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Rafter-Birdsmouth-Cut

The birdsmouth is the notch where a rafter sits on the wall plate. Plumb cut follows roof pitch; seat cut is horizontal. IRC limits seat depth to 1/3 of rafter depth.

Concept Fundamentals
arctan(Pitch/12)
Plumb Angle
90ยฐ โˆ’ plumb
Seat Angle
Depth รท 3
Max Seat
Depth โˆ’ seat
HAP
Calculate BirdsmouthEnter rafter size, pitch, and wall plate width.

Why This Construction Metric Matters

Why: Correct birdsmouth ensures structural integrity and code compliance. Exceeding 1/3 seat depth weakens the rafter.

How: Plumb angle = arctan(pitch/12). Seat angle = 90ยฐ โˆ’ plumb. Max seat depth = rafter depth รท 3. HAP = depth โˆ’ seat depth.

  • โ—4:12 pitch โ†’ 18.43ยฐ plumb; 6:12 โ†’ 26.57ยฐ; 12:12 โ†’ 45ยฐ.
  • โ—IRC and IBC limit seat cut to 1/3 of rafter depth.
  • โ—Minimum HAP typically 2" for insulation clearance.
  • โ—Mark plumb cut first, then seat cut; use speed square.

Birdsmouth Cut Calculator

Plumb & seat angles โ€ข HAP โ€ข Code compliance โ€ข Roof framing

Quick Examples โ€” Click to Load

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2ร—6 Rafter 4:12 Pitch

Standard residential rafter

๐Ÿ˜๏ธ

2ร—8 Rafter 6:12 Pitch

Medium pitch roof

๐Ÿ›๏ธ

2ร—10 Rafter 8:12 Pitch

Steeper residential roof

โ›ช

2ร—12 Rafter 12:12 Pitch

45ยฐ steep roof

๐Ÿญ

Low Slope 3:12

Shallow pitch roof

โš ๏ธ

Maximum Seat Cut

Maximum allowed depth (1/3)

๐Ÿ“ Rafter Size

๐Ÿ  Roof Pitch

:12

Common pitches: 3:12 (shallow), 4:12 (standard), 6:12 (medium), 8:12 (steep), 12:12 (45ยฐ)

๐Ÿงฑ Wall Plate

โœ‚๏ธ Cut Specifications

๐Ÿ“‹ Building Code

Output
Plumb: 18.43ยฐ | Seat: 71.57ยฐ | HAP: 3.667 in | Non-Compliant โœ—

๐Ÿ“Š Results

Plumb Cut Angle

18.43ยฐ

Seat Cut Angle

71.57ยฐ

Seat Cut Length

3.689 in

HAP

3.667 in

Bevel Angle

18.43ยฐ

For compound miter saw

Max Seat Depth

1.833 in

Code limit (1/3 rule)

Code Compliance

โš ๏ธ Non-Compliant

โš ๏ธ Code Warnings

  • Seat depth limited to maximum allowed (1/3 of rafter depth)
  • โš ๏ธ Seat cut depth (1.833") exceeds code maximum (1.833")

Step-by-Step Calculation

=== Birdsmouth Cut Calculation ===
Rafter Size: 1.50" ร— 5.50"
Roof Pitch: 4:12
Wall Plate Width: 3.50"

=== Plumb Cut Angle ===
Plumb Angle = arctan(Pitch/12)
Plumb Angle = arctan(4/12)
Plumb Angle = arctan(0.3333)
Plumb Angle = 18.43ยฐ

=== Seat Cut Angle ===
Seat Angle = 90ยฐ - Plumb Angle
Seat Angle = 90ยฐ - 18.43ยฐ
Seat Angle = 71.57ยฐ

=== Maximum Seat Cut Depth ===
Max Seat Depth = Rafter Depth / 3
Max Seat Depth = 5.50" / 3
Max Seat Depth = 1.833"
Building Code Limit: Maximum 1/3 of rafter depth

=== Seat Cut Length ===
Seat Length = Wall Plate Width / cos(Plumb Angle)
Seat Length = 3.50" / cos(18.43ยฐ)
Seat Length = 3.50" / 0.9487
Seat Length = 3.689"

=== HAP (Height Above Plate) ===
Seat Cut Depth (calculated): 1.833"
Based on HAP requirement: 2.00"
HAP = Rafter Depth - Seat Depth
HAP = 5.50" - 1.833"
HAP = 3.667"

=== Bevel Angle (Compound Miter) ===
Bevel Angle = Plumb Cut Angle
Bevel Angle = 18.43ยฐ
Set your compound miter saw to this angle

๐Ÿ“ˆ Visualizations

๐Ÿ“Š HAP Comparison

๐Ÿ“ Cut Angles

๐Ÿ“ Seat Depth Comparison

Planning estimates only. Verify with a licensed engineer or contractor before construction.

