Birdsmouth Cut Calculator · Rafter Notch, HAP & Compliance

Birdsmouth Cut Calculator

Seat cut, plumb cut, HAP, notch depth & IRC compliance for rafters

Rafter Assembly Illustration
WALL WALL PLATE RIDGE θ HAP seat cut plumb cut RAFTER overhang run to wall
Seat cut = horizontal surface on the wall plate · Plumb cut = vertical face at the outer plate edge · HAP = Height Above Plate at the plumb cut · θ = roof pitch angle · Run = ridge to outer wall · Overhang = eave tail past the plate.
Roof Details
:12
Common pitches: 4:12 (~18.4°), 6:12 (~26.6°), 8:12 (~33.7°), 12:12 (45°).
Rafter & Plate
Results
✅ IRC Compliant
Height Above Plate (HAP)
—
—
Pitch angle
—
Seat cut
—
Plumb cut
—
Notch depth
—
📋 Rafter Summary
Enter the roof pitch, rafter size and plate width to see the birdsmouth cut dimensions.
Max notch allowed
—
Rafter depth
—
Line length (ridge→wall)
—
Total rise
—
🧾 Cut Dimensions Breakdown
Item
Value
Detail
Roof pitch
—
—
Seat cut (horizontal)
—
—
Plumb cut (vertical)
—
—
Notch depth (perpendicular)
—
—
HAP (height above plate)
—
—
Compliance
—
—
📊 Birdsmouth Quick Reference
Item
Typical Value
Notes
Seat cut length
= plate width
Full bearing on the wall plate.
Max notch depth
¼ × rafter depth
IRC R802.7.1 requirement.
Min rafter depth for 6:12
2×6 (3.5" plate)
2×4 will fail the notch rule.
Min rafter depth for 8:12
2×8 (3.5" plate)
At 8:12, 2×6 may exceed ¼ depth.
Plumb cut height
seat × tan(θ)
Vertical face of the notch.
HAP
plate × tan(θ) + depth/cos(θ)
Used for rafter line-length layout.
Ridge cut angle
= pitch angle
Top of rafter, opposite side.
Estimate only. Always verify against the IRC (or your local code) and the rafter manufacturer's span tables before cutting.

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Faiq Ur Rahman

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Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.

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Introduction

The birdsmouth is the notch cut into the underside of a rafter so it sits flat on the wall plate while the rafter above continues at the roof pitch. Cut it correctly and the roof bears evenly on the plate with the rafter’s full depth preserved above the notch. Cut it too deep and the remaining timber is too thin to carry the load, a failure mode that building codes address with a hard limit. This calculator works out every dimension of the notch from three inputs, then compares the resulting depth against the IRC ¼-depth rule. It is built for carpenters and owner-builders cutting rafters on site, for designers checking whether a proposed rafter size will pass at a given pitch, and for anyone who needs to confirm that a stack of pre-cut rafters is actually compliant before they go up.

 

How to Use the Birdsmouth Cut Calculator

  1. Enter the Run, the horizontal distance from the ridge to the outer face of the wall and pick the matching unit.

  2. Add the Overhang if the rafter extends past the wall; leave it at zero for a rafter that terminates at the plate.

  3. Choose the Pitch type, an X:12 ratio or a direct angle in degrees and enter the value.

  4. Select the Rafter size from the dropdown, or choose Custom to enter a specific depth.

  5. Select the Wall plate width the rafter will bear on, or set a custom width.

  6. Read the HAP in the hero display, with the seat cut, plumb cut and notch depth directly below.

  7. Check the compliance badge, green for compliant, amber for near the limit, red for a fail.

  8. Review the cut dimensions breakdown table for a row-by-row summary of every figure.

 

How the Birdsmouth Cut Calculator Formula Works

Everything follows from the pitch angle, the rafter depth and the plate width. The seat cut is horizontal and equal to the plate width, because the rafter must bear on the full plate. The plumb cut and notch depth follow from that seat length and the pitch.

Formula: Pitch Angle θ = atan(Rise ÷ 12) (for X:12 pitch)
Formula: Seat Cut = Plate Width (horizontal)
Formula: Plumb Cut = Plate Width × tan(θ) (vertical)
Formula: Notch Depth = Plate Width × sin(θ) (perpendicular to rafter)
Formula: Max Notch = Rafter Depth ÷ 4 (IRC R802.7.1)
Formula: HAP = Plate Width × tan(θ) + Rafter Depth ÷ cos(θ)
Formula: Line Length = Run ÷ cos(θ)
Formula: Total Rise = Run × tan(θ)

Three validation rules apply. Pitch must be greater than 0° and less than 89°. Rafter depth and plate width must both be positive. The run and overhang may be zero but cannot be negative. If any rule is broken, the results panel shows a message rather than a partial figure.

