Birdsmouth Cut Calculator: Seat Cut, Heel Depth, and Rafter Length
Enter your building width, roof pitch, seat cut length, and overhang to get every birdsmouth notch dimension in one step. The calculator gives you the seat cut length, heel cut depth, rafter run, rafter rise, total rafter length, height above plate, and the IRC minimum rafter depth. Switch between metric and imperial, and the show-your-work panel explains each calculation with your actual numbers.
Formula
Worked example
For a 24 ft wide building, 1.5 in ridge board, 6:12 pitch (26.57 deg), 3.5 in seat cut, and 12 in overhang: rafter run X = (288 - 1.5) / 2 = 143.25 in. Rafter rise Y = 143.25 x 0.5 = 71.63 in. Total rafter length L = (143.25 + 12) / 0.8944 = 173.6 in. Heel cut depth c_h = 3.5 x 0.5 = 1.75 in. Minimum rafter depth = 3 x 1.75 = 5.25 in (2x6 is sufficient).
What is a birdsmouth cut?
A birdsmouth cut is a triangular notch carved into the underside of a common rafter at the point where the rafter sits on the top plate of the wall. The notch has two faces: a seat cut (horizontal) that rests flat on the wall plate, and a heel cut (vertical, also called the plumb cut at the wall) that butts against the outer edge of the plate. Together they let the rafter bear solidly on the wall while its upper face remains flush with the ridge and the lower face aligns with the fascia or soffit.
Every common rafter in a gable or hip roof needs a birdsmouth where it crosses the top plate. Without it, the rafter would bear only on its corner, concentrating load on a narrow edge and making alignment impossible. The depth of the notch is strictly limited by building codes to preserve the structural integrity of the rafter member.
How to use this calculator
Select your unit system (imperial or metric). Enter the building width as the total exterior dimension from one wall face to the other. Enter the actual ridge board thickness (1.5 in for standard dimensional lumber). Choose your pitch input format, then enter the pitch: X:12 ratio, degrees, or percent slope. Enter the seat cut length, which is the horizontal dimension of the notch that sits on the wall plate (for a standard 2x4 plate this is 3.5 in, for a 2x6 plate it is 5.5 in). Finally, add the eave overhang distance.
The calculator immediately returns the heel cut depth, rafter run, rafter rise, total rafter length (including overhang), the pitch angle in degrees, the height above plate, and the IRC minimum rafter depth. The show-your-work panel walks through each formula with your actual numbers so you can verify the layout on the rafter itself.
Birdsmouth cut formulas explained
All formulas derive from the roof pitch angle theta. The rafter run (X) is the horizontal distance from the wall centerline to the face of the ridge board: X = (W - t) / 2, where W is the building width and t is the ridge board thickness. The rafter rise is Y = X * tan(theta). The slant length of the rafter from wall to ridge is X / cos(theta), and the total rafter length adds the overhang tail: L = (X + O) / cos(theta).
The heel cut depth (c_h) is the vertical dimension of the notch, and it depends on both the seat cut length and the pitch: c_h = c_s * tan(theta). For a 6:12 pitch (theta = 26.57 deg) with a 3.5 in seat cut, the heel cut depth is 3.5 * 0.5 = 1.75 in. The minimum rafter depth required to keep the notch within the IRC one-third rule is simply d_min = 3 * c_h.
IRC building code limits for birdsmouth depth
The International Residential Code (IRC, Section R802.7) limits the depth of a birdsmouth notch to one-third of the actual rafter depth. If a rafter is 5.5 in deep (nominal 2x6), the maximum allowable heel cut depth is 5.5 / 3 = 1.83 in. Exceeding this limit weakens the rafter at the bearing point, which is the highest-stress location in a common rafter.
This calculator enforces the rule by calculating d_min = 3 * c_h: the rafter you choose must have an actual depth greater than or equal to this value. If the result pushes beyond 5.5 in (2x6), the framer must step up to a 2x8, 2x10, or 2x12. The reference table above lists the maximum allowable heel cut depth for each common lumber size.
