacks, use the hip rafter calculator before laying out the sequence.
That equal step is called the common difference. It is the on-center spacing measured along the wall plate multiplied by the common rafter's pitch multiplier. At 6/12, the multiplier is sqrt(1 + 0.5^2) = 1.1180. A 16 in spacing consequently produces a common difference of 17 7/8 in. Once the first jack is established, each successive jack changes by that same amount until the sequence reaches the common rafter position or the end of the run.
A theoretical jack length runs to the centerline geometry used to establish the roof planes. A physical board cannot occupy the same space as the hip, so the jack is shortened where it meets that member. For a regular 45-degree hip, the shortening along the jack's slope is (hip thickness x sqrt(2) / 2) x pitch multiplier. The sqrt(2) term accounts for measuring half the hip thickness across the diagonal joint, and the multiplier converts that horizontal allowance into length along the sloped jack.
With a 1.5 in thick hip at 6/12, the shortening is 1 3/16 in. Apply the same end allowance consistently according to the chosen centerline convention; do not also shorten the board again because a generic cutting list mentions a hip deduction. The calculator's sequence makes the distinction visible by showing line length and cut length side by side. If your framing method measures from the hip's actual face rather than its centerline, establish that convention before cutting and keep it through the entire set.
| Jack | Run position | Line length | Cut length after 1 3/16 in shortening |
|---|---|---|---|
| 1 | 16 in | 17 7/8 in | 16 11/16 in |
| 2 | 32 in | 35 3/4 in | 34 9/16 in |
| 3 | 48 in | 53 11/16 in | 52 1/2 in |
| 4 | 64 in | 71 9/16 in | 70 3/8 in |
| 5 | 80 in | 89 7/16 in | 88 1/4 in |
| 6 | 96 in | 107 5/16 in | 106 1/8 in |
For a 6/12 roof with jacks spaced 16 in on center, start with the pitch multiplier of 1.1180. The first jack at a 16 in run position has a theoretical line length of 17 7/8 in. Subtract 1 3/16 in of hip shortening to get 16 11/16 in for its cut length under the calculator's convention. The second jack is one common difference longer in line length, not one spacing unit plus another new deduction calculation.
Continue adding 17 7/8 in of line length for each step and apply the same hip-end convention to each physical board. The table gives the first six in the sequence. In a real roof, stop the pattern at the layout boundary and compare the longest jack with the adjacent common rafter layout; a mismatch usually reveals that the first position, spacing direction or hip centerline was marked from the wrong point.
A 16 in plate spacing at 6/12 gives 16 x 1.1180. Every successive jack changes by this amount in line length.
For a 1.5 in hip, (1.5 x sqrt(2) / 2) x 1.1180 gives the amount removed at the hip end under the centerline method.
At 6/12, the side cut on the top face is not the same as the common rafter's seat or plumb angle. It must be laid out for the diagonal joint.
A jack has the familiar plumb and seat cuts of a common rafter, plus a cheek cut where its upper end meets the diagonal member. On this site, the cheek angle is measured on the top face from the top edge of the board. At 6/12 it is 41.8 degrees. That angle should not be confused with the common rafter's 26.6-degree pitch angle or with the hip rafter's shallower 19.5-degree slope angle. Each describes a different line in the joint.
Lay out one jack completely and test it between the plate and hip before cutting the set. Check bearing at the seat, alignment of the top edge with the roof plane, and full contact at the cheek. Mark its position and orientation; jack rafters are handed by the side of the hip and by the direction of the cheek. When the test piece fits, use it or a verified cutting list as the pattern, and recheck the final jack rather than assuming accumulated layout marks are exact.
The arithmetic progression makes jack layout efficient, but it also repeats an early mistake. Confirm whether spacing is measured from the corner, the hip centerline, the first common rafter or another plan-defined origin. Those choices can shift every jack even when spacing itself is correct. Also confirm that the run in a hand calculation is the jack's position along the plate, not the length of the hip and not a diagonal distance across the corner.
Use this calculator for regular hips and valleys where the intersecting pitches are equal and the diagonal is at 45 degrees in plan. It does not choose lumber size or establish structural capacity. Closely spaced, long or heavily loaded jacks still need species, grade and span checks. For irregular hips, unequal pitches or manufactured roof systems, derive the sequence from the actual plan geometry or the manufacturer's framing layout.
Every result on this page comes from the method described above, using standard framing geometry and the published data credited below. Found a number that looks wrong? Use Report an Error — every report is read.
Measure from the layout origin specified by the framing plan. In the standard regular-hip sequence, each jack's run steps by the on-center spacing, and its line length increases or decreases by the same common difference.
It is the change in line length between successive jack rafters. Because the jacks lie in the same plane as the common rafters, it equals their spacing along the plate multiplied by the common rafter pitch multiplier.
The hip occupies space at the joint. The jack is shortened by half the hip's diagonal thickness projected into a length along the common slope: (hip thickness x sqrt(2) / 2) x pitch multiplier.
It is the side cut where the jack meets the hip, measured here from the top edge of the board. At a 6/12 pitch on a regular 45-degree hip, it is 41.8 degrees. It changes with pitch, so do not reuse that number for another roof.
The length pattern follows the same diagonal geometry, but the supporting member is a valley rather than a hip and the installation details differ. Confirm the layout origin and end condition from the valley framing plan.
First check that spacing was laid out along the plate, the pitch multiplier is correct, and shortening was not applied twice. A small origin error repeats through the whole sequence, so correct it before cutting the remaining jacks.
The full common rafter: length, angles, birdsmouth and materials.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
Where two roof planes meet — valley length and its cut angles.
Single-slope rafters between two different wall heights.
Seat cut, heel height and HAP, checked against the IRC one-quarter limit.
Plumb, seat and cheek angles — plus the saw settings to cut them.
Convert pitch, rise/run, degrees and percent, both ways.
How far a board can span — IRC tables by species, grade and load.
The lumber size a span actually needs. The inverse of the span tool.
Two pitches, one roof — upper and lower rafter lengths.
The full pitch × run table, printable for the workshop wall.
Figure any rafter by hand — formula and framing-square methods.