Hip and valley rafters run at 45 degrees in plan, so their run is the common run × √2. That makes the hip shallower than the common rafter at the same pitch. This tool returns hip length, backing angle, jack rafter lengths and the common difference between jacks.
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| Pitch | Angle | Slope % | Multiplier | Hip / valley | Rafter per 12" run |
|---|---|---|---|---|---|
| 0.25/12 | 1.19° | 2.08% | 1.0002 | 1.4144 | 12.00" |
| 0.5/12 | 2.39° | 4.17% | 1.0009 | 1.4148 | 12.01" |
| 1/12 | 4.76° | 8.33% | 1.0035 | 1.4167 | 12.04" |
| 1.5/12 | 7.13° | 12.50% | 1.0078 | 1.4197 | 12.09" |
| 2/12 | 9.46° | 16.67% | 1.0138 | 1.4240 | 12.17" |
| 2.5/12 | 11.77° | 20.83% | 1.0215 | 1.4295 | 12.26" |
| 3/12 | 14.04° | 25.00% | 1.0308 | 1.4361 | 12.37" |
| 3.5/12 | 16.26° | 29.17% | 1.0417 | 1.4440 | 12.50" |
| 4/12 | 18.43° | 33.33% | 1.0541 | 1.4530 | 12.65" |
| 4.5/12 | 20.56° | 37.50% | 1.0680 | 1.4631 | 12.82" |
| 5/12 | 22.62° | 41.67% | 1.0833 | 1.4743 | 13.00" |
| 5.5/12 | 24.62° | 45.83% | 1.1000 | 1.4866 | 13.20" |
| 6/12 | 26.57° | 50.00% | 1.1180 | 1.5000 | 13.42" |
| 6.5/12 | 28.44° | 54.17% | 1.1373 | 1.5144 | 13.65" |
| 7/12 | 30.26° | 58.33% | 1.1577 | 1.5298 | 13.89" |
| 7.5/12 | 32.01° | 62.50% | 1.1792 | 1.5462 | 14.15" |
| 8/12 | 33.69° | 66.67% | 1.2019 | 1.5635 | 14.42" |
| 8.5/12 | 35.31° | 70.83% | 1.2255 | 1.5817 | 14.71" |
| 9/12 | 36.87° | 75.00% | 1.2500 | 1.6008 | 15.00" |
| 9.5/12 | 38.37° | 79.17% | 1.2754 | 1.6207 | 15.31" |
| 10/12 | 39.81° | 83.33% | 1.3017 | 1.6415 | 15.62" |
| 11/12 | 42.51° | 91.67% | 1.3566 | 1.6853 | 16.28" |
| 12/12 | 45.00° | 100.00% | 1.4142 | 1.7321 | 16.97" |
| 13/12 | 47.29° | 108.33% | 1.4743 | 1.7815 | 17.69" |
| 14/12 | 49.40° | 116.67% | 1.5366 | 1.8333 | 18.44" |
| 15/12 | 51.34° | 125.00% | 1.6008 | 1.8875 | 19.21" |
| 16/12 | 53.13° | 133.33% | 1.6667 | 1.9437 | 20.00" |
| 18/12 | 56.31° | 150.00% | 1.8028 | 2.0616 | 21.63" |
| 20/12 | 59.04° | 166.67% | 1.9437 | 2.1858 | 23.32" |
| 24/12 | 63.43° | 200.00% | 2.2361 | 2.4495 | 26.83" |
Why is the hip a lower angle than the common rafter?
The hip covers a longer horizontal distance to reach the same height, because it travels diagonally across the corner. A 6/12 common rafter sits at 26.57 degrees, while its hip sits at about 19.47 degrees. That is why hips are easier to walk than the main roof planes.
What is the common difference?
It is the fixed amount each successive jack rafter gets shorter by. Work it out once and you can cut the whole set without measuring each one.
Why must the heel heights match?
If the hip heel height differs from the commons, the hip sits proud or low and the roof plane goes humpy along the corner. Set the heel heights equal before anything else.
