What is the birdsmouth cut formula?

Pitch angle = atan(rise / 12). Seat cut length = wall plate width / cos(pitch angle). Heel cut depth = wall plate width x tan(pitch angle). The pitch angle is also the angle to set your saw for the seat cut.

What wall plate width should I use?

A standard 2x4 wall top plate is 3.5 inches wide, and a 2x6 wall top plate is 5.5 inches wide (actual dressed lumber dimensions). Enter the actual width of your top plate, including any double top plate if the seat cut needs to span both boards.

Is the heel cut the same as the plumb cut?

Yes, in the context of a birdsmouth the heel cut is a short plumb cut — a vertical cut at the pitch angle from level — sized to the wall plate's outside edge. It's distinct from the longer plumb cut typically made at the ridge or the tail of the rafter.

What angle do I set my saw to?

Set your saw's bevel/miter angle to the pitch angle shown on the Cut Angle tab — the same atan(rise/12) value used for the seat cut. Most circular saws and miter saws read this directly off their angle scale.

Does the wall plate width include a double top plate?

Only if you want the seat cut to bear on both boards of a doubled top plate. Enter the combined width (e.g. 3.5 in for one 2x4, or the same 3.5 in if the rafter only needs to seat on the top board of a doubled plate) based on how your framing plan calls for the bearing surface.

Birdsmouth Cut Calculator — Rafter Seat & Heel Cut

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Walk-through

How to Use This Calculator

3 steps

1

Enter your roof pitch

Enter the roof pitch as rise per 12 inches of horizontal run — for example, 6 for a 6/12 pitch. Common residential pitches range from about 4/12 to 9/12.

2

Enter your wall plate width

Enter the width of the wall's top plate in inches. Use 3.5 in for a standard 2x4 wall or 5.5 in for a 2x6 wall, or pick a preset button. The calculator updates instantly.

3

Cut the seat, then the heel

Mark and cut the seat face first, then the heel (plumb) face, using the lengths shown in the result card. Switch to the Cut Angle tab to see the exact saw bevel setting for the seat cut.

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Reference

Formula & Methodology

3 formulas

Seat cut length

seatCut = wallPlateWidth / cos(atan(rise / 12))

The seat cut is the face of the notch that bears flat on top of the wall plate. Its length depends on the wall plate width and the roof pitch angle: as the pitch gets steeper, the seat cut gets longer for the same plate width.

Heel cut depth

heelCut = wallPlateWidth * tan(atan(rise / 12)) = wallPlateWidth * (rise / 12)

The heel cut (plumb cut) is the near-vertical face of the notch that sits against the wall plate's outside edge. Its depth is the wall plate width times the tangent of the pitch angle — which, since tan(atan(x)) = x, simplifies to wallPlateWidth * (rise / 12).

Pitch angle (saw bevel)

pitchAngle = atan(rise / 12)

The roof pitch angle, measured in degrees from level, is also the bevel/miter angle to set your saw for the seat cut. A 6/12 pitch gives an angle of atan(6/12) = 26.565 degrees; an 8/12 pitch gives atan(8/12) = 33.69 degrees.

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YMYL

Trust, Methodology & Sources

Written by Quinn Sumner · Updated 2026-07-23 · 2 sources

Editorial accountability

Author: Quinn Sumner - Editor

Owner: Quinn Sumner - Editorial owner

Last reviewed: 2026-07-23

Last verified: 2026-07-23

Data effective: 2026-01-01

Methodology

Applies standard right-triangle trigonometry to the roof pitch (rise per 12 in of run) and wall plate width to derive the birdsmouth notch's seat cut length, heel cut depth, and saw bevel angle, following the classic carpentry framing-square layout method and general IRC rafter-notching guidance.

Assumption: The entered roof pitch and wall plate width reflect the as-built or as-designed framing.

Assumption: The rafter is a standard solid-sawn dimensional-lumber rafter, not an engineered I-joist or truss chord, which may have different or prohibited notching rules.

