Calculate jack rafter lengths and side cut angles for hip and valley roof systems. Supports variable on-center spacing.
Enter the pitch as rise per 12 inches of run and the on-center spacing of your rafters, commonly 16 or 24 inches. Jack rafters run parallel to the commons but land on a hip or valley, so each one is shorter than its neighbor by a fixed amount.
The tool first computes the unit rafter length √(144 + rise²) — the sloped length in inches for every 12 inches of run. At 6/12 pitch that is √180, about 13.42 inches per foot of run.
The common difference is spacing × unit length ÷ 12. At 16 inch centers on a 6/12 roof each successive jack is about 17.89 inches shorter; at 24 inch centers the step grows to about 26.83 inches. Cut the longest jack first, then subtract the common difference repeatedly.
It is the constant length step between adjacent jacks along a hip or valley: spacing × √(144 + rise²) ÷ 12. Because spacing and pitch are both constant, every jack shortens by exactly this amount, letting you gang-cut the whole set from one measurement.
Proportionally. Moving from 16 to 24 inch centers multiplies the common difference by 1.5 — on a 6/12 roof that is 17.89 versus 26.83 inches — because each jack meets the 45° hip a further 8 inches along in plan.
The sloped distance a rafter travels for every 12 inches of horizontal run: √(144 + rise²) inches. It is about 13.42 for a 6/12 pitch and 14.42 for 8/12 (√208), and it converts plan dimensions into true lengths along the roof surface.
Measure or compute the longest jack next to the common rafter, then subtract the common difference once per position toward the corner. A set of five jacks spans four steps, so the shortest is four common differences shorter than the longest.