Birdsmouth Cut Calculator
Find the seat cut depth for a birdsmouth notch, from the roof pitch and rafter width.
Reviewed by the ToolNestr Editorial Team — July 2026
How the birdsmouth cut calculator works
A birdsmouth is the notch cut into a rafter where it crosses the wall's top plate, made of two cuts meeting at a right angle: a level seat cut that lies flat across the plate, and a plumb heel cut that runs vertically down from the rafter's outer edge to meet it. Together they let an angled rafter bear flat and square on a level wall, instead of resting on just the sharp edge of its bottom face.
The seat cut's depth — measured straight down into the rafter — is found from simple trigonometry: it equals the plate's width times the sine of the roof pitch angle. A steeper roof pitch means the rafter crosses the plate at a sharper angle, so the seat cut has to reach deeper into the rafter to lie flat across the same plate width.
Cutting too deep weakens the rafter right at its bearing point, the spot carrying the roof's full load down to the wall. A widely used guideline caps the seat cut at no more than about one-third of the rafter's total depth, so this calculator checks the computed seat cut against that one-third limit and flags if a deeper rafter is needed. This is a general framing guideline, not a substitute for your local building code's specific rafter and notching requirements.
The one-third rafter-depth notching limit follows conventional framing guidance referenced in the IRC (International Residential Code).
Enter the pitch
Rise per 12 inches of run.
Set the plate width
Usually 3.5 in for a 2× wall plate.
Check against limit
Verify the cut stays under 1/3 rafter depth.
The formula explained
Pitch angle
= atan(rise ÷ 12). A 6/12 pitch: atan(6÷12) = 26.57°.
Seat cut depth
= plate width × sin(angle). A 3.5 in plate: 3.5 × sin(26.57°) = 1.57 in.
Max recommended
= rafter depth ÷ 3. A 9.25 in rafter: 9.25 ÷ 3 = 3.08 in max.
Worked example
A steep 10/12 pitch roof, 3.5 in plate, 2×8 (7.25 in) rafter.
Real-world context
A shallow 4/12 ranch-style roof, framed with 2×6 rafters (5.5 in) on a standard 3.5 in plate, produces an 18.4° pitch angle and a seat cut of just 1.11 in — well under the 1.83 in limit (5.5 ÷ 3). This is why low-slope roofs rarely run into birdsmouth depth problems even with modest rafter stock.
Push the pitch up to 8/12, a common suburban roof slope, and keep the same 2×6 rafter: the angle jumps to 33.7°, and the seat cut grows to 1.94 in — now slightly over the 1.83 in limit for that rafter depth. This is a realistic scenario where a framer would need to step up to a deeper 2×8 rafter (7.25 in, giving a 2.42 in limit) simply because the pitch got steeper, not because the span changed.
At the steep end, a 12/12 pitch bearing on a doubled 2×6 top plate (5.5 in combined width) with a 2×10 rafter (9.25 in) computes a 45° angle and a seat cut of 3.89 in against a 3.08 in limit — a clear fail. Steep roofs on wide plates are exactly the case where birdsmouth depth becomes a real structural constraint, sometimes pushing designers toward a shallower plate, an engineered rafter, or a plumb-cut heel design that doesn't rely on a deep seat notch at all.
Common misconceptions
"A deeper birdsmouth just means a stronger connection." Cutting deeper removes wood exactly where the load concentrates. The rafter's bearing point is already a stress concentration — notching past about a third of the rafter's depth removes so much cross-section that the rafter can fail there under load, even though the seat itself looks more "solidly seated."
"Seat cut depth only depends on the rafter size." It's actually driven by pitch and plate width, independent of rafter size. The seat cut formula (plate width × sine of the pitch angle) doesn't include rafter depth at all — rafter depth only sets the allowable maximum. A steep pitch on a wide plate can demand a deep seat cut even on a large rafter.
"Any framer can eyeball a birdsmouth on site." The angle and depth are precise geometry, not a guess. A seat cut that's a little shallow leaves the rafter resting on the plate's outer edge, concentrating load on a thin sliver of wood; a little too deep and it eats into the one-third structural limit — both errors are avoidable by working from the pitch angle and plate width rather than test-fitting by eye.
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Frequently asked questions
What is a birdsmouth cut?
A birdsmouth is a notch cut into the underside of a rafter where it crosses the top plate of a wall, made of two cuts — a level seat cut that rests flat on the plate, and a plumb heel cut perpendicular to it — so the rafter sits securely on the wall instead of just touching it at one edge.
How deep should a birdsmouth seat cut be?
A common guideline limits the seat cut depth to no more than one-third to one-quarter of the rafter's actual depth, to avoid removing so much wood that the rafter is structurally weakened at its bearing point. This calculator computes the seat cut based on the roof pitch and reports it against a conservative one-third-depth limit.
How is the seat cut depth calculated from pitch?
The seat cut depth (measured plumb, along the rafter's vertical face) equals the horizontal plate width times the sine of the roof's pitch angle. A steeper pitch increases how much the seat cut needs to angle into the rafter for a given plate bearing width.
Why does a birdsmouth matter structurally?
Without a proper seat cut, a rafter resting at an angle on a flat top plate only touches it along one sharp edge, concentrating the whole roof load onto a small area of wood and the plate. The birdsmouth spreads that bearing load across a flat seat, which is a safer, more stable connection.
Sources & references
This tool uses standard formulas and reference values from:
- • American Concrete Institute — ACI 318, Building Code Requirements for Structural Concrete. concrete.org
- • ICC — International Residential Code (IRC), span, footing and framing tables. codes.iccsafe.org
- • APA – The Engineered Wood Association, allowable span and load guidance.
Estimates for planning only. Span, load and code values vary by jurisdiction — verify against your local adopted code and a licensed engineer before building.