Assumption: The one-third rafter-depth notch guideline referenced in the result and FAQ is a general framing rule of thumb, not a substitute for a jurisdiction-specific code check.

Limitations & guidance

Does not check the resulting notch depth against the rafter's actual dimensional depth or perform any structural load calculation.

Does not account for engineered lumber, truss, or long-span rafter requirements, which often restrict or prohibit birdsmouth notching entirely.

Local building codes and structural requirements vary by jurisdiction and may impose stricter notch-depth or bearing-length limits than the general rule of thumb referenced here.

Professional guidance: This calculator is for planning and estimating purposes only and is not a substitute for design by a licensed engineer or contractor. Verify the resulting notch depth and bearing length against your local building code and manufacturer specifications, and consult a structural engineer for engineered lumber, long spans, or high load conditions before cutting.

Primary sources

International Residential Code (IRC) — Chapter 8 Roof-Ceiling Construction - International Code Council

NRCA Roofing Manual - National Roofing Contractors Association

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Glossary

Key Terms Explained

7 terms

Birdsmouth A triangular notch cut into the underside of a rafter where it crosses the wall's top plate, allowing the rafter to seat flat on the plate instead of resting only on its bottom corner.

Seat cut The face of the birdsmouth notch that runs roughly parallel to the ground and bears directly on top of the wall's top plate. Its length is computed from the wall plate width divided by the cosine of the pitch angle.

Heel cut Also called the plumb cut of the birdsmouth — the near-vertical face of the notch that sits against the outside edge of the wall's top plate. Its depth is the wall plate width times the tangent of the pitch angle.

Plumb cut Any cut on a rafter made vertically (relative to the finished building, not the rafter's length) at the pitch angle. The heel cut of a birdsmouth is a short plumb cut; the ridge cut at the top of the rafter is a longer plumb cut.

Roof pitch The steepness of a roof, expressed as inches of vertical rise for every 12 inches of horizontal run — for example, a 6/12 pitch rises 6 inches for every 12 inches of run, an angle of about 26.6 degrees from level.

Wall plate The horizontal framing member (typically a doubled 2x4 or 2x6) that sits on top of a stud wall and supports the ends of the rafters or trusses. Also called a top plate.

Rafter A sloped structural framing member that runs from the wall plate (or a birdsmouth notch on it) up to the ridge, supporting the roof sheathing and covering above it.

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Scenarios

Real-World Examples

3 worked examples

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Typical gable roof

6/12 pitch on a standard 2x4 wall

Roof pitch (rise/12) 6 Wall plate width (in) 3.5

At a 6/12 pitch on a 3.5 in wall plate, the pitch angle is 26.57 degrees, the seat cut comes out to 3.91 in, and the heel cut depth is 1.75 in. This is the most common combination for a standard single-story gable roof — a moderate pitch on a single 2x4 top plate.

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Steep roof, wider wall

10/12 pitch on a 2x6 wall

Roof pitch (rise/12) 10 Wall plate width (in) 5.5

Increasing both the pitch (to 10/12, a 39.81-degree angle) and the wall plate width (to 5.5 in for a 2x6 wall) grows both cuts substantially: the seat cut is 7.15 in and the heel cut is 4.58 in. The heel cut in particular grows almost linearly with pitch — steeper roofs need deeper heel cuts, which is why the one-third rafter-depth rule matters more on steep pitches.

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Setting the saw

8/12 pitch — reading the cut angle

Roof pitch (rise/12) 8 Wall plate width (in) 3.5

For an 8/12 pitch, the Cut Angle tab shows a saw bevel of 33.69 degrees — the same angle used to derive the 4.21 in seat cut and 2.33 in heel cut. Set a circular saw's bevel gauge (or a speed square held against the rafter) to this angle before making the seat cut.

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Deep Dive

Understanding the Birdsmouth Cut Calculator

3 chapters · 4 min read

A birdsmouth is the notch carpenters cut into a rafter so it seats flat on the wall's top plate instead of balancing on a single corner. Getting its two faces — the seat cut and the heel cut — right by hand means working through a bit of trigonometry with a speed square or framing calculator. This calculator does that math directly from your roof pitch and wall plate width, and gives you the exact saw angle to cut with.

