Roof geometry
Common rafter line length
- where
- rise (mm)
- horizontal run (mm)
- roof pitch (°)
- rafter line length (mm)
- tail line length (mm)
- horizontal overhang (mm)
Explain this equation
Gives the theoretical line length of a common rafter from its horizontal run and pitch, including the tail over the eaves.
x is the horizontal run, usually from the wall plate line to the ridge centre line, in millimetres. θ is the roof pitch. R is the vertical rise. L is the rafter line length, and o the horizontal overhang beyond the plate, giving the tail length Lt.
Run, rise and rafter form a right-angled triangle. The rise is x tan θ, and the slope length is the run divided by cos θ. The tail follows the same slope, so it is the overhang divided by cos θ.
A 3000 mm run at 30° has a 1732 mm rise and a 3464 mm line. A 450 mm overhang adds 520 mm, for about 3984 mm in total.
Watch out: these are line lengths on the pitch line. Ridge deductions, birdsmouths and fascia details are separate.
Calculate a common rafter theoretical line from horizontal run and pitch.
Enter your values to see the result.
Good to know
Run is to the ridge centreline or other stated datum. These are theoretical line lengths, not fabrication lengths; ridge deductions, seat cuts, bearings and fascia details are separate.
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
- Roof geometry / designer-controlled details
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.