How this instrument works
A birdsmouth cut is a notch cut into the underside of a rafter where it crosses and rests on a wall's top plate — a seat cut that sits level on the plate, paired with a heel cut that runs plumb alongside the wall face, together forming the beak-like shape that gives the joint its name. The seat cut depth, how much material is removed from the rafter at that notch, follows directly from the rafter's width and the roof's pitch angle: seat depth = rafter width x sin(pitch angle).
The trig behind it is straightforward: as a rafter runs up a roof at some pitch angle, the vertical drop from the rafter's top edge down to where a level seat cut would sit is exactly the rafter's width times the sine of that pitch angle. A steeper roof pitch angle means a deeper notch relative to the same rafter width, since a steeper rafter needs to give up more of its depth to sit flat on a level plate.
Framing carpentry limits how deep that notch can safely go — removing too much of a rafter's cross-section at the birdsmouth weakens it right where the load transfers down into the wall. A widely used rule of thumb caps the notch at no more than roughly one third of the rafter's total depth, and the steeper the pitch, the more likely a wide rafter is needed simply to keep the seat cut within that limit.
This calculation gives the geometric seat depth from pure trigonometry; it does not check that depth against a rafter's structural capacity or a building code's notching limits. Always verify the resulting cut against the applicable framing code and, for anything beyond a straightforward gable roof, a span table or engineer's specification before cutting stock.
- Enter the rafter's dimensional width into Rafter width (in) — the full depth of the rafter stock, such as 8 for a nominal 2x8.
- Enter the roof's slope into Roof pitch angle (degrees) — convert a rise-over-run pitch to degrees first if that's how your plans specify it.
- Read Birdsmouth seat cut depth (in) beneath the inputs — how deep the seat cut notch should run into the rafter's underside.
- Pitch angle accepts 0 to 90 degrees; entering a value outside that range triggers a prompt, since a roof pitch can't be steeper than a vertical wall.
Worked example — 8 in rafter at a 30-degree pitch
Enter 8 into Rafter width (in) and 30 into Roof pitch angle (degrees). The instrument multiplies 8 by sin(30°), and since sin(30°) = 0.5 exactly, Birdsmouth seat cut depth (in) reads 4.0 in — the notch removes exactly half the rafter's width.
That 4.0 in notch on an 8 in rafter removes half the rafter's total depth, well beyond the roughly one-third-depth rule of thumb many framers use — a real-world flag to double-check the pitch, rafter size, or engineering spec before cutting, since this instrument reports the trig result only, not a structural pass or fail.
Questions
What is a birdsmouth cut?
It's a notch cut into the underside of a rafter, near where the rafter crosses a wall's top plate, so the rafter sits flat and level on the plate instead of resting only on its sloped bottom edge. The notch is made from two cuts — a seat cut that lies flat on the plate, and a heel (plumb) cut that runs vertically alongside the outside wall face — together forming the beak-shaped notch the joint is named for.
Why does a steeper pitch produce a deeper seat cut?
Because seat depth equals rafter width times the sine of the pitch angle, and sine grows as the angle grows, all the way up toward 1 at 90 degrees. A steeply pitched rafter has to give up more of its own depth to sit level on a horizontal plate than a shallow, gently sloped rafter of the identical width does — the notch is doing more work to level out a bigger angle.
Is there a limit to how deep a birdsmouth notch can go?
Yes — cutting too deep weakens the rafter right at the point where roof load transfers into the wall. A commonly cited rule of thumb keeps the notch to no more than roughly one third of the rafter's total depth, though the actual limit depends on the rafter's species, grade, span, and load, so it should be checked against the applicable building code or an engineer's span table rather than assumed.
What happens at a 90-degree pitch angle?
The seat depth equals the full rafter width, since sin(90°) = 1 exactly — the instrument accepts this as a valid boundary case, though a true 90-degree 'roof' is a vertical wall, not a pitched roof, so this edge case mostly serves as a sanity check on the formula rather than a real framing condition.
My plans give pitch as rise-over-run, not degrees — what do I enter?
Convert it to degrees first: pitch angle in degrees equals the arctangent of rise divided by run. A common 6-in-12 roof pitch, for example, works out to arctan(6/12), or about 26.57 degrees — enter that converted figure into Roof pitch angle (degrees), since this instrument expects degrees rather than a rise-over-run ratio directly.
Does this calculator check whether the notch is structurally safe?
No — it returns the geometric seat depth from rafter width and pitch angle only, a pure trigonometry result. It does not evaluate the notch against a rafter's load capacity, species and grade, or a building code's maximum-notch rule, so always verify the computed depth against the framing code and span tables that apply to the actual roof before cutting.