Sixteenth
Rafter Calculator
Enter the pitch and the building span. You get the common rafter length with overhang, the cut angles, the birdsmouth, and the hip, valley and jack rafters for the same roof.
Pitch as 6, 6/12 or 6:12. Lengths like 24', 23' 9", or 7.3 m. Plain numbers are inches.
How rafter length is calculated
The run of a common rafter is half the span, less half the ridge board, measured level. The rafter's length is the run times the slope factor, which is how much longer the slope is than the level run.
run = span ÷ 2 − ridge ÷ 2 · slope factor = √(144 + pitch²) ÷ 12
rafter = run × slope factor · tail = overhang × slope factor
Lengths are measured along the top edge of the rafter (the measuring line), from the ridge plumb cut to the outside of the wall, and then to the end of the tail.
Birdsmouth: the seat cut sits flat on the wall plate and the heel cut is plumb. The height above plate (HAP) is the plumb distance from the top of the wall to the top of the rafter; keep it the same on every rafter so the roof plane stays flat.
Hip and valley: for a roof with the same pitch on both sides, the hip runs at 45° in plan, so its run is the common run × 1.414 and its pitch is the common pitch over 17.
Questions
How do you calculate rafter length?
Find the run: half the building span, less half the ridge board thickness. Multiply the run by the slope factor √(12² + pitch²) ÷ 12. For a 6/12 pitch the factor is 1.118, so a 12' run gives a 13' 5" rafter from the plate to the ridge. Add the overhang (horizontal overhang × the same factor) for the total length.
What angle do I cut a rafter at?
The plumb cut (at the ridge and the tail) is the roof angle: atan(pitch ÷ 12). A 6/12 roof is 26.6°. On a framing square, hold 12 on the body and the pitch number on the tongue and mark along the tongue.
How deep can a birdsmouth be?
A common rule of thumb is to keep the seat notch to no more than 1/3 of the rafter depth so enough wood is left above the wall. The calculator warns you when the seat cut goes past that.
How long is a hip rafter?
On a roof with the same pitch on both sides, the hip run is the common run × √2 (1.414), and the hip rises the same amount. That makes the hip pitch the common pitch over 17 instead of over 12.