Birdsmouth Cut Calculator (seat cut, heel height & ¼-depth check)

Understanding the birdsmouth cut calculator — concept and principle

A birdsmouth is the notch cut into a rafter so that it sits flat on the wall plate. This calculator works out the heel (plumb) cut height, the notch depth, the timber left above the plate and checks the notch against the common rule of no more than one-quarter of the rafter depth.

Seat and plumb cuts: with the default inputs the result is 44.5 mm plumb (21.6% of depth (≤ ¼)).

How it is calculated

Pitch angle θ = atan(rise ÷ 12) for a pitch given as rise in 12

Plumb (heel) cut height = seat length × tan θ

Notch depth square to the rafter edge = seat length × sin θ

Height above plate (HAP) = rafter depth ÷ cos θ − plumb cut height

Longest seat within the ¼ rule = (rafter depth ÷ 4) ÷ sin θ

The principle

The birdsmouth is a right-angled notch: a level seat cut and a vertical plumb cut. Because the rafter is sloped, right-triangle trigonometry links the seat length to the cut heights. The notch removes wood from the rafter's bearing end, so building codes limit its depth; the US IRC (R802.7.1) allows end notches up to one-quarter of the rafter depth.

Worked example

Default inputs: rafter depth 184 mm, pitch 6 in 12, seat 89 mm.

θ = atan(6 ÷ 12) = 26.6°.
Plumb cut = 89 × 0.5 = 44.5 mm.
Notch depth = 89 × sin 26.6° = 39.8 mm = 21.6% of 184 → within the ¼-depth limit.
HAP = 184 ÷ cos 26.6° − 44.5 = 161.2 mm; longest seat within the rule = 46 ÷ 0.447 = 102.9 mm.

Each point is the calculator re-run with only “Pitch” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pitch	Plumb (heel) cut height (mm)
1.5	11.1
3	22.3
4.5	33.4
6	44.5
7.5	55.6
9	66.8
12	89

How to read the result

Keep the notch within the limit and make the seat bear fully on the plate. HAP matters when matching rafters of different depths or setting roof heights. Steep pitches give deeper notches for the same seat, so shorten the seat if needed.

Common mistakes

Using the plumb cut height as the notch depth; they differ.
Overcutting the corner, which weakens the rafter; finish with a handsaw.
Ignoring engineered or larger rafters, which may have their own rules.

Keep in mind: Roof framing is structural. Follow local building codes and the advice of a qualified professional.

Frequently asked questions

How deep can a birdsmouth be?

Under the US IRC, end notches can be up to one-quarter of the rafter depth.

What is HAP?

Height above plate, the depth of rafter left above the wall plate measured plumb.

How long should the seat be?

Usually the width of the wall plate, within the depth limit.

Sources: International Code Council, 2021 International Residential Code, Section R802.7.1 · Uhler T, "Sizing the Birdsmouth", Journal of Light Construction, 2021

Checked 9 Nov 2026. Right-triangle trigonometry of the notch; end-notch limit of one-fourth of the member depth, 2021 International Residential Code R802.7.1, as explained by T. Uhler, “Sizing the Birdsmouth”, Journal of Light Construction (6 May 2021).

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