Roof geometry
Ridge thickness line deduction
- where
- horizontal deduction (mm)
- ridge thickness (mm)
- line deduction (mm)
- pitch (°)
Explain this equation
Gives how much to shorten a common rafter where it meets a ridge board.
t is the ridge board thickness in millimetres. dh is the horizontal deduction. θ is the roof pitch. dl is the same deduction measured along the rafter.
The rafter line is worked out to the centre of the ridge. Each rafter actually stops at the face of the board, half its thickness short, so dh = t/2. Measured along the slope, that horizontal amount becomes dh / cos θ.
A 38 mm ridge loses 19 mm horizontally. At 30° that is about 21.9 mm along the rafter.
Watch out: this assumes a vertical ridge board centred on a symmetrical roof.
Calculate the geometric deduction for half a vertical ridge thickness.
Enter your values to see the result.
Good to know
Symmetrical roof with a centred vertical ridge board and common rafter. This is not a bearing or joint 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.
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.