Roof geometry
Equal-pitch hip / valley line
- where
- plan diagonal (mm)
- common horizontal run (mm)
- rise (mm)
- common roof pitch (°)
- hip diagonal line length (mm)
Explain this equation
Gives the line length and slope of a hip or valley rafter where two roofs of the same pitch meet at a 90° corner.
x is the horizontal run of the common rafters, in millimetres. θ is the common pitch. xp is the hip's run on plan. R is the rise, the same as for the commons. L is the hip line length. The calculator also gives the hip's own inclination.
On plan the hip runs at 45°, across the diagonal of a square with side x, so its run is x√2. It reaches the same ridge height, so its rise is x tan θ. Pythagoras on plan run and rise gives the line length.
A 3000 mm run at 30° gives a 4243 mm plan diagonal, a 1732 mm rise and a 4583 mm hip line. The hip is shallower than the commons, at about 22.2°.
Watch out: this is ideal geometry for equal pitches only. It includes no backing, side cuts, ridge or overhang allowances.
Calculate the diagonal line at a 90° plan intersection of equal-pitch roofs.
Enter your values to see the result.
Good to know
Ideal equal-pitch 90° geometry only. No backing, side-cut, ridge or overhang allowances. Unequal pitches need a separate design.
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.