The Birdsmouth Calculator simplifies the complex process of calculating the dimensions needed to make precise cuts on rafters for them to fit perfectly onto the wall plates. By inputting basic information about the roof’s dimensions and the desired pitch, the calculator outputs the exact measurements for the birdsmouth cut, rafter length, and other essential details. This not only saves time but also reduces the margin for error, ensuring a structurally sound roof.
Formula of Birdsmouth Calculator
To understand the outputs provided by the Birdsmouth Calculator, it’s essential to grasp the underlying formulas. These mathematical expressions take into account the width of the building, the thickness of the ridge board, the roof pitch angle. The overhang distance, and the minimum depth required for the rafter. Here are the key formulas used:
- Rafter Run (X):
X = (W - tridge board) / 2 - Rafter Rise (Y):
Y = X × tan(θ) - Rafter Segment Length (Lsegment):
Lsegment = X / cos(θ) - Total Rafter Length (Lrafter):
Lrafter = Lsegment + O / cos(θ) - Minimum Ridge Board Depth (dmin ridge board):
dmin ridge board = dmin rafter / cos(θ)
Variables:
W– Building width (ft)tridge board– Thickness of the ridge board (ft)θ– Roof pitch angle (degrees)O– Overhang distance (ft)dmin rafter– Minimum depth required for the rafter (ft) (refer to building codes for your area)
General Terms and Conversion Table
| Term | Description | Example Values / Conversions |
|---|---|---|
| Building Width (W) | The total horizontal distance across the building that the roof will cover. | 20 ft, 25 ft, 30 ft |
| Ridge Board Thickness (tridge board) | Thickness of the central board at the apex of the roof where the two slopes meet. | 1 in, 1.5 in, 2 in |
| Roof Pitch Angle (θ) | The angle formed by the rise of the roof to the horizontal run. A key factor in determining the slope of the roof. | 15° (low slope), 30° (standard slope), 45° (steep slope) |
| Overhang Distance (O) | The length by which the roof extends beyond the walls of the building. | 1 ft, 1.5 ft, 2 ft |
| Minimum Rafter Depth (dmin rafter) | The depth of the rafter required to support the weight of the roof, which can vary based on building codes and the span of the roof. | 5.5 in (2×6), 7.25 in (2×8), 9.25 in (2×10) |
| Rafter Run (X) | Half the building width minus half the thickness of the ridge board, representing the horizontal distance from the top plate to the center of the roof. | Calculated based on W and tridge board |
| Rafter Rise (Y) | The vertical distance from the top plate to the apex of the roof, dependent on the roof pitch angle. | Calculated based on X and θ |
| Rafter Segment Length (Lsegment) | The length from the top plate to the ridge board, not including the overhang. | Calculated based on X and θ |
| Total Rafter Length (Lrafter) | The total length of the rafter, including the overhang. | Calculated based on Lsegment and O |
Example of Birdsmouth Calculator
Consider a scenario where you need to calculate the birdsmouth cut for a roof with a 25-foot wide building. A 1-foot ridge board thickness. A 30-degree roof pitch, a 2-foot overhang, and a minimum rafter depth of 9 inches (0.75 feet). Using the formulas provided. The calculator would output the precise measurements for each component of the rafter, ensuring accurate and reliable cuts.
Most Common FAQs
A birdsmouth cut is a notch cut into a rafter that allows it to sit flush with the top plate of a wall. Providing stability and support to the roof structure.
The roof pitch angle can be calculated by measuring the rise over a 12-inch run. Then finding the corresponding angle.