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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.

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.

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.

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

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.
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.
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.
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.
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.
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.
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.
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