Birdsmouth cut calculator
The birdsmouth for a common rafter: the seat cut, the plumb cut, and the HAP, from your pitch, rafter depth, and wall plate. It flags the pitch where the notch gets too deep to leave a sound rafter. Same math the CutOnce app runs on the jobsite.
Updated
A 2x8 rafter is 7-1/4 in deep; a 2x4 wall plate is 3-1/2 in wide. Type depths the way your tape reads.
- Seat cut (along the plate)
- 3-1/2 in
- Plumb cut (down the seat)
- 1-3/4 in
- HAP (height above plate)
- 6-3/8 in
- Roof angle
- 26.57°
What a birdsmouth is
A birdsmouth is the L-shaped notch cut into a rafter where it crosses the wall plate, so the rafter sits flat on the wall instead of on a point. It has two cuts: the seat cut, which lies flat on top of the plate and is as wide as the plate, and the plumb cut, which runs down vertically against the outside of the plate. On a 6/12 with a 2x8 rafter and a 3-1/2 in plate, the seat is 3-1/2 in and the plumb cut is 1-3/4 in.
A worked 6/12 example
A 2x8 rafter (7-1/4 in deep) on a 3-1/2 in wall plate at 6/12. Every value is computed by the same function that drives the calculator above.
| Roof angle | 26.57° |
| Seat cut (along plate) | 3-1/2 in |
| Plumb cut (down the seat) | 1-3/4 in |
| HAP (height above plate) | 6-3/8 in |
How the cuts are figured
- 01
Seat cut is the plate width
The seat sits flat on the plate and runs its full width, so on a 2x4 wall the seat cut is 3-1/2 in. Cut it any wider and the rafter loses bearing past the plate; any narrower and it does not sit flat.
- 02
Plumb cut comes from the angle
The plumb cut is the seat width times the tangent of the roof angle. At 6/12 the angle is 26.57 degrees, so a 3-1/2 in seat gives a 1-3/4 in plumb cut. Steeper pitch, deeper plumb cut.
- 03
HAP is what is left above the notch
Height above plate is the rafter's plumb depth, the stock depth divided by the cosine of the roof angle, minus the plumb cut. That is why a 7-1/4 in rafter at 6/12 leaves about 6-3/8 in of HAP, not 5-1/2 in: the depth is measured down a plumb line, not square across the board. It is the number that has to match on every common rafter, because that is what holds the ridge at one height. If the HAP varies, the ridge waves.
When the notch is too deep
There is a limit built into the geometry: the plumb cut should stay well shy of the full rafter depth. When it reaches the depth of the stock, on a steep pitch with a shallow rafter, the notch is far too deep to leave a sound rafter, and the calculator flags it. Well before that point, keep enough material above the notch to carry the load, and give the seat real bearing on the plate, typically at least 1-1/2 in. Rafter sizing and notching allowances are a code question, so confirm against the code your jurisdiction adopts.
The app marks the too-deep case when it prints a cut plan, and sizes the ridge to the rafter's plumb-cut depth.
Common questions
- How deep should a birdsmouth be?
- Deep enough for the seat to bear flat on the plate, no deeper. The seat cut equals the plate width, 3-1/2 in on a 2x4 wall, and the plumb cut follows from the pitch. The one hard limit is that the plumb cut should stay well shy of the full stock depth; the calculator warns you when it reaches it.
- What is HAP on a rafter?
- Height above plate: the rafter depth left above the birdsmouth seat, measured down a plumb line. It works out to the stock depth divided by the cosine of the roof angle, minus the plumb cut. Every common rafter on the roof needs the same HAP, because that is what sets the ridge to a consistent height.
- Does a steeper roof need a deeper birdsmouth?
- The plumb cut gets deeper, yes, because it is the seat width times the tangent of the angle. On a 12/12 a 3-1/2 in seat gives a 3-1/2 in plumb cut, so a shallow rafter can run out of depth. The calculator warns you before it does.
- Is the birdsmouth the same on a hip or valley rafter?
- No. Hips and valleys run at a shallower effective angle and need their own seat and plumb cuts, plus backing and drop. This page is for common rafters; the app's hip and valley calculator handles the rest.
Mark the notch on the board
The app draws the birdsmouth dimensioned on the rafter, checks the too-deep case, and prints a plan with the seat, plumb cut, and HAP called out.
See also