Birdsmouth Heel Height and Seat Cut Calculator

The Birdsmouth Heel Cut Calculator determines the heel cut for a rafter based on the seat cut, roof pitch, and rafter size. It ensures that the notch size remains within safe limits to prevent the weakening of the rafter.

Birdsmouth Maximums and Minimums

If you are cutting a birdsmouth in your rafter, your local building code will limit the depth of the notch
into the rafter. It can be the rafter size divided by 3 or whatever the local requirement is. The limiting factor can be the minimum size of the seat cut on the wall. The International Residential Code stipulates a minimum bearing of 1 1/2 inches on the top plate, and here in our location, the rafter requires a minimum of 3 inches on the top plate.

It's important to note that while the IRC provides these prescriptive measures, local building codes or specific engineering requirements may impose additional restrictions or considerations. Always consult with a qualified professional or local building authority to ensure compliance with all applicable codes and standards.

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Calculator

1. enter the vertical rise of the roof per 12 inches of horizontal run
2. the length of the seat cut in inches (e.g. 3 1/2)
3. the size of the rafter in inches (e.g. 9 3/8)

Results

1. the length of the heel cut in inches
2. the vertical depth of the cut into the rafter (notch depth) in inches
3. the remaining depth of the rafter measured from the top of the rafter to the deepest point of the birdsmouth notch into the rafter in inches

Birdsmouth Seat Cut Calculator - Formulas

The birdsmouth cut is calculated using trigonometric formulas based on the roof pitch and rafter dimensions.

1. Roof Pitch Angle Calculation

The pitch angle \( \theta \) is calculated using the roof rise per 12 inches of run: \[ \theta = \tan^{-1} \left( \frac{\text{Rise}}{12} \right) \]

2. Heel Cut Calculation

The heel cut is determined using the seat cut and the roof pitch: \[ \text{Heel Cut} = \sqrt{(\text{Seat Cut} \times \text{Slope})^2 - \text{Seat Cut}^2} \] where \[ \text{Slope} = \frac{\sqrt{p^2 + 12^2}}{12} \]

3. Notch Size Calculation

The notch size is the horizontal projection of the heel cut: \[ \text{Notch Size} = \text{Heel Cut} \times \cos(\theta) \]

4. Remaining Rafter Depth Calculation

The remaining rafter depth after the notch is cut: \[ \text{Remaining Depth} = \text{Rafter Size} - \text{Notch Size} \]

5. Height Above Plate Calculation

The height above the wall plate is: \[ \text{HAP} = \frac{\text{Rafter Size}}{\cos(\theta)} - \text{Heel Cut} \]

Example Calculation

Given the following values:

• Roof Pitch: \(6:12\) (Rise = 6 inches per 12 inches run)
• Seat Cut: \(3\) inches
• Top Plate Width: \(3 \frac{1}{2}\) inches
• Rafter Size: \(9 \frac{1}{4}\) inches

Calculations:

• Pitch Angle: \[ \theta = \tan^{-1} \left( \frac{6}{12} \right) = \tan^{-1}(0.5) \approx 26.57^\circ \]
• Slope: \[ \text{Slope} = \frac{\sqrt{6^2 + 12^2}}{12} = \frac{\sqrt{36 + 144}}{12} = \frac{\sqrt{180}}{12} \approx 1.118 \]
• Heel Cut: \[ \text{Heel Cut} = \sqrt{(3 \times 1.118)^2 - 3^2} \] \[ = \sqrt{(3 \frac{3}{8})^2 - 3^2} = \sqrt{11 \frac{1}{4}} \approx 2 \frac{3}{16} \text{ inches} \]
• Notch Size: \[ \text{Notch Size} = 2 \frac{3}{16} \times \cos(26.57^\circ) \] \[ = 2 \frac{3}{16} \times \frac{223}{250} \approx 1 \frac{7}{8} \text{ inches} \]
• Remaining Depth: \[ \text{Remaining Depth} = 9 \frac{1}{4} - 1 \frac{7}{8} = 7 \frac{3}{8} \text{ inches} \]
• Height Above Plate: \[ \text{HAP} = \frac{9 \frac{1}{4}}{\cos(26.57^\circ)} - 2 \frac{3}{16} \] \[ = \frac{9 \frac{1}{4}}{0.894} - 2 \frac{3}{16} \approx 8 \frac{1}{8} \text{ inches} \]

Point-Form Summary

• Heel Cut: \(2 \frac{3}{16}\) inches
• Notch Size: \(1 \frac{7}{8}\) inches
• Remaining Depth: \(7 \frac{3}{8}\) inches
• Height Above Plate: \(8 \frac{1}{8}\) inches

THORVALD 6-in-1 Carpenter Square 7 inch (1/16" Precision) T Square Multi-Purpose Carpenter Tools : Wrench, Square, Protractor, Ruler, Marking Gauge, Drill Gauge, Includes 2-in-1 Carpentry Pencil >