Birdsmouth Cut Calculator
Birdsmouth measurement sheet
Lay out a common-rafter notch from a seat length, target HAP or perpendicular cut depth. Use the actual dressed timber size.
1.75 in vertical heel · 6.3557 in HAP
21.59% of the board depth removed; 5.6848 in remains perpendicular to the edges.
Full-width bearing on the plate.
Geometry only. Strength, connections and local-code approval require separate checks.
Decimals or fractions are accepted: 3.5, 3 1/2 or 7/2. Results update as you edit.
Read the cut in the right direction
Seat length 3.5 in
Cut detail; the upper board edge can lie outside this view.
Ochre: rafter · Coral: removed triangle · Teal: plate and seat. The highlighted line shows the selected measurement. The drawing is not a full-size cutting template.
| Measure | Decimal / nearest 1/32 in |
|---|---|
| Horizontal seat | 3.5 in≈ 3 1/2 in |
| Vertical heel | 1.75 in≈ 1 3/4 in |
| HAP · vertical | 6.3557 in≈ 6 11/32 in |
| Notch · perpendicular | 1.5652 in≈ 1 9/16 in |
| Remaining · perpendicular | 5.6848 in≈ 5 11/16 in |
| Seat endpoints along lower edge | 3.9131 in≈ 3 29/32 in |
| Actual bearing | 3.5 in≈ 3 1/2 in |
Fractional inches are rounded to the nearest 1/32; decimal displays are rounded too. They are not a cutting tolerance: compare limits with the unrounded geometry and trial-fit one rafter before marking a batch.
Roof / seat line to board edge: 26.565°. Plumb line to board edge: 63.435°. These are line angles, not a universal saw setting.
Check your chosen dimensional limits
Within selected 25% notch screen. Meets selected 1.5 in bearing minimum.
Seat interval for these two screens, within this plate: 1.5 in to 3.5 in.
Starting screens: ¼-depth end notch and 1½-in wood/metal bearing (2025 New York reference). They do not check loads, notch position, cantilever provisions or local adoption.
Try a complete layout
Formulas and measurement directions
Let θ be the roof angle, d the actual stock depth perpendicular to its edges, and s the horizontal seat length. Then:
- Vertical heel = s × tan θ.
- Perpendicular notch depth = s × sin θ.
- HAP = d / cos θ − s × tan θ.
- Remaining perpendicular depth = d − s × sin θ = HAP × cos θ.
- From target HAP h: s = (d − h × cos θ) / sin θ.
- From perpendicular notch n: s = n / sin θ.
HAP and heel are vertical; board depth and removed depth are perpendicular. Comparing heel directly with board depth mixes directions and overstates the fraction removed. A double top plate is taller, not wider.
Scope, reference limits and next steps
This is the geometry of a horizontal seat and vertical heel in one straight, sawn common rafter. It does not design hips, valleys, trusses, I-joists, engineered timber, structural connections or a raised-heel assembly. Do not alter an engineered product without the required manufacturer or engineer design.
The 2025 Residential Code of New York State, R502.8.1, gives end-notch depth and other notch-position limits; R802.6 distinguishes bearing on wood/metal from masonry/concrete. R802.7.1.1 and its figure (printed page 428) add specific cantilever conditions. The drawing measures stock and notch depth perpendicular to the rafter. A universal “one third is safe” statement is not used here. New York adoption notice; this is a jurisdictional reference, not proof that it is the rule adopted where you build.
A seat longer than its plate does not gain that extra bearing. A shorter seat leaves part of the plate uncovered; whether its bearing, notch location and load path are acceptable requires the project design. The two numerical screens above cannot answer those questions.
For span, ridge deduction and tail line geometry, use the common-rafter length calculator. Line length is not a finished cutting length. Make a trial fit and confirm the adopted requirements before cutting the full batch.
Your dimensions stay in this browser as a local draft. They are not placed in a shared URL or sent as calculator analytics.
Lay out a common-rafter birdsmouth from seat length, target HAP or notch depth. See true perpendicular removal, plate bearing, angles and a printable measurement sheet.