Some jurisdictions adopt earlier IRC editions with slightly different ratios, and engineered lumber (LVL) may have its own manufacturer limits. Always verify with your local building department and the lumber manufacturer for structural applications.
Marking the cuts on the rafter
Once you have the heel cut depth and seat cut length from this calculator, mark the rafter as follows. Lay the rafter on a flat surface with the crown edge up. Using a speed square or rafter square, draw the plumb line at the pitch angle at the heel cut location. From the foot of the plumb line, measure along the bottom edge the seat cut length and draw the level line (the seat cut). The notch to remove is the triangle bounded by these two lines and the bottom edge of the rafter. Verify that the heel cut depth you measured matches the calculator output before cutting.
The plumb cut at the ridge end and the tail cut at the overhang end are both also cut at the same pitch angle. The ridge cut is simply a plumb line; the tail cut is a plumb line at the desired fascia location. Once one rafter is cut and test-fitted, use it as a template for all the remaining common rafters in the run.
Common lumber sizes and maximum seat cut for IRC compliance
| Nominal size | Actual depth (in) | Max heel cut depth (in) | Seat cut at 6:12 pitch (in) |
|---|---|---|---|
| 2x6 | 5.5 | 1.83 | 3.20 |
| 2x8 | 7.25 | 2.42 | 4.20 |
| 2x10 | 9.25 | 3.08 | 5.36 |
| 2x12 | 11.25 | 3.75 | 6.51 |
The IRC requires the birdsmouth notch depth to be no more than one-third of the rafter depth. Actual lumber dimensions are smaller than nominal.
Frequently asked questions
What is the maximum birdsmouth cut depth allowed by code?
The IRC limits the birdsmouth notch depth to one-third of the actual rafter depth. For a 2x6 rafter (actual depth 5.5 in), the maximum heel cut depth is 1.83 in. For a 2x8 (7.25 in actual), it is 2.42 in. This calculator shows the minimum rafter depth needed for your seat cut and pitch, so you can select the right lumber size.
How do I calculate heel cut depth from a 6:12 pitch and a 3.5 in seat cut?
Multiply the seat cut length by tan(pitch angle). A 6:12 pitch has an angle of arctan(6/12) = 26.57 degrees. Tan(26.57 deg) = 0.5, so heel cut depth = 3.5 x 0.5 = 1.75 in. A standard 2x6 rafter (5.5 in actual depth) allows a maximum of 1.83 in, so 1.75 in is within code.
What is the difference between a seat cut and a heel cut?
The seat cut is the horizontal face of the birdsmouth notch that bears flat on the wall plate. The heel cut is the vertical face of the notch that butts against the outer edge of the plate. Together they form a right-angle notch. The seat cut length is usually set to match the plate width (3.5 in for 2x4, 5.5 in for 2x6 plates). The heel cut depth is calculated from the seat cut and the pitch angle.
Does the birdsmouth cut affect rafter strength?
Yes. Cutting a notch reduces the effective depth of the rafter at the bearing point, which is the location of highest bending stress in a common rafter. This is why the IRC caps the notch at one-third of the rafter depth. Deeper notches require stepping up to a larger rafter size. Always follow the code limit and consult a structural engineer for unusual spans or loading conditions.
How do I find rafter length using this calculator?
Enter the building width, ridge board thickness, roof pitch, and eave overhang. The calculator returns the total rafter length along the slope, including the overhang tail. This is the minimum length of lumber you need to order. Add a few inches to allow for final trimming at the ridge and fascia.
What seat cut length should I use for a 2x4 wall plate?
Use 3.5 in for a 2x4 wall (actual dimension). For a 2x6 wall plate, use 5.5 in. The seat cut should span the full width of the top plate so the rafter bears on the entire plate surface, maximising load transfer and preventing splitting of the plate edge.