Calculate the rafter length for a gable roof from the pitch, building width, and overhang — exact trigonometry.
rafter = (building_width ÷ 2) × √(rise²+run²)÷run + overhang
The horizontal run is half the building width. Multiply by the pitch's slope multiplier and add the overhang to get the rafter length.
This gives the common rafter length. Hip and valley rafters are longer — they run diagonally.
For a 24 ft wide building with a 6:12 pitch, the horizontal run is half the width: 12 ft. The slope multiplier at 6:12 is 1.118, so the rafter from ridge to wall is 12 x 1.118 = 13.4 ft. Add a 1 ft overhang and you'd cut each common rafter at about 14.4 ft.
This is the common rafter length along the slope. You still need to mark the bird's-mouth (the notch that sits on the wall plate) and the plumb cuts at each end, so order stock a little longer than the calculated length.
Pure trigonometry — no estimation. Add for the bird's-mouth cut and plumb cut when ordering stock length.
The common rafter length is the hypotenuse of the triangle formed by the horizontal run (half the building span, minus half the ridge thickness) and the vertical rise. It equals the run times the pitch factor, or run divided by the cosine of the roof angle. Add the overhang (the tail beyond the wall) to get the total length to order.
A rafter is more than a length: the top gets a plumb cut against the ridge, the seat gets a birdsmouth notch where it rests on the top plate, and the tail is cut plumb or square at the eave. The overhang adds to the ordered length but not to the structural span. Account for the ridge board thickness by subtracting half of it from the run.
About 13.4 ft plus overhang — the 12 ft run times the 1.118 slope multiplier.
Take the horizontal run (half the span, less half the ridge thickness) and multiply by the pitch factor, or divide by the cosine of the roof angle. Then add the overhang for the total length to cut.
A birdsmouth is the notch cut into the underside of a rafter where it seats on the top plate of the wall, transferring the roof load down into the wall.
Yes. The overhang (the rafter tail beyond the wall) adds to the length you order and cut, though it does not count toward the structural span.