Birdsmouth Cut Calculator: Rafter Seat and Heel

A birdsmouth cut calculator determines the seat and heel dimensions where a pitched rafter rests on a wall plate, using the rafter’s plumb-cut depth and the required bearing width. Enter those two measurements to get the heel depth and the remaining rafter depth at the seat; confirm the result against your framing plan and local requirements before cutting.

Formula

This calculator uses the geometry of the plumb cut to estimate how much rafter depth is consumed by the horizontal seat cut. The rafter depth is measured parallel to the rafter’s long edges, while seat width is measured horizontally across the wall plate.

• d = rafter depth at the plumb cut, in inches.
• w = horizontal seat width, in inches.
• h = heel depth, the vertical depth removed by the seat, in inches.
• r = remaining rafter depth at the seat, in inches.

The formula is h = d − w × √(1 + (d ÷ 12)²), followed by r = d − h. The factor 12 converts the rise-per-foot slope convention into a dimensionless ratio when d and w are entered in inches. The expression accounts for the sloping rafter edge: the horizontal seat width corresponds to a slightly longer distance measured along the rafter.

This is a geometric estimate, not a structural design calculation. It assumes the dimensions are entered consistently, the rafter has a straight edge, and the seat is level. The calculator does not determine an appropriate bearing width, allowable notch size, lumber capacity, or whether a particular roof design is safe.

Worked Example

Using the default values, the rafter depth is 7.25 inches and the seat width is 3.5 inches. First calculate the slope correction:

√(1 + (7.25 ÷ 12)²) = √(1 + 0.3650) ≈ 1.1683.

Then find the heel depth:

h = 7.25 − 3.5 × 1.1683 ≈ 7.25 − 4.0891 = 3.16 inches.

The remaining depth is:

r = 7.25 − 3.16 = 4.09 inches.

Results are rounded to two decimal places. A physical layout can differ slightly because of rounding, saw kerf, pencil-line thickness, and measurement technique, so mark the cut from the actual layout rather than treating a rounded display as a precision guarantee.

What a Birdsmouth Cut Does

A birdsmouth is a notch near the lower end of a rafter. Its horizontal portion, called the seat cut, bears on the top of a wall plate. Its vertical portion, called the heel or plumb cut, meets the outside face or another specified reference point. Together, the cuts help the rafter sit in position instead of sliding off a flat support.

“Birdsmouth” can refer to the whole notch, while “seat” and “heel” describe its two faces. These are not interchangeable dimensions. The seat width is a horizontal bearing dimension; heel depth is measured vertically. The calculator reports the heel depth implied by its inputs, not a recommended notch size.

A related misconception is that a wider seat always means a safer rafter. Wider bearing may be useful, but a larger notch also removes more wood. The adequacy of the rafter depends on loads, span, lumber grade and species, connections, and the applicable design requirements—not on one measurement alone.

How to Measure and Use the Result

1. Identify the rafter’s plumb-cut depth at the location where the notch will be laid out. Do not substitute the board’s nominal size: a piece sold as a 2-by-8 is commonly smaller than its nominal dimensions, and actual dimensions vary.
2. Choose the seat width from the framing detail or applicable construction plan. Measure it horizontally, not along the sloped top edge of the rafter.
3. Enter both measurements in inches. If working in millimetres, convert both values to the same unit before calculating; 1 inch equals 25.4 millimetres.
4. Use the heel-depth output to check the vertical cut layout, and the remaining-depth output to see how much rafter depth remains at the notch.
5. Transfer the layout to the board with a framing square or another suitable measuring method, then verify the fit against the actual wall plate before repeating the cut on other rafters.

For a metric layout, multiply an inch result by 25.4 to obtain millimetres. For example, 3.16 inches is about 80.3 mm. Do not mix inches and millimetres within the same calculation: the formula’s fixed 12 is in inches, so using metric inputs without adapting the formula gives an incorrect result.

Common Errors and Limitations

• Using nominal lumber dimensions: Measure the actual board. A nominal label is not the finished depth or thickness.
• Confusing vertical depth with board depth: The rafter depth is measured across the board’s profile; the seat is horizontal, and the heel is vertical.
• Entering seat length along the rafter: The formula expects horizontal seat width. A length measured along the slope is a different quantity.
• Assuming the output sets the notch limit: It does not. Structural rules and project-specific details may limit cuts, and requirements vary with the framing system and jurisdiction.
• Cutting to rounded values: Keep the unrounded calculation for layout where possible and account for the saw kerf so the cut does not extend beyond the marked lines.

The expression is intended for an ordinary level seat and a straight rafter profile. It does not handle a sloped bearing surface, compound cuts, irregular lumber, overhang layout, ridge connections, or unusual framing geometry. It also cannot establish whether the remaining section is strong enough. If the design is unclear, use the project drawings or seek guidance from a qualified building professional rather than increasing or deepening the notch by guesswork.

Frequently Asked Questions

What measurements do I need for a birdsmouth cut calculator?
For this calculator, enter the rafter’s actual depth at the plumb cut and the horizontal width of the seat. Use the same unit for both measurements.

How deep should a birdsmouth cut be?
There is no single correct depth for every roof. This calculator estimates heel depth from your rafter depth and seat width; the design must also satisfy the applicable structural details and notch limits.

Is seat width the same as heel depth?
No. Seat width is the horizontal distance bearing on the plate. Heel depth is vertical. The slope of the rafter means the two dimensions are not generally equal.

Can I enter metric measurements?
Not directly in this version, because its formula uses inches and a 12-inch slope conversion. Convert millimetres to inches first, or use a version formulated consistently in metric units.

Does the calculator tell me if my rafter is structurally safe?
No. It calculates geometry only. It does not assess roof loads, lumber properties, span, fasteners, or code requirements.

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in d | Rafter depth at plumb cut | in | 7.25 | 0
in w | Seat width | in | 3.5 | 0
out h | Heel depth | in | d - w * sqrt(1 + (d / 12)^2) | 2
out r | Remaining depth at seat | in | d - h | 2