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On a regular hip roof, where both roof planes share one pitch, the hip rafter runs at 45° in plan and travels 16.97 in horizontally for every 12 in of common run. Its length per foot of common run is √(288 + rise²) inches — 18.00 in at 6/12 — and its pitch is the same rise over 17. Jack rafters shorten by a common difference of spacing × √(144 + rise²) ÷ 12, which is 17 7/8 in at 16 in centres and 26 13/16 in at 24 in centres on a 6/12 roof. These are the same figures stamped in the rafter table of a steel framing square. Enter the building width, pitch, spacing and overhang and the Hip Rafter Calculator returns the hip and common lengths, the hip tail, every jack rafter length and the side cuts. A 28 ft wide house at 6/12 has a 21 ft hip plus a 1 ft 6 in tail and 80 jack rafters at 16 in centres.
On a regular hip roof both planes share one pitch and the hip runs at 45° in plan, so it travels 16.97 in for every 12 in of common run. Hip length per foot of common run is √(288 + rise²) inches; jack rafters shorten by spacing × √(144 + rise²) ÷ 12. These are the figures stamped in the rafter table of a steel framing square.
| Pitch | Common / ft | Hip / ft | Jacks 16 in | Jacks 24 in | Side cut jacks | Side cut hip |
|---|---|---|---|---|---|---|
| 3/12 | 12.37 in | 17.23 in | 16 1/2 in | 24 3/4 in | 11 5/8 | 11 13/16 |
| 4/12 | 12.65 in | 17.44 in | 16 7/8 in | 25 5/16 in | 11 3/8 | 11 11/16 |
| 5/12 | 13.00 in | 17.69 in | 17 5/16 in | 26 in | 11 1/16 | 11 1/2 |
| 6/12 | 13.42 in | 18.00 in | 17 7/8 in | 26 13/16 in | 10 3/4 | 11 5/16 |
| 7/12 | 13.89 in | 18.36 in | 18 1/2 in | 27 13/16 in | 10 3/8 | 11 1/16 |
| 8/12 | 14.42 in | 18.76 in | 19 1/4 in | 28 7/8 in | 10 | 10 7/8 |
| 9/12 | 15.00 in | 19.21 in | 20 in | 30 in | 9 5/8 | 10 5/8 |
| 10/12 | 15.62 in | 19.70 in | 20 13/16 in | 31 1/4 in | 9 3/16 | 10 5/16 |
| 12/12 | 16.97 in | 20.78 in | 22 5/8 in | 33 15/16 in | 8 1/2 | 9 13/16 |
Multiply the common run in feet by √(288 + rise²) and divide by 12. On a regular hip the hip travels 16.97 in horizontally for every 12 in of common run, so at 6/12 it is 18.00 in per foot: a 28 ft wide house (14 ft common run) has a hip 14 × 18 ÷ 12 = 21 ft long before the overhang and the ridge shortening.
The same rise over 17 instead of 12. A 6/12 roof has hips at 6 in 17 (19.47°), a 12/12 roof hips at 12 in 17 (35.26°). Use 17 on the body of the framing square and the rise on the tongue to mark the plumb and seat cuts.
The amount each jack is shorter than the next: spacing × √(144 + rise²) ÷ 12. At 6/12 that is 17 7/8 in at 16 in centres and 26 13/16 in at 24 in centres — the same figures printed in the rafter table of a steel framing square.
Read them from the framing-square table and use them with 12 on the other arm. At 6/12 the jack side cut is 10 3/4 and the hip side cut 11 5/16; at 12/12 they are 8 1/2 and 9 13/16. This calculator works both figures out for any pitch.
Each side of each hip gets one jack per spacing along the plate, short of the common run. A 14 ft run at 16 in centres fits 10 jacks per side, so a plain rectangular hip roof with four hips needs 4 × 2 × 10 = 80 jack rafters.
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