Roof geometry
Common rafter length from span and pitch, with ridge board and overhang
- where
- run of the rafter, plate to face of ridge board (mm)
- span, outside of wall plates (m)
- ridge board thickness (mm)
- rafter length, plate to ridge (mm)
- roof pitch (°)
- overhang length along the rafter (mm)
- eaves overhang measured horizontally (mm)
- total rafter length (mm)
- rise of the rafter (mm)
Explain this equation
Works out how long to cut a common rafter for a given span and pitch, including the eaves overhang, and the rise it gives. Use it for ordering timber and for setting out a pattern rafter.
S is the span in metres, so 1000 S / 2 is half the span in millimetres. Each rafter stops at the face of the ridge board, so half the board thickness t comes off to give the true run G. Dividing a horizontal distance by cos p gives the matching length along the slope, both for the main run and for the overhang o. G tan p is the height the rafter climbs.
The rafter is the long side of a right-angled triangle whose base is the run, so slope length equals plan length divided by the cosine of the pitch.
Sense check: an 8 m span at 35° with a 50 mm ridge board gives a run of 3975 mm and a plate-to-ridge length of about 4.85 m. Steeper pitches make cos p smaller and the rafter longer.
Watch out: these are line lengths along the rafter. Allow extra for the plumb cut, birdsmouth and any trimming, and buy the next stock length up.
Sloping length of a common rafter on a symmetrical duo-pitch roof: from the ridge board to the wall plate line, plus the eaves overhang.
Enter your values to see the result.
Good to know
Lengths are measured along the top edge (the line used for setting out) from the plumb cut at the ridge to the plate line, then on to the eaves. Add a little for trimming the plumb and fascia cuts. Run is half the span less half the ridge board. For a roof without a ridge board (rafters meeting on a plate or nail plate), set the thickness to 0.
Common mistake
Measuring the overhang along the slope and then dividing by cos θ again, which over-orders. Enter the overhang as the horizontal projection beyond the plate.
Limits
Equal pitches either side. Does not cut the birdsmouth or allow for its depth; rafter sizing and spans are a structural matter (Approved Document A and span tables).
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the roof covering manufacturer’s fixing specification, BS 5534, BS 8000-6, BS 6229, the Lead Sheet Training Academy guidance and Building Regulations. Wind uplift and structural design need a competent designer.