What is a birdsmouth cut?

A birdsmouth is a notch cut into the underside of a roof rafter where it sits on the wall plate (top plate). It consists of two cuts: a horizontal seat cut (sometimes called a level cut) that bears on the top of the wall plate, and a vertical plumb cut that sits flush against the face of the plate or the rafter tail.

What is the seat cut depth?

The seat cut is the horizontal bearing length across the wall plate. This calculator uses the entered wall plate width (typically 3.5 in for a 2x4 plate or 5.5 in for a 2x6 plate).

What is the plumb cut depth?

The plumb cut is the vertical leg of the notch. Its height equals seat_cut × tan(pitch_angle). The structural notch depth perpendicular to the rafter equals seat_cut × sin(pitch_angle).

Why is the one-third rule important?

A deep notch weakens a rafter structurally. While one-third rafter depth is a traditional framing rule of thumb, IRC R802.7.1.1 limits sawn lumber end notches to D/4. Always confirm local code requirements.

What rafter dimension should I enter?

Enter the actual dressed size, not the nominal size. A nominal 2x8 has an actual width of 7.25 in; a nominal 2x10 is 9.25 in; a nominal 2x12 is 11.25 in. Check the lumber tag or measure the board directly.

Does this calculator handle hip or valley rafters?

No. This tool is for common rafters only. Hip and valley rafters have a compound angle cut (backing angle) that requires a separate calculation.

Birdsmouth Cut Calculator

Calculate the seat cut and plumb cut dimensions for a birdsmouth notch in roof rafters based on roof pitch and rafter dimensions.

Roof & Rafter Dimensions

Roof Pitch (in/12)

Rafter Actual Depth (in) — e.g. 7.25 for 2x8

Wall Plate Width (in) — e.g. 3.5 for 2x4

Quick-select rafter size:

Enter your roof and rafter dimensions on the left to see the birdsmouth cut.

Birdsmouth Cut Results

Pitch Angle

—

degrees

Seat Cut Depth

—

inches (horizontal)

Plumb Cut Depth

—

inches (vertical)

Code Limit (1/3)

—

max notch depth

Parameter	Value
Roof Pitch	—
Pitch Angle	—
Rafter Actual Depth	—
Wall Plate Width	—
Seat Cut Depth (horizontal)	—
Plumb Cut Depth (vertical)	—
Max Allowed Notch Depth (1/3 rule)	—
Remaining Rafter Depth Above Notch	—

Birdsmouth Layout Diagram

How the Formulas Work

1
Pitch angle: θ = arctan(rise ÷ run). For a 6/12 pitch: θ = arctan(6 ÷ 12) ≈ 26.57°.
2
Seat cut depth (horizontal): Seat = wall_plate_width. This gives the rafter full bearing across the plate.
3
Plumb cut depth (vertical): Plumb = seat × tan(θ). This is the vertical height from the seat edge back to the rafter underside.
4
One-third check: Notch depth = plumb × cos(θ) = seat × sin(θ). Compare this perpendicular depth with rafter_depth ÷ 3.
5
Remaining depth: rafter_depth − notch_depth = the structural depth of the rafter above the notch.

Summary

A free online birdsmouth cut calculator that determines the exact seat cut depth and plumb cut depth for a birdsmouth notch. Enter your roof pitch (or rise and run), rafter width, and wall plate width to get precise layout measurements. The tool also checks that the notch depth does not exceed one-third of the rafter depth, a common framing rule of thumb (note IRC R802.7.1.1 limits end notches to D/4).

How it works

Enter the roof pitch as rise/run (e.g. 6/12) or supply the rise and run directly.
Enter the rafter actual width (depth) — the dimension perpendicular to the rafter face, e.g. 7.25 in for a 2x8.
The pitch angle is computed as arctan(rise / run).
Seat cut length equals the wall plate width for full bearing.
Plumb cut height = seat cut × tan(pitch angle).
The perpendicular notch depth equals seat cut × sin(pitch angle); the tool compares it with one-third of the rafter depth.

Use cases

Laying out birdsmouth notches on common rafters for gable or hip roofs.
Verifying that a notch depth stays within recommended rafter notch framing limits.
Teaching carpentry students the geometry behind plumb cuts and seat cuts.
Checking rafter layout before making cuts on the job site.
Creating a cut list for pre-fabricating rafters in a shop.

Frequently Asked Questions

Last updated: 2026-05-25 · Reviewed by Nham Vu