Pitch & Span

Birdsmouth Cut Calculator

This calculator finds the seat cut length, heel plumb depth, and remaining rafter material (HAP) for a birdsmouth notch, using seatCut = plateWidth and heelPlumb = plateWidth × pitch ÷ 12 — and checks the result against the trade's 1/3-of-rafter-depth limit automatically.

History

Saved

    No saved results yet. Use "Save this result" to pin one.

    Recent

      No recent results yet. Copy or print a result to see it here.

      Birdsmouth Cut Calculator

      This calculator finds the seat cut length, heel plumb depth, and remaining rafter material (HAP) for a birdsmouth notch, using seatCut = plateWidth and heelPlumb = plateWidth × pitch ÷ 12 — and checks the result against the trade's 1/3-of-rafter-depth limit automatically.

      Scenario presets

      Rise in inches per 12" of run — the same pitch used to frame the rafter.

      Actual dressed depth of the rafter stock.

      Actual width of the wall's top plate the rafter bears on.

      Roof rafter profile diagram Live-updating roof profile showing run, rise, rafter length, and cut angles.
      HAP (material above notch) 4.4"
      Seat cut length
      3.5"
      Heel plumb depth
      1.75"
      Notch depth as % of rafter
      31.8%

      How it works

      A birdsmouth is a two-cut notch: a horizontal seat cut that rests flat on the top plate, and a vertical heel (plumb) cut that meets it at the "heel" — the deepest point of the notch.

      seatCut = plateWidth · heelPlumb = plateWidth × pitch ÷ 12 · HAP = (rafterDepth × slopeFactor) − heelPlumb

      • Seat cut — the horizontal cut length, equal to the plate width so the rafter bears on the full plate.
      • Heel plumb — the vertical depth of the notch's inner cut, driven by pitch and plate width.
      • HAP — Heel Amount Plumb, the solid rafter material remaining above the notch, measured along the plumb line.
      • The 1/3 rule — heel plumb depth should not exceed one-third of the rafter's total depth. This calculator checks it on every keystroke and flags the result if it's exceeded.

      Worked example

      A 2x6 rafter (5.5" actual depth) bears on a standard 2x4 wall (3.5" plate width) at a 6/12 pitch.

      Seat cut. = plateWidth = 3.5".

      Heel plumb. = 3.5 × 6 ÷ 12 = 1.75".

      HAP. = (5.5 × 1.118) − 1.75 = 6.149 − 1.75 = 4.40" of solid rafter remaining above the notch.

      Check against the 1/3 rule. 1.75" heel plumb ÷ 5.5" rafter depth = 31.8% — under the 33.3% limit, so this notch is fine as designed.

      Now compare a 2x4 rafter (3.5" depth) at 12/12 pitch on the same 3.5" plate: heel plumb = 3.5 × 12 ÷ 12 = 3.5", which is 100% of the rafter's depth — the calculator flags this immediately as exceeding the 1/3 rule, since there would be no rafter material left at the bearing point at all.

      Tips from the field

      • Cut one test rafter and check its fit on the wall before notching the full run.
      • If the notch flags as too deep, stepping up one rafter size (say 2x6 to 2x8) almost always solves it without changing the plate or pitch.
      • Mark the seat cut and heel plumb with a speed square set to your roof's pitch, not a generic angle — small angle errors compound at the bearing point.
      • Double-check actual plate width in hand — a doubled top plate is thicker (taller) but the same width as a single plate.

      What this tool does not do

      • Does not calculate rafter length or cut angles — use the Rafter Length Calculator for those.
      • Does not size the rafter for structural load — use the Joist Span Calculator or a local engineer.
      • Does not model raised-heel (energy heel) framing, which changes the bearing detail beyond a standard notch.

      For rafter length and the plumb/seat cut angles this notch pairs with, see the Rafter Length Calculator.

      Did this calculator help you?

