Calculators/Hip & valley rafter
Hip length and hip angle on a regular equal-pitch roof, plus the common difference that steps every jack rafter down from the corner.
Half the building width, less half the ridge — the same run the common rafter uses.
Regular hips only. This assumes equal pitch on both sides, which is what puts the hip at 45° in plan. An unequal-pitch hip is a different problem and these numbers will not apply to it.
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Check the result against the job. This does the arithmetic from the values you enter. Building codes, span tables and material specifications vary by jurisdiction and by product, and the governing document is your approved drawings and your local code. Nothing you type here leaves your browser: the calculation runs on your device and we never receive it.
How this is checked. Every formula on this site runs from one shared calculation engine, and every one has a test fixture whose expected answer was worked out from the geometry or taken from a figure the trade already publishes — never from what the code returns. Some land exactly, which is the point: a 6/12 hip over a 144″ run is exactly 216″, a 45° crown in a square corner bevels at exactly 30°, and a 30° conduit bend has a multiplier of exactly 2. Where a number is a convention rather than arithmetic — a code limit, a waste allowance, bundles per square — it is an input with a stated default rather than a hidden constant. Found something wrong? Tell us at [email protected] and we will fix it and say so.
On a regular hip — equal pitch both sides — the hip runs diagonally across the corner at 45° in plan. That means it covers √2 times as much horizontal distance as the common while climbing exactly the same rise. Same rise over a longer run is a shallower angle, which is why a 6/12 roof has commons at 26.57° and hips at 19.47°.
It is also why the framing square has a separate hip scale marked 17: the hip travels 12√2 = 16.97 inches of plan run for every 12 the common travels, and 17 is the shop rounding. This calculator uses the exact figure.
Each jack sits one spacing further along the plate than the last, so its run drops by exactly that spacing — and its length drops by the spacing times the common slope factor, not the hip's. That fixed step is the common difference, and it is what lets you cut a whole set of jacks by subtracting the same number each time instead of measuring every one.
Cut the longest jack first, check it in place, then work down. A common difference applied to a wrong first jack produces a wrong set.
A valley is a hip turned inward. The run, length and angle come out identically; what changes is which way the cuts face and that the jacks run from the valley up to the ridge rather than from the plate up to the hip.
On a regular hip the hip runs at 45 degrees in plan, so its horizontal run is the common run times the square root of 2. The hip length is then the diagonal of that plan run and the total rise. A 6/12 roof over a 144 inch common run gives a hip of exactly 216 inches.
Because the hip travels 12 times the square root of 2, which is 16.97 inches of plan run, for every 12 inches the common travels. Seventeen is the shop rounding of that. This calculator uses the exact 16.97 rather than the rounded figure.
The fixed amount each successive jack rafter gets shorter. Each jack sits one spacing further along the plate, so its run drops by that spacing, and its length drops by the spacing times the common slope factor. At 16 inch centres on a 6/12 roof that is about 17 7/8 inches per jack.