The two cuts, and the angle behind them
A birdsmouth is a plumb cut (the vertical face, set to the roof pitch) meeting a seat cut (the horizontal face that sits on the wall plate). The plumb cut's angle is just the arctangent of the pitch. The seat cut is its complement, so the two always sum to 90 degrees.
Angles by pitch
| Pitch | Plumb cut | Seat cut |
|---|---|---|
| 2:12 | 9.46° | 80.54° |
| 3:12 | 14.04° | 75.96° |
| 4:12 | 18.43° | 71.57° |
| 5:12 | 22.62° | 67.38° |
| 6:12 | 26.57° | 63.43° |
| 8:12 | 33.69° | 56.31° |
| 10:12 | 39.81° | 50.19° |
| 12:12 | 45.00° | 45.00° |
At 12:12 the roof rises as fast as it runs, so both cuts land at 45 degrees.
The seat cut cannot pass one third of the rafter
The seat cut removes material from the bottom of the rafter, and that is where its strength lives. Codes cap the depth at one third of the rafter's depth. On a 2×8 (7.25 in deep) that limit is about 2.4 inches.
The seat cut may take at most the shaded third. Anything deeper leaves too little rafter to carry the load safely.
Getting the layout right
- Seat length rests on the plate. Size the seat cut so its horizontal face fully bears on the top plate — a common plate is 3.5 inches wide, and full contact spreads the load.
- Hip and valley rafters. Because of the compound angle, reduce the notch depth further (roughly 25%) versus a common rafter.
- Cut clean, seal it. Gaps let water in; an unsealed notch can rot within a few years in a damp attic. Treat the cut before you set the rafter.
Common questions
What is the difference between the plumb cut and the seat cut?
The plumb cut is the vertical face, angled to match the roof pitch. The seat cut is the horizontal face that actually rests on the top plate. Together they form the notch shaped like a bird's mouth.
Why can the birdsmouth not be deeper than a third of the rafter?
The rafter carries load like a beam. Cutting more than one third of its depth removes too much material and can drop its strength sharply, risking cracking or buckling. Building codes cap the seat cut at about one third of the rafter depth for that reason.
How do I turn a roof pitch into an angle?
Take the arctangent of the pitch divided by 12. A 6:12 pitch is arctan(6 divided by 12), which is 26.57 degrees. That angle is the plumb cut; the seat cut is 90 degrees minus it.