 

Worked Example

A carpenter is cutting rafters for a 6:12 gable roof with a 14-foot run to the outer wall and a 16-inch overhang. The rafters are 2×8 (7.25-inch actual depth) and the wall plate is a 2×4 (3.5-inch width).

  • Pitch angle = atan(6 ÷ 12) = 26.57°

  • Seat cut = 3.5 in = 3.5 in

  • Plumb cut = 3.5 × tan(26.57°) = 3.5 × 0.500 = 1.75 in

  • Notch depth = 3.5 × sin(26.57°) = 3.5 × 0.4472 = 1.57 in

  • Max notch allowed = 7.25 ÷ 4 = 1.81 in

  • HAP = 3.5 × 0.500 + 7.25 ÷ 0.8944 = 1.75 + 8.11 = 9.86 in

  • Line length = 14 ÷ cos(26.57°) = 14 ÷ 0.8944 = 15.65 ft

  • Total rise = 14 × 0.500 = 7.0 ft

The takeaway: this rafter passes the IRC notch rule with room to spare, the 1.57-inch notch is well below the 1.81-inch maximum. The HAP of 9.86 inches is the figure used to lay out the rafter line from the ridge to the outer edge of the plate, and it is the dimension many fitters forget to calculate before marking the birdsmouth.

Frequently Asked Questions

What is a birdsmouth cut on a rafter?

It is a triangular notch cut into the underside of a rafter where it crosses the wall plate, allowing the rafter to sit flat on the plate while continuing at the roof pitch. The horizontal face of the notch is the seat cut; the vertical face is the plumb cut.

 

How deep can a birdsmouth notch be?

The International Residential Code limits the notch to one-quarter of the rafter’s actual depth. A 2×8 rafter with a 7.25-inch actual depth can have a notch no deeper than 1.81 inches. Anything deeper removes too much of the load-bearing section.

 

What is HAP in rafter layout?

HAP stands for Height Above Plate. It is the vertical distance from the top of the wall plate to the top edge of the rafter at the plumb cut. It is used as the anchor dimension when marking the rafter line from the ridge to the outer wall.

 

How do I convert a 6:12 pitch to degrees?

Take the arctangent of 6 divided by 12. The result is 26.57°. A 4:12 pitch works out to 18.43°, an 8:12 to 33.69°, and a 12:12 to 45°.

 

What is the difference between seat cut and plumb cut?

The seat cut is the horizontal face of the birdsmouth that bears on the plate; its length equals the plate width. The plumb cut is the vertical face at the outer edge of the plate; its height is the plate width multiplied by the tangent of the pitch angle.

 

Why is my notch depth too deep for the rafter?

Either the pitch is steep, the plate is wide, or the rafter is too shallow for the application. A 2×4 rafter at a 6:12 pitch on a 2×4 plate produces a 1.57-inch notch, which exceeds the quarter-depth limit of 0.875 inches. Switching to a 2×6 or 2×8 rafter resolves the issue.

 

Can I use a birdsmouth on engineered lumber?

Yes, but engineered lumber such as LVL or I-joists usually has its own manufacturer guidance on allowable notches, which may be stricter than the IRC rule for solid sawn timber. Always check the manufacturer’s literature before cutting.

 

What happens if I over-cut the birdsmouth?

The rafter loses section depth at the point of highest bending stress near the wall, increasing the risk of sagging or, in extreme cases, failure under snow or wind load. Over-cut rafters should be replaced rather than patched.

 

What is the standard plate width for a house wall?

A 2×4 wall has an actual plate width of 3.5 inches. A 2×6 wall has 5.5 inches, and a 2×8 wall has 7.25 inches. The calculation uses the actual width, not the nominal size.

 

Does the overhang affect the birdsmouth cut?

No. Overhang determines the tail length of the rafter past the wall, but the birdsmouth geometry depends only on pitch, plate width and rafter depth. The overhang does affect the total rafter length and the fascia position.

 

What pitch is best for a residential roof?

The most common residential pitch in North America is 6:12, which balances drainage, material usage and appearance. Pitches below 4:12 are usually restricted to specific roofing materials such as membrane or standing seam metal, and pitches above 9:12 are considered steep-slope.

 

Does this calculator handle metric rafters?

Yes. The pitch can be entered in degrees, and the run, overhang and custom rafter or plate dimensions can all be entered in millimetres, centimetres or metres. The output echoes back in whichever unit was used for the run.

Disclaimer

This birdsmouth cut calculator provides geometric results based on the pitch, rafter depth and plate width you enter, together with an indicative check against the IRC ¼-depth rule. It does not replace a structural assessment, a span-table review or a building permit check. Rafter sizing depends on span, spacing, load, species and grade, none of which are captured here. Always verify your rafter specification against the applicable building code and, where the structure is load-bearing or spans a habitable space, consult a qualified engineer before cutting material.

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