Article — Birdsmouth Cut Calculator
Birdsmouth Cut Calculator: Lay Out the Rafter Notch
The plumb-cut angle of a birdsmouth equals arctan(pitch/12). For a 6:12 roof: 26.57°. The seat-cut angle is the complement, 63.43°. With a 3.5-inch wall plate the plumb-cut depth into the rafter is 1.75 inches — and code keeps that within 1/3 of the rafter's depth.
A birdsmouth is the small two-face notch carpenters cut at the bottom edge of every roof rafter where it crosses a wall plate. Cut it right and the rafter sits flat, bears evenly, and transfers gravity load straight down through wood-on-wood compression. Cut it wrong and the rafter rocks, the eaves sag, or worse, the cut weakens the rafter at the highest-stress section.
What is a birdsmouth cut?
A birdsmouth is a two-cut notch in the underside of a rafter, shaped like an open bird's beak when viewed from the side. The two cuts are:
- Plumb cut: The vertical face. Tilted at the roof pitch angle. Bears against the outside of the wall plate.
- Seat cut: The horizontal face. Rests on top of the wall plate. Perpendicular to gravity.
- Inside corner: Always 90°. The two faces meet at a right angle.
- Heel: Where the plumb cut meets the lower edge of the rafter.
- Toe: Where the seat cut meets the lower edge of the rafter, on the building-interior side.
- Bearing line: The actual length of seat-to-rafter contact along the sloped rafter.
Birdsmouth cuts appear on every traditional rafter-cut roof from medieval Europe to current Habitat for Humanity builds. The geometry hasn't changed in 600 years — only the tools. Modern engineered roof trusses skip the birdsmouth entirely because they use metal plates and gusset connections instead.
The birdsmouth cut formula
The angles come directly from the roof pitch. Pitch is expressed as rise over a 12-inch run — a 6:12 roof rises 6 inches per foot of horizontal travel. The angles follow:
θ_plumb = arctan(pitch / 12) vertical face angleθ_seat = 90° − θ_plumb horizontal face angled_plumb = w_plate · tan(θ_plumb) plumb-cut depthL_bear = w_plate / cos(θ_plumb) bearing lengthThe seat-cut depth (vertical drop into the rafter) is a design choice, bounded by structural rules. The plumb-cut depth — how far up the rafter the vertical face climbs — follows from plate width and pitch.
Birdsmouth cut vs. rafter tail
Don't confuse the birdsmouth with the rafter tail. The birdsmouth is the notch over the wall plate; it transfers gravity load. The rafter tail is the portion of the rafter that extends beyond the wall to create the eave overhang. The tail can be cut to several profiles: plumb-cut (vertical face), level-cut (horizontal soffit), or square (perpendicular to rafter).
On a typical eave, you start with the birdsmouth (notch over the plate), then extend the rafter outward by the overhang length (typically 12-24 inches), and finally trim the tail to the chosen profile. The birdsmouth uses one set of angles; the tail-cut uses different angles depending on the eave style.
The 1/3 rule for birdsmouth depth
The seat-cut depth — how deep you notch into the rafter — is capped by structural rules. The IRC, USDA Wood Handbook, and most builder references all converge on the same limit: no more than one-third of the rafter's depth.
A 2x10 rafter has 9.25 inches of actual depth. Maximum seat-cut depth: 3.08 inches. Cutting deeper removes too much wood at the rafter's highest-stress section. The remaining 2/3 of depth must carry the entire bending moment of the loaded rafter, plus the bearing reaction from the wall plate below.
The structural logic: bending stress σ = M·c/I peaks at the extreme fiber, and removing material at the bottom of the rafter near the plate doesn't reduce bending capacity by much — but it does reduce shear capacity. For most residential rafters the 1/3 limit gives a 2× safety margin against shear failure at the notch.
Birdsmouth cut layout, step by step
Six steps with a speed square and a saw will give you a perfect birdsmouth every time:
- Mark the heel: measure along the bottom edge to the point where the plumb cut will start.
- Set the speed square's pivot at that point. Tilt until the pitch numbers align — "6" on the common scale for a 6:12 roof.
- Strike the plumb-cut line across the rafter's full depth (top edge to bottom).
- Measure the seat depth (typically 1.5-2 inches) down from the rafter's top edge along the plumb line.
- Set the square on that mark and strike a horizontal line back toward the heel — that's the seat cut.
- Cut the plumb line first (most carpenters use a circular saw), then the seat. Test-fit before nailing.
Cut one rafter, test-fit it against the wall plate, then trace it as a template for every subsequent rafter. This catches small measurement errors before you've ruined every rafter in the pile. Most production framers cut a "first-and-test" rafter every time they move to a new wall.
Birdsmouth cut for hip and valley rafters
Common rafters run perpendicular to the ridge — straight up the slope. Hip rafters and valley rafters run diagonally across corners and carry the meeting plane of two roof slopes. Their geometry uses 17:12 in place of pitch/12, because the diagonal travel distance is 12 × √2 = 16.97 inches per 12 inches of perpendicular run.
For a 6:12 hip rafter: plumb-cut angle = arctan(6 / 16.97) = 19.47°. Notice this is less steep than the common rafter's 26.57° — the hip travels the same vertical rise over a longer diagonal run. Most speed squares have a separate "hip/valley" scale alongside the common scale.
Common birdsmouth mistakes
Five errors recur across rough framing crews:
- Cutting too deep: Exceeding 1/3 rafter depth weakens the rafter at peak stress.
- Cutting too shallow: If the seat doesn't extend the full plate width, the rafter rocks instead of bearing flat.
- Wrong pitch reading: Mistaking 6:12 for 6° instead of 26.57° gives a useless cut.
- Inverting plumb and seat: Plumb is vertical, seat is horizontal — easy to flip when tired.
- Forgetting to deduct for ridge thickness: Theoretical span is measured from outside-wall to outside-wall, but the rafter terminates at the ridge centerline minus half-ridge-thickness.
- Skipping the test-fit: The first rafter should always go up and come down before all 30 are cut.
Tools for cutting birdsmouths
Three tool combinations get the job done. Pick by speed and accuracy needs:
- Speed square + circular saw: Universal. Every framing crew has both. Two-cut accuracy ±1/16 inch.
- Sliding compound miter saw: Setup-heavy but cuts perfectly for production. Set angle once, cut 30 rafters identically.
- Hand saw + chisel: Trim carpenter and timber-frame method. Slow but capable on irregular stock.
- Jigsaw: Useful for the inside-corner cleanup after the two straight cuts.
- CNC router: Modern timber-frame fabricators. Bird mouths are computed by the design software and routed to ±0.005 inch.
- Pre-engineered metal connector: Skip the cut entirely. Simpson Strong-Tie variable-pitch connectors mount the rafter to the plate without notching.