Find the line length, cut length, tail and angles for a hip rafter on an equal-pitch roof. Enter the common run and pitch, then add the overhang and ridge thickness you will actually build with.
A hip rafter runs diagonally from the corner of the wall plate to the end of the ridge. In plan it crosses the corner at 45 degrees on a regular, equal-pitch roof, so it travels farther horizontally than the common rafter that shares the same rise. If you are laying out the complete roof, begin with the common rafter length calculator for the regular rafters, use this page for the hips, and use the valley rafter length calculator where two roof planes form an internal angle. Keeping those three members separate matters because their runs, angles and deductions are not interchangeable.
For an equal-pitch hip, the hip run is the common run multiplied by the square root of two. The rise stays the same as the common rafter's rise, which makes the hip shallower: its pitch angle is atan(tan(common pitch angle) / sqrt(2)). The hip line length is then sqrt(hip run squared + rise squared). That one change in run explains the familiar shortcut that a 6/12 common pitch becomes 4.24/12 when the same rise is expressed over 12 inches of hip run. The calculator uses the full geometry rather than rounding the hip to a nearby common-pitch equivalent.
Enter the common run, not the full building span unless your plans already define run from the ridge centerline to the outside of the wall. Add roof pitch, eaves overhang measured horizontally, and ridge-board thickness. The result separates line length from cut length. Line length is the theoretical slope distance between layout points; cut length adjusts that figure for the tail and the ridge connection so it corresponds to the board you mark.
The tail is calculated as overhang x sqrt(2) / cos(hip angle), because the eave also turns the corner diagonally. The ridge deduction is (ridge thickness / 2) x sqrt(2) / cos(hip angle), reflecting the hip's diagonal approach to the ridge. The page also reports plumb and seat angles from the top edge of the board. That convention is important when transferring numbers to a framing square or saw: a correct length paired with an angle measured from the wrong reference will still produce a poor joint.
| Common pitch | Hip rise per 12 in of hip run | Hip angle | Hip length per 1 ft of common run |
|---|---|---|---|
| 4/12 | 2.83/12 | 13.3° | 17.44 in |
| 5/12 | 3.54/12 | 16.3° | 17.69 in |
| 6/12 | 4.24/12 | 19.5° | 18.00 in |
| 8/12 | 5.66/12 | 25.2° | 18.76 in |
| 10/12 | 7.07/12 | 30.5° | 19.70 in |
| 12/12 | 8.49/12 | 35.3° | 20.78 in |
Take a regular hip roof with a 12 ft common run and a 6/12 pitch. The common rise is 6 ft. The hip run is 12 ft multiplied by sqrt(2), or 16 ft 11 5/8 in. Combining that run with the unchanged 6 ft rise gives sqrt(16.9706^2 + 6^2) = 18 ft exactly. The resulting hip angle is 19.5 degrees. This is a useful benchmark because the clean 18 ft line length makes it easy to spot a misplaced decimal or an accidental span-versus-run entry.
Now add a 12 in horizontal overhang and a 1.5 in ridge board. The diagonal tail is 18 in along the hip slope. The ridge deduction is 1 1/8 in. The final cut length is therefore 18 ft + 18 in - 1 1/8 in = 19 ft 4 7/8 in. Those adjustments are not optional trim allowances; they locate the birdsmouth, eave and ridge faces where the framing plan expects them.
12 ft common run x sqrt(2) gives a 16 ft 11 5/8 in hip run. The rise remains 6 ft at a 6/12 common pitch.
Square the hip run and rise, add them, and take the square root. The numbers resolve to an exact benchmark in this example.
A 12 in overhang becomes an 18 in diagonal tail. Half of a 1.5 in ridge, projected along the hip, deducts 1 1/8 in.
Lay out from a consistent reference edge and mark the plumb and seat cuts using the angles reported from the top edge of the board. The hip's shallower angle is the first visual check: at a 6/12 common pitch, its plumb and seat geometry is based on 19.5 degrees, not the common rafter's 26.6 degrees. Mixing those two angle sets is a common reason a hip stands proud at the ridge or drops at the eave even though its measured length looked plausible.
Cut one hip and test it against the ridge and both wall plates before treating it as a pattern. Check that the birdsmouth bears properly and that the top edges align with the adjoining roof planes. Small plan irregularities—an out-of-square corner, a plate that is not straight, or a ridge set off center—show up first at the hip. Adjust the pattern for the building you have, not the perfect rectangle in the example. Once both ends and the seat are proven, duplicate the pattern carefully and keep the crown orientation consistent.
Use this calculator for a conventional hip where the intersecting roof planes have the same pitch and meet over a square corner, producing a 45-degree hip line in plan. It is suitable for estimating board length, checking a framing-square layout and planning the principal cuts before test-fitting. The lumber must still be sized for span, load, species, grade and local code; a geometrically correct 2x8 is not automatically a structurally adequate 2x8.
Do not use the equal-pitch formulas for an irregular hip where the two slopes have different pitches, for a bay or offset corner that does not turn at 45 degrees in plan, or where the ridge is intentionally displaced. Those roofs change both the plan angle and the hip pitch. Model the actual plan geometry or use a framing method intended for irregular hips. Likewise, engineered trusses and structural ridge systems follow their manufacturers' layouts rather than these conventional rafter calculations.
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.
It covers the same rise but a longer horizontal run. On an equal-pitch roof its plan run is the common run multiplied by sqrt(2), so the sloped length is greater and its pitch angle is shallower.
It expresses the same rise over hip run instead of common run. Divide the common pitch by sqrt(2): 6 / sqrt(2) = 4.24. The roof has not changed; only the run used to describe the hip angle has changed.
Yes. The cut-length result adds the diagonal tail for the horizontal overhang you enter and subtracts the ridge deduction based on half the ridge thickness projected along the hip slope.
For equal pitches, the basic length geometry is the same, but the valley sits in an internal angle and has different installation and flashing concerns. Use the dedicated valley calculator so the guidance and layout checks match the member.
Check the corner angle, ridge position, plate straightness and angle reference. Most fit problems come from an out-of-square building, using common-rafter angles on the hip, or inconsistent birdsmouth layout rather than from the slope-length formula.
No. It calculates geometry and cut length. Select species, grade and depth from the applicable span requirements and local building code, taking snow, roof load and ceiling conditions into account.
The full common rafter: length, angles, birdsmouth and materials.
Where two roof planes meet — valley length and its cut angles.
First jack length and the common difference for your spacing.
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.