Roof geometry
Equal-pitch jack length difference
- where
- line length difference (mm)
- spacing along eaves (mm)
- common pitch (°)
Explain this equation
Gives the difference in length between neighbouring jack rafters running into a hip on an equal-pitch roof.
s is the spacing of the jacks along the eaves, in millimetres. θ is the common pitch. Δ is how much each successive jack changes in line length.
With a 45° hip on plan, moving one spacing along the eaves moves the hip one spacing closer, so each jack's run changes by s. That run is converted to a slope length by dividing by cos θ, just as for a common rafter.
At 400 mm spacing and 30° pitch each jack differs by about 462 mm. A steeper pitch makes the difference bigger.
Watch out: this is the step between jacks, not the length of the first one, and it does not include side cuts.
Calculate theoretical successive common-jack differences at a 45° plan hip.
Enter your values to see the result.
Good to know
Equal pitches and a 90° plan corner only. This gives a difference, not the first jack length, side cut, or cutting allowance.
Limits
Roof lines are theoretical datum-to-datum lengths. They are not fabricated member lengths with ridge, bearing, seat, overhang or fascia details resolved. Equal-pitch hip and jack tools assume a 90-degree plan corner.
Sources
- Geometry / arithmetic
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.