Hip rafter calculator
Hip rafter length, run, and every cut angle from a building width and a roof pitch, plus the backing angle and the jack rafter run-down. The same hip math the CutOnce app runs on the jobsite.
Updated
A regular hip sits on a square corner, so the common run is half the building width. Pitch is the common rafter's rise per 12 in of run.
- Hip rafter length
- 21 ft
- Hip run
- 19 ft 9-9/16 in
- Ridge height
- 7 ft
- Plumb cut
- 19.5°
- Seat cut
- 70.5°
- Cheek cut
- 43.3°
- Backing angle
- 18.4°
- Hip drop
- 1/4 in
- Jack common difference
- 17-7/8 in
- Jack side cut
- 41.8°
- First jacks (long to short)
- 14 ft 10-7/8 in · 13 ft 5 in · 11 ft 11-1/8 in · 10 ft 5-1/4 in
Cheek cut angles are measured from the board's top edge. Subtract from 90° for the angle from square.
How a hip rafter is calculated
A hip runs diagonally across a square corner, so for every 12 inches a common rafter runs, the hip runs 12 times the square root of 2, about 16.97 inches. Its length is that longer unit run and the roof's rise worked through the Pythagorean theorem. On a regular hip, both roof planes share one pitch, and the common run is half the building width.
A worked example
A 28 ft wide building at 6/12, with a 1-1/2 in hip and jacks 16 in on center. Every number below is computed by the same function that drives the calculator above.
| Hip run (diagonal to the corner) | 19 ft 9-9/16 in |
| Hip rafter length | 21 ft |
| Ridge height | 7 ft |
| Plumb cut | 19.5° |
| Seat cut | 70.5° |
| Cheek (side) cut | 43.3° |
| Backing angle | 18.4° |
| Jack common difference | 17-7/8 in |
Hip length and cut angles by pitch
Per foot of common run, a hip is this long, with these plumb and cheek cut angles. The hip length grows with run; the angles are set by pitch alone. Read your building's run off the calculator, then scale the length here.
| Pitch | Hip length / ft run | Plumb cut | Cheek cut |
|---|---|---|---|
| 3/12 | 17-1/4 in | 10.0° | 44.6° |
| 4/12 | 17-7/16 in | 13.3° | 44.2° |
| 5/12 | 17-11/16 in | 16.4° | 43.8° |
| 6/12 | 18 in | 19.5° | 43.3° |
| 7/12 | 18-3/8 in | 22.4° | 42.8° |
| 8/12 | 18-3/4 in | 25.2° | 42.1° |
| 9/12 | 19-3/16 in | 27.9° | 41.5° |
| 10/12 | 19-11/16 in | 30.5° | 40.7° |
| 12/12 | 20-13/16 in | 35.3° | 39.2° |
How to lay out a hip rafter
- 01
Find the run
On a regular hip the corner is square, so the common run is half the building width. A 28 ft building gives a 14 ft common run and a hip that travels the diagonal of that square in plan.
- 02
Mark the plumb, seat, and cheek cuts
The plumb cut at the ridge and the seat cut at the wall come straight from the hip's slope, which is shallower than the common rafter's because the hip runs farther for the same rise. The cheek cut is measured from the board's top edge, so subtract it from 90 degrees for the angle from square.
- 03
Back or drop the hip, then cut the jacks
The backing angle bevels the hip's top edge so the sheathing planes meet flush, or you drop the hip by the hip drop instead. Jacks step down from the hip by a fixed common difference set by their spacing, each with the same side cut.
Common questions
- How long is a hip rafter?
- For a 28 ft building at 6/12, the hip rafter line length is 21 ft before any overhang or ridge deduction. It is longer than the common rafter on the same roof because the hip runs the diagonal of the corner, not straight across.
- Why is the hip longer than the common rafter?
- Both climb to the same ridge, but the hip travels farther in plan to get there, out to the corner instead of straight in. A common rafter runs 12 units of plan per foot; a hip runs about 16.97, so its line length per foot of common run is always greater.
- What is backing or dropping a hip?
- The two roof planes meet along the top of the hip at an angle, so a square-topped hip would leave the sheathing proud on both sides. You either bevel the top to the backing angle (18.4 degrees at 6/12) or set the hip lower by the hip drop, about 1/4 in on a 1-1/2 in hip, so the planes land flush.
- Does this handle irregular (unequal pitch) hips?
- This page solves the regular hip, where both roof planes share one pitch. The app also solves irregular hips, where the two planes run different pitches, with a separate backing angle and plan angle on each face. That case is in the app.
- How are the jack rafters calculated?
- Each jack is shorter than the last by a fixed common difference, set by the spacing and the common rafter's slope, and all of them share one side cut where they meet the hip. Enter a spacing and the calculator lists the run-down from longest to shortest.
- Why do both slopes show the same HAP on an unequal-pitch hip?
- On an unequal-pitch hip CutOnce holds one height above the plate for both slopes. The slope with the shorter HAP sets it, which is not always the steeper pitch, and the other slope's birdsmouth plumb cut runs deeper so both sides land at the same height. The equal HAP you see is by design, not a rounding coincidence.
Cut the whole hip roof, offline
The app frames regular and irregular hips and valleys, lays out every jack, and prints a cut list, all working with no signal. Part of the one-time toolbox, no subscription.
See also