How the Birdsmouth Cut Calculator works

The calculator starts from the roof pitch, expressed as rise per 12 inches of run (the standard framing convention), and converts it to a pitch angle with atan(rise / 12). From there, the seat cut — the face that bears on top of the plate — is wallPlateWidth / cos(pitchAngle), and the heel cut — the plumb face against the plate's outside edge — is wallPlateWidth * tan(pitchAngle). Because these are pure trigonometric relationships, the same pitch angle also gives you the bevel setting for your saw, shown on the Cut Angle tab.

Inputs and what they mean

Roof pitch is entered as the rise-per-12 number carpenters use on the job site — 6 for a 6/12 pitch, 8 for an 8/12 pitch, and so on. A pitch of 0 is treated as a flat roof, where the seat cut equals the plate width and the heel cut is zero. Wall plate width is the actual width of the top plate the rafter sits on, in inches — 3.5 in for a standard 2x4 wall and 5.5 in for a 2x6 wall are the two most common values, both provided as quick-select presets. Entering the wrong plate width is the most common source of an undersized or oversized seat cut, so double-check it against your actual framing lumber.

Limits and edge cases

This calculator gives you the geometry of the notch, not a structural sign-off. As a general rule of thumb, keep the notch depth (roughly the heel cut depth measured perpendicular to the rafter) within about one-third of the rafter's total depth, and make sure the heel point doesn't land past the inside edge of the wall plate — cutting deeper reduces the rafter's effective structural depth at its most heavily loaded point. Steep pitches (above roughly 9/12–10/12) and wide wall plates both push the heel cut deeper, so they're the cases most likely to bump into that one-third limit on standard dimensional lumber. For engineered rafters, long spans, high snow or wind loads, or any notch depth you're unsure about, verify against your local building code and consult a structural engineer before cutting.

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Questions

Frequently Asked Questions

6 questions

What is a birdsmouth cut?+

A birdsmouth is a triangular notch cut into the underside of a rafter where it crosses the wall's top plate. It has two faces: the seat cut, which bears flat on top of the plate, and the heel cut (plumb cut), which sits against the plate's outside edge — together they let the rafter seat squarely instead of balancing on one corner.

How accurate is this calculator?+

The calculator uses exact trigonometric relationships — seatCut = wallPlateWidth / cos(pitchAngle) and heelCut = wallPlateWidth * tan(pitchAngle), where pitchAngle = atan(rise/12) — so the geometry is exact given your inputs. Real-world accuracy still depends on measuring your actual wall plate width and pitch correctly and cutting precisely to your marked lines; always dry-fit or test-cut on scrap before cutting your full rafter set.

What units does the Birdsmouth Cut Calculator expect?+

Roof pitch is entered as rise per 12 inches of run (a unitless ratio in the standard framing convention, e.g. 6 for 6/12). Wall plate width, seat cut, and heel cut are all in inches. The pitch angle is shown in degrees on the Cut Angle tab.

How deep can a birdsmouth notch be cut?+

As a general framing rule of thumb, the notch depth should not exceed about one-third of the rafter's total depth, and the heel cut point should land no lower than the inside edge of the wall plate. Steeper pitches and wider wall plates both increase the heel cut depth, so always verify against your local building code and, for engineered or long-span rafters, a structural engineer.

Can I share my results?+

Yes. The calculator encodes your roof pitch and wall plate width into the page's URL as you type, so copying the current URL from your browser's address bar (or using the Share button) is enough to send your exact scenario to a colleague or open it again later.

Where does the formula come from?+

The seat cut, heel cut, and saw angle formulas are standard right-triangle trigonometry applied to the classic carpentry framing-square method for laying out a birdsmouth: the roof pitch defines the angle of a right triangle, and the wall plate width is the triangle's known side, from which the other two sides (seat cut and heel cut) follow from cosine and tangent.

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Birdsmouth Cut Calculator