      Frequently asked questions

      These are the questions that come up right before the saw touches the rafter — how deep to cut, what the trade's hard limit is, and why it matters.

      What is a birdsmouth cut?

      It is a notch cut into the underside of a rafter where it crosses the top plate, made of two cuts: a horizontal seat cut (resting on the plate) and a vertical heel (plumb) cut. It lets the rafter sit flush and level on the wall.

      Why can't the notch be as deep as I want?

      Cutting too deep removes too much of the rafter's structural cross-section right at its most stressed point — where it bears on the wall. The trade's rule of thumb, reflected in most engineering guidance, caps the notch at one-third of the rafter's depth.

      What happens if I exceed the 1/3 rule?

      The rafter is weakened at the bearing point and may not carry its design load safely. This calculator flags the notch in red and recommends stepping up to a deeper rafter or a narrower plate instead of cutting deeper.

      What is "HAP" and why does it matter?

      HAP (Heel Amount Plumb) is the rafter material remaining above the notch, measured along the plumb line. A larger HAP means more solid wood is left to carry the load past the bearing point — it is effectively the inverse of how deep you cut.

      Why does the seat cut length equal the plate width?

      The seat cut needs to rest flat on the full width of the top plate for even bearing — cutting it shorter than the plate width would leave the rafter unsupported on part of the plate; cutting it longer serves no purpose.

      Does a steeper pitch make the notch deeper for the same plate width?

      Yes — heel plumb depth scales directly with pitch (heelPlumb = plateWidth × pitch/12). A steep roof on a narrow plate is more likely to trip the 1/3 rule than a shallow roof on the same plate.

      What is the difference between rafter depth and plate width?

      Rafter depth is the actual dressed height of the rafter stock (5.5" for a 2x6, for example) — it is what the 1/3 rule is measured against. Plate width is the actual width of the top plate the rafter rests on, which drives how deep the notch has to be.

      Should I use a doubled top plate's width or a single plate's width?

      Use the width of whichever plate the rafter actually sits on — a doubled top plate is still the same width as a single one (2x4 = 3.5" either way); doubling adds height, not width, so it does not change this calculation.

      How do I fix a birdsmouth that exceeds the 1/3 rule?

      Switch to a deeper rafter (the most common fix), use a narrower top plate if your wall framing allows it, or in some cases use a raised-heel design that avoids notching the rafter's full depth at the bearing point.

      Does this calculator account for a raised heel (energy heel) truss or rafter?

      No — it calculates a standard birdsmouth notch. A raised-heel design changes the bearing detail specifically to add attic insulation clearance and needs separate, engineered framing details beyond this calculator's scope.

      Is the 1/3 rule an actual building code requirement?

      It is a widely applied framing rule of thumb rather than a single, universally cited code section — some jurisdictions and engineers apply stricter limits for high-load or long-span rafters. When in doubt, check with a local building official or engineer, especially for anything beyond a standard residential rafter.

      How we checked this page

      Written by
      Pitch & Span Editorial
      Reviewed by
      Formulas checked against standard birdsmouth-notch geometry; the 1/3-of-rafter-depth limit reflects widely applied trade practice rather than a single cited code section — see the FAQ for that distinction.
      Last reviewed
      2026-07-28
      Publisher
      Pitch & Span
      Scope
      Birdsmouth notch geometry for common rafters
      What we checked
      • Worked example (2x6 rafter, 3.5" plate, 6/12 pitch) verified against the live calculator.
      • A shallow-rafter, steep-pitch case confirmed to trigger the 1/3-rule warning correctly.
      • Seat cut confirmed to equal plate width exactly across all tested inputs.

      Methodology

      Cite this calculator

      Pitch & Span. "Birdsmouth Cut Calculator." Pitch & Span, https://pitchandspan.com/birdsmouth-cut-calculator/. Accessed .

      Related tools

      Comments and suggestions

      Found a bug, have a suggestion, or just want to say hi? Post it below.