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 depth is how far the horizontal cut goes across the width of the rafter. It equals rafter_width × cos(pitch_angle). Most builders match this to the width of the wall plate (typically 3.5 in for a 2x4 plate or 5.5 in for a 2x6 plate), but it must not exceed one-third of the rafter depth.

What is the plumb cut depth?

The plumb cut depth is the vertical measurement of the notch, equal to rafter_width × sin(pitch_angle). This is how far the vertical cut drops into the rafter.

Why is the one-third rule important?

Cutting deeper than one-third of the rafter depth weakens it structurally and violates most residential building codes (e.g. IRC R802.7.1). If your seat cut depth exceeds this limit, use a deeper rafter (e.g. 2x10 instead of 2x8) or reduce the pitch.

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

Name: Birdsmouth Cut Calculator
Availability: InStock
Author: Nham Vu

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:

Birdsmouth Cut Results

Pitch Angle

—

degrees

Seat Cut Depth

—

inches (horizontal)

Plumb Cut Depth

—

inches (vertical)

Code Limit (1/3)

—

max seat cut depth

Parameter	Value
Roof Pitch	—
Pitch Angle	—
Rafter Actual Depth	—
Wall Plate Width	—
Seat Cut Depth (horizontal)	—
Plumb Cut Depth (vertical)	—
Max Allowed Seat Cut (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 = rafter_depth × cos(θ). This is how far the level cut extends across the rafter face.
3
Plumb cut depth (vertical): Plumb = rafter_depth × sin(θ). This is the height of the vertical cut at the notch.
4
One-third code check: Maximum allowed seat cut = rafter_depth ÷ 3. Exceeding this violates IRC R802.7.1 and weakens the rafter.
5
Remaining depth: rafter_depth − seat_cut_depth = the structural depth of the rafter above the notch, which carries the roof load.

Summary

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

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 depth (horizontal cut) = rafter width × cos(pitch angle).
Plumb cut depth (vertical cut) = rafter width × sin(pitch angle).
Birdsmouth notch depth equals the seat cut depth; the tool warns if it exceeds one-third the rafter depth per code.

Use cases

Laying out birdsmouth notches on common rafters for gable or hip roofs.
Verifying that a notch depth stays within the one-third rafter depth code limit.
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: 2026-05-23 · Reviewed by Nham Vu