Birdsmouth Cut Calculator
Birdsmouth (seat) cut dimensions for a rafter at a given pitch.
Result appears here
Fill in the fields and press Calculate.
Formula, calculation, assumptions and sources
Slope factor = √(pitch² + 12²) ÷ 12
Heel height = seat length × (pitch ÷ 12)
Depth removed (⊥ to rafter) = heel height ÷ slope factor
Remaining depth = rafter depth − depth removed; keep depth removed ≤ 1/3 (IRC: 1/4) of rafter depth
Run the calculation to see each step with your own numbers.
6-in-12 pitch, 3.5 in seat (2x4 wall), 2x8 rafter (7.25 in deep).
Slope factor = 1.1180
Heel height = 3.5 × 6/12 = 1.75 in
Depth removed ⊥ = 1.75 ÷ 1.118 = 1.57 in → 21.6% of 7.25 in (within the 1/4 limit)
Remaining depth = 7.25 − 1.57 = 5.68 in
- Common rafter, plumb/seat birdsmouth bearing on a level top plate.
- IRC R802.7.1 limits the notch to 1/4 of the rafter depth at the end; check your local code — some jurisdictions and many framers use 1/3. The calculator reports the depth removed so you can check either limit.
- Seat length is normally the full bearing width of the wall plate so the rafter is fully supported.
- Structural adequacy of the rafter itself is a separate check (span tables / engineer).
- How deep can a birdsmouth be?
- The IRC limits the notch at the end of a rafter to one-quarter of the rafter's depth. Cutting deeper removes too much of the rafter over the bearing point and weakens it. If the notch comes out too deep, use a smaller seat cut or a raised heel / structural ridge detail.
- What seat length should I use?
- The full bearing width of the wall plate, so the rafter is fully supported — 3.5 in on a 2x4 wall, 5.5 in on a 2x6. A longer seat on a steep pitch cuts a deeper notch, which is what the depth check is for.
- The notch came out too deep — what now?
- Use a shorter seat cut, move to a deeper rafter, or switch to a raised-heel or structural-ridge detail so the rafter bears without a deep notch over the plate.
Birdsmouth geometry
Right-triangle layout: heel height = seat run × slope (rise/run). Standard roof-framing practice; notch depth limit per IRC R802.7.1 (1/4 depth at the end).
About the Birdsmouth Cut Calculator
The Birdsmouth Cut Calculator lays out the seat (bearing) cut where a rafter sits on the wall plate: it returns the heel height, the depth removed from the rafter, and the depth remaining above the notch, then checks that against the IRC limit of one-quarter of the rafter depth (many framers hold to one-third). Enter the pitch, the seat length — normally the full width of the top plate — and the actual rafter depth.
What you enter
- Roof pitch (rise-in-12) — Rise per 12 of run.
- Seat cut length (bearing on the plate) — The horizontal cut. Usually the full top-plate width — 3.5 in for a 2x4 wall, 5.5 in for 2x6.
- Rafter depth (actual) — Actual depth: 2x6 = 5.5 in, 2x8 = 7.25 in, 2x10 = 9.25 in, 2x12 = 11.25 in. (Default 7.25 in = a 2x8.)
What you get back
- Heel (plumb) cut height — Vertical height of the plumb cut at the outside face of the wall = seat length × (pitch ÷ 12).
- Rafter depth remaining above the notch — the exact result of the calculation.
- Max seat length for the 1/3 rule — The notch (heel height) may not exceed 1/4 of the rafter depth for a nominal-depth rafter per IRC R802.7.1 — many framers use 1/3. This is the seat length that puts the heel at 1/3 depth.
- Plumb-line depth lost to the notch — the exact result of the calculation.
The formula, a worked example, the assumptions behind it and the sources are shown in full below the calculator.
Related calculators
- Rafter Length Calculator — Common rafter length from the building span and roof pitch.
- Roof Pitch Calculator — Roof angle, slope factor and rise-in-12 pitch from a rise and run.
- Framing Calculator — Stud count and lineal feet for a wall at a given stud spacing.
Part of the Roofing calculators.