Roofs and rafters
Rafter length calculator: ridge, overhang and birdsmouth cut
A rafter you can cut needs more than the slope length: the ridge board takes a little off the top, the overhang adds a tail at the bottom, and the birdsmouth notch sits it on the wall. Here is each step for a 24 ft wide gable roof at 6/12.
Start with the run and the slope factor
The run of a common rafter on a simple gable roof is half the span, measured from the outside of one wall to the outside of the other. The slope factor for the pitch, √(1 + (pitch ÷ 12)²), turns that level run into a length along the rafter.
Example. Span 24 ft, so the run is 12 ft (144 in). At 6/12 the slope factor is 1.118, and the rafter from the outside of the wall to the center of the ridge is 144 × 1.118 = 161.0 in, or 13 ft 5 in.
How high is the ridge?
The rafter's measuring line climbs the pitch for every foot of run: 6 in × 12 ft = 72 in, so it meets the center of the ridge 6 ft above the top of the wall plate.
Take off half the ridge board
The rafters meet the face of the ridge board, not its center, so shorten each rafter by half the ridge thickness, measured level and turned into a length along the slope.
Example. A 1 1/2 in ridge board: half is 3/4 in, and 0.75 × 1.118 = 0.84 in, about 13/16 in. The rafter to cut, without the tail, is 161.0 − 0.84 = 160.16 in, or 13 ft 4 3/16 in.
Add the tail for the overhang
An overhang measured level from the outside of the wall becomes a tail along the rafter of overhang × slope factor.
Example. A 12 in overhang adds 12 × 1.118 = 13.42 in, about 13 7/16 in. The rafter with its tail is 173.57 in, or 14 ft 5 9/16 in, before any fascia cut.
What are the plumb and seat cut angles?
The plumb cut at the ridge is arctan(pitch ÷ 12) from square: 26.57° for 6/12. The level (seat) cut is the rest of the right angle, 90 − 26.57 = 63.43°.
How deep should a birdsmouth cut be?
The birdsmouth is the notch that sits the rafter on the wall plate: a plumb cut, the heel, and a level cut, the seat. A common rule of thumb, and the one Clad uses, keeps the heel to no more than a third of the rafter's width. The seat length then follows from the pitch: seat = heel × 12 ÷ pitch. Your code or an engineer may ask for something else.
Example. A 2x6 rafter is 5 1/2 in wide. A third of that is 1.83 in, about 1 13/16 in for the heel. At 6/12 the seat is 1.83 × 12 ÷ 6 = 3.67 in, about 3 11/16 in, a little more than the 3 1/2 in top of a 2x4 wall.
Check it with a framing square
Step the rafter off with a framing square at 6 and 12 or measure the line length with a tape: the two should agree to within a mark. If they do not, look for a run measured to the wrong face of the wall.
Rafters in Clad
Clad's gable roof tool takes the span, the pitch, the overhang, the ridge thickness and the rafter width, and gives the run, the ridge height, the take-off for the ridge, the rafter to cut with and without the tail, both cut angles and the birdsmouth heel and seat. The rafters tool also does hip, valley and jack rafters.