How this birdsmouth calculator works
The birdsmouth is a right triangle: a level seat cut the width of the plate, and a plumb heel cut whose height comes straight from the pitch:
HAP = rafter depth ÷ cos(angle) − heel cut
At the defaults — a 6/12 pitch, a 3.5 in seat, a 2×8 rafter — that is a 1.75 in heel cut at a 26.6° plumb angle, a height above plate of 6.36 in, and a notch of 1.57 in — within the quarter-rafter rule. The full chain is in the worked example. Cut one, check it, and repeat it on every common rafter.
The parts of a birdsmouth
Three cuts and one number describe the whole notch — get them straight and every rafter matches:
- Seat cut: the level cut that bears on the top plate — as wide as the plate, 3.5 in on a 2×4 wall.
- Heel / plumb cut: the vertical cut against the wall face — its height is seat × pitch ÷ 12.
- Height above plate (HAP): the rafter left above the seat, plumb — it sets the ridge height.
- Plumb angle: atan(pitch ÷ 12), the same angle as the ridge and tail cuts — roof pitch calculator.
- The run: where the seat lands along the rafter — measured from the rafter length.
Marking and cutting the seat
The birdsmouth is a layout job before it is a saw job — the marks are what make it fit:
- Mark the plumb line with the pitch on a framing square — rise on the tongue, 12 on the blade.
- Mark the seat square to it at the plate depth, meeting at the inner corner.
- Don’t overcut: stop each cut at the inner corner — running past it weakens the rafter.
- Keep the notch shallow: under about a quarter of the rafter depth leaves enough over the plate.
- Repeat, don’t re-measure: use the first good rafter as the pattern for the rest.
Cuts by pitch, and HAP by rafter
Table 1 runs the heel cut and HAP by pitch for a 2×8 on a 3.5 in seat; Table 2 is HAP by rafter size at 6/12.
| Pitch | Heel | HAP |
|---|---|---|
| 4/12 | 1.17 in | 6.48 in |
| 6/12 | 1.75 in | 6.36 in |
| 8/12 | 2.33 in | 6.38 in |
| 10/12 | 2.92 in | 6.52 in |
| 12/12 | 3.50 in | 6.75 in |
| Rafter | HAP |
|---|---|
| 2×6 | 4.40 in |
| 2×8 | 6.36 in |
| 2×10 | 8.59 in |
| 2×12 | 10.83 in |
How to lay out a birdsmouth
- Set the pitch — rise per 12 — which fixes the plumb angle and the heel height.
- Set the seat depth to the plate width — 3.5 in for a 2×4 wall, 5.5 in for a 2×6.
- Pick the rafter size so the notch stays within about a quarter of its depth.
- Read the heel cut, HAP and angle, and mark them with a framing square.
- Cut one and test-fit, then use it as the pattern for the rest.
Worked example: a 2×8 rafter at 6/12
The default, worked line by line — a 6/12 pitch, a 3.5 in seat, a 2×8 rafter (7.25 in deep):
heel cut = 3.5 × 6 ÷ 12 = 1.75 in
HAP = 7.25 ÷ cos 26.6° − 1.75 = 8.11 − 1.75 = 6.36 in
notch = 3.5 × sin 26.6° = 1.57 in ≤ 1.81 (¼ × 7.25) ✓
Keep the same seat and rafter but steepen the pitch to 12/12 and the heel cut doubles to 3.5 in — half the rafter — while the notch grows to 2.48 in, past the quarter-rafter line for a 2×8. That is the moment to step to a 2×10 or reduce the seat, because a deep notch on a steep roof is exactly where rafters split at the plate.
What this birdsmouth layout doesn’t cover
It gives the notch geometry; the rest of the rafter is its own layout:
- Rafter length. The overall cut length and tail — on the rafter length calculator.
- Ridge and tail cuts. The plumb cut at the ridge and the tail/overhang cuts.
- Structural sizing. Whether the rafter spans the load — an engineer or a span table.
- Connectors. Hurricane ties and the nailing that holds the rafter to the plate.
- Ridge-board thickness. Half the ridge is deducted from the run before the seat is located.
Birdsmouth FAQ
What is a birdsmouth cut?
A birdsmouth (bird’s mouth) is the notch cut near the lower end of a rafter so it seats flat on the top plate. It is a right-angle notch with two cuts: a horizontal seat cut that bears on the plate, and a vertical plumb (heel) cut against the outside of the wall. The two together let a sloped rafter sit solidly on a level wall.
How do you calculate a birdsmouth?
The heel (plumb) cut height equals the seat depth times the pitch ratio: seat × rise ÷ 12. At a 3.5 in seat and a 6/12 pitch that is 3.5 × 0.5 = 1.75 in. The cut angle is the plumb-cut angle, atan(pitch ÷ 12) — 26.6° at 6/12 — which is the same angle you use for the ridge and tail cuts.
How deep should a birdsmouth be?
The seat should be as deep as the plate is wide for full bearing — 3.5 in on a 2×4 wall, 5.5 in on a 2×6 — and no deeper. A common rule of thumb keeps the notch within about a quarter of the rafter depth so enough rafter is left above the seat; the calculator flags when a steep pitch pushes the notch past that.
What is HAP (height above plate)?
HAP is the height of the rafter left above the seat cut, measured plumb — 6.36 in for a 2×8 at 6/12 with a 3.5 in seat. It matters because HAP is what sets the ridge height, and it is the same on every common rafter, so cutting one birdsmouth correctly and repeating it lands the whole ridge level.
How do I cut a birdsmouth with a framing square?
Mark the plumb line at the seat location using the pitch on the square (rise on the tongue, 12 on the blade), then mark the seat line square to it at the plate depth. Cut both to the inside corner and stop — overcutting past the corner weakens the rafter. A circular saw finishes to the line and a handsaw cleans the corner.
Can a birdsmouth be too big?
Yes. If the notch removes more than about a quarter of the rafter depth, too little wood is left over the plate and the rafter can split or crush. A steep pitch on a shallow rafter is where this bites — a 12/12 cut on a 2×6 over-notches. The fix is a deeper rafter or a structural connector instead of a deep seat.
Where does the seat cut go on the rafter?
The seat sits on the top plate at the outside wall, with the plumb (heel) cut flush to the wall’s outer face. The rafter tail runs past it to form the overhang. Locate the seat by measuring the run from the ridge; the birdsmouth is what fixes that run in place, so mark it carefully off the rafter length.
Sources and standards
The geometry is exact; the notch limit is good practice:
- Rafter trigonometry: heel = seat × rise ÷ 12; angle = atan(rise ÷ 12); HAP = depth ÷ cos(angle) − heel.
- Full bearing: the seat is as wide as the plate — 3.5 in on a 2×4, 5.5 in on a 2×6 wall.
- Notch rule of thumb: keep the birdsmouth within about a quarter of the rafter depth.
- The design governs: rafter size and connections are a span-table or engineer’s call.
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