Hip, Valley and Jack Rafter Calculator
Last reviewed How we calculate
Hip and valley rafters run diagonally across the corner of a building, so they are longer than the common rafters and climb at a shallower angle. Jack rafters fill the space between a hip and the wall, and each one is shorter than the last. This works out all three from the span and the pitch.
Hip, valley and jack rafter lengths
Hip and valley rafter lengths, the hip factor, and the step between jack rafters for any pitch.
This calculator needs JavaScript to work. The measurements below are the ones you would need to do the sum by hand.
Hip or valley rafter, including tail Line length, before deductions for the ridge and hip thickness.
- Common rafter, line length
- Hip rafter, corner to ridge
- Hip and valley factor Hip length for each unit of common run.
- Hip slope angle
- Jack rafter step Each jack is this much shorter than the one before it.
- Jacks on each side of a hip
- Longest jack, line length
- Shortest jack, line length
Line lengths only, measured on center lines, before the deductions for half the ridge and half the hip thickness and before the side cuts every hip and jack needs. Jack lengths exclude their tails. Valley rafters between two faces of equal pitch are the same length as hips. These members carry more load than common rafters, so their size belongs to your span tables or an engineer.
How the calculation works
On plan, a hip rafter crosses the corner at 45 degrees, so it covers about 1.414 times the run of a common rafter. Combine that with the rise and you get the hip and valley factor: the square root of the pitch over 12 squared, plus two. Multiply the common run by it for the hip line length. Jack rafters sit at the rafter spacing along the wall, and each one is shorter than the next by the spacing times the common pitch multiplier.
A worked example
For a 28 ft span at 6 in 12, the common run is 14 ft and the common rafter line length is 15.65 ft. The hip factor at 6 in 12 is 1.5, so the hip is 21 ft from corner to ridge, and a 12 in overhang brings it to 22.5 ft. At 24 in spacing each jack is 2.24 ft shorter than the next, which gives six jacks on each side of the hip, from 13.42 ft down to 2.24 ft.
What still has to be done by hand
These are line lengths along the center of each member. The hip has to be shortened by half the thickness of the ridge, measured at 45 degrees, and each jack by half the thickness of the hip. Every hip and jack also needs a side cut where it meets the member beside it. Valley rafters between two faces of the same pitch are the same length as hips.
Hips and valleys carry more load than common rafters because the jacks bear on them, so they are usually deeper, and sometimes doubled. Their size comes from your span tables or an engineer, not from a length calculator.
Frequently asked questions
What is the hip and valley factor?
It is how much longer a hip or valley rafter is for every unit of common run: the square root of the pitch over 12 squared, plus two. At 6 in 12 it is exactly 1.5, so a 14 ft common run gives a 21 ft hip.
Are valley rafters the same length as hip rafters?
Where the two roof faces meeting at the valley have the same pitch, yes. The valley is a hip turned inside out, and the same factor applies.
What is a jack rafter?
A shortened rafter that runs from the wall plate up to a hip, or from a valley up to the ridge. Each jack is shorter than the one next to it by the same step, which the calculator gives.