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Birdsmouth Cut Calculator

Construction

Calculate the heel cut depth and seat cut length for a birdsmouth notch where a roof rafter meets the wall top plate, based on roof pitch and plate width.

Reviewed by the thecalcu.com team · Last updated July 13, 2026

1.55.5

Heel Cut Depth (in)

1.75
Seat Cut Length (in)
3.913

This calculator computes your Heel Cut Depth (in), Seat Cut Length (in) from the values you enter.

Inputs
Roof Pitch (rise per 12 in run)Wall Top Plate Width
Outputs
Heel Cut Depth (in)Seat Cut Length (in)

What is a Birdsmouth Cut?

A Birdsmouth Cut Calculator determines the heel cut depth and seat cut length needed to notch a roof rafter so it sits flush on the wall's top plate, based on your roof's pitch and the plate's width. The birdsmouth is one of the most precise cuts in roof framing, get it wrong and the rafter either doesn't sit flat on the plate or gets notched too deep, weakening the structural member.

Traditionally calculated using a framing square and rafter tables, this calculator gives you the exact dimensions instantly from your roof pitch selection. Pair it with the Rafter Length Calculator for the rafter's full length, or the Framing Calculator for broader wall framing material estimates.

Why Use a Birdsmouth Cut Calculator?

Calculating birdsmouth dimensions by hand with a framing square requires understanding trigonometric rafter tables that many DIYers and even some tradespeople find error-prone under job-site conditions. This calculator applies the underlying trigonometry directly, giving you precise heel and seat cut measurements from a simple pitch selection and plate width entry.

It's especially useful for cutting multiple rafters consistently, once you have the correct dimensions, every rafter can be marked and cut to the same specification, avoiding the variation that comes from manually marking each one by eye.

Who Should Use This Calculator?

Framing carpenters use this calculator on job sites to quickly confirm birdsmouth dimensions before cutting a batch of rafters. DIY builders constructing a shed, porch roof, or small addition use it to get professional-quality rafter notches without years of framing experience. Roofing contractors reference it when replacing or repairing individual rafters to match existing roof geometry. Trade school and apprenticeship instructors use it to teach the trigonometric principles behind traditional rafter square techniques. Timber framers working on traditional joinery projects use similar geometric calculations for notch layout.

What Insights Does the Birdsmouth Cut Calculator Give You?

The Heel Cut Depth is the primary result, the depth of the vertical plumb cut into the rafter, measured in inches. This is the dimension to mark on your rafter stock before making the plumb cut. The Seat Cut Length shows the horizontal cut length that will rest on the wall plate, which is slightly longer than the plate width itself due to the pitch angle. Together these two dimensions define the complete birdsmouth notch, mark both before cutting to ensure the rafter sits correctly and check that the heel cut depth doesn't exceed your local code's maximum notch depth relative to rafter size.

How to use this Birdsmouth Cut calculator

  1. Select your Roof Pitch (rise per 12 inches of run) from the dropdown, matching your roof's design.
  2. Enter your Wall Top Plate Width in inches (commonly 3.5 in for a standard 2×4 plate, or wider for doubled plates).
  3. Review the Heel Cut Depth result, mark this depth for your vertical plumb cut.
  4. Review the Seat Cut Length result, mark this length for your horizontal seat cut.
  5. Confirm your rafter stock is deep enough that the heel cut depth doesn't exceed your local code's maximum notch depth before cutting.
Show formula & methodology ↓Show less ↑

Formula & Methodology

The calculator applies standard roof framing trigonometry:

Pitch Angle = arctan(Roof Pitch Rise ÷ 12)

Heel Cut Depth = Wall Plate Width × tan(Pitch Angle)

Seat Cut Length = Wall Plate Width ÷ cos(Pitch Angle)

Worked example: For a 6/12 roof pitch with a standard 3.5 in wall plate width:

Pitch Angle = arctan(6 ÷ 12) = arctan(0.5) ≈ 26.57°

Heel Cut Depth = 3.5 × tan(26.57°) ≈ 3.5 × 0.5 = 1.75 in

Seat Cut Length = 3.5 ÷ cos(26.57°) ≈ 3.5 ÷ 0.894 ≈ 3.92 in

Frequently Asked Questions

What is a birdsmouth cut?
A birdsmouth cut is a notch cut into the underside of a roof rafter where it rests on and meets the wall's top plate, consisting of a horizontal seat cut (where the rafter sits on the plate) and a vertical heel cut (the plumb face behind it). This notch lets the rafter sit flush and level on the wall while the rest of the rafter continues up at the roof's pitch angle.
How do I calculate the heel cut depth for a birdsmouth?
Heel cut depth is calculated by multiplying the wall plate width by the tangent of the roof pitch angle, which the calculator does automatically once you select your roof pitch and enter your plate width. This depth represents how far the vertical plumb cut extends into the rafter.
What is the seat cut length in a birdsmouth notch?
The seat cut length is the horizontal cut length that rests directly on the wall top plate, calculated by dividing the plate width by the cosine of the pitch angle. This is slightly longer than the plate width itself since the cut runs at a slight angle relative to the rafter's long axis.
Why does roof pitch affect the birdsmouth cut dimensions?
Steeper roof pitches create a larger angle between the rafter and the horizontal wall plate, which increases both the heel cut depth and seat cut length needed for the rafter to sit flush. A shallow pitch produces a shallow, wide notch, while a steep pitch produces a deeper, more angled notch.
How deep can a birdsmouth cut go without weakening the rafter?
Building codes typically limit the birdsmouth notch depth to no more than one-third to 40% of the rafter's total depth to avoid excessively weakening the structural member, check your local building code and rafter dimensions before cutting, especially on shallow-depth rafters or unusually steep pitches.
What tools do I need to mark a birdsmouth cut?
A framing square (or speed square) and a rafter square with pitch angle markings are the traditional tools for marking birdsmouth cuts by hand, though many carpenters also use rafter calculation apps or printed rafter tables alongside a calculator like this one to confirm dimensions before cutting.
Does wall plate width affect birdsmouth cut size?
Yes, a wider wall top plate (such as a doubled 2×6 plate versus a standard single 2×4) increases both the heel cut depth and seat cut length proportionally, since the notch needs to span the full width of whatever plate the rafter rests on.
How does this calculator relate to overall rafter length?
This calculator focuses specifically on the birdsmouth notch dimensions at the wall connection point, for the rafter's total length including the ridge cut and overhang, use the [Rafter Length Calculator](/rafter-length-calculator/) alongside this tool.
Also known as
birds mouth cut calculatorrafter seat cut calculatorroof rafter notch calculatorheel cut calculatorbirdsmouth notch calculator