๐Ÿ“ Construction Industry Facts

๐Ÿ“

Plumb cut angle = arctan(Pitch/12); 4:12 = 18.43ยฐ.

โ€” IRC

โœ‚๏ธ

Max seat cut depth = 1/3 of rafter depth per IRC.

โ€” IRC R802

๐Ÿ“

HAP (Height Above Plate) ensures structural depth remains.

โ€” AWC

๐Ÿ 

Named for resemblance to a bird's open mouth.

โ€” Framing tradition

๐Ÿ“‹ Key Takeaways

  • โ€ข Plumb angle = arctan(Pitch/12)
  • โ€ข Seat angle = 90ยฐ โˆ’ plumb angle
  • โ€ข Max seat depth = rafter depth รท 3 (1/3 rule)
  • โ€ข HAP = Height Above Plate = rafter depth โˆ’ seat depth

What is a Birdsmouth Cut?

A birdsmouth cut is a notch cut into the bottom of a rafter where it sits on the wall plate. This cut consists of two parts: the plumb cut (vertical cut that follows the roof pitch) and the seat cut (horizontal cut that sits on the plate). The birdsmouth allows the rafter to sit securely on the wall plate while maintaining proper roof pitch and structural integrity.

๐Ÿ“

Plumb Cut

Vertical cut matching roof pitch

๐Ÿ“

Seat Cut

Horizontal cut for plate contact

๐Ÿ“Š

HAP

Height Above Plate measurement

โœ…

Code Compliance

Verify building code limits

How to Calculate Birdsmouth Cuts

Key Formulas

Plumb Angle = arctan(Pitch/12)

Convert roof pitch to angle

Seat Angle = 90ยฐ - Plumb Angle

Complementary angle for seat cut

Max Seat Depth = Rafter Depth / 3

Building code limit (1/3 rule)

Quick Reference

4:12 pitch: 18.43ยฐ plumb cut
6:12 pitch: 26.57ยฐ plumb cut
8:12 pitch: 33.69ยฐ plumb cut
12:12 pitch: 45.00ยฐ plumb cut

When to Use Birdsmouth Cuts

๐Ÿ 

Residential Roofs

Standard rafter-to-plate connections

๐Ÿ—๏ธ

Framing Projects

Traditional stick framing

๐Ÿ”จ

DIY Roofing

Homeowner roof projects

๐Ÿ“

Precision Cuts

Accurate angle calculations

Birdsmouth Formulas

Plumb: ฮธ = arctan(Pitch/12)
Seat: ฮฑ = 90ยฐ โˆ’ ฮธ
Seat length: L = Plate Width / cos(ฮธ)
Max seat depth: D_max = Rafter Depth / 3

Building Code Requirements

CodeMax Seat DepthMin HAPDescription
International Residential Code33.33%2"Standard residential code - max 1/3 depth cut
International Building Code33.33%2"Commercial building code
Conservative (25%)25%2.5"More conservative approach

โš ๏ธ Important: Max seat cut depth is typically 1/3 of rafter depth. Verify local codes before cutting.

Common Pitch Angles

3:12 โ†’ 14.04ยฐ plumb
4:12 โ†’ 18.43ยฐ plumb
6:12 โ†’ 26.57ยฐ plumb
8:12 โ†’ 33.69ยฐ plumb
12:12 โ†’ 45.00ยฐ plumb

Frequently Asked Questions

Why is it called a birdsmouth?

The notch resembles a bird's open mouth when viewed from the sideโ€”the plumb and seat cuts form a V shape.

Can I cut deeper than 1/3?

Generally no. IRC and IBC limit seat depth to 1/3 of rafter depth. Deeper cuts weaken the rafter.

What is HAP used for?

HAP (Height Above Plate) ensures adequate rafter depth remains for structural strength and insulation clearance.

Cutting Tips

  • โ€ข Mark plumb cut first, then seat cut
  • โ€ข Use a speed square or rafter square for accuracy
  • โ€ข Cut seat depth slightly shallow and test fit
  • โ€ข Verify local building codes before cutting
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