Birdsmouth Cut Calculator

A birdsmouth is the L-shaped notch cut into the underside of a rafter so it can bear on the top plate of a wall while the rafter itself stays at the roof angle. It is made of two intersecting cuts: a level seat cut that sits flat on the plate and transfers load vertically into the wall, and a plumb heel cut that registers against the outside face of the plate and stops the rafter from sliding outward. Both cut lengths follow from the roof angle, the arctangent of the pitch over 12. For a seat depth d and angle A, the plumb cut face measures d divided by cos A and the seat cut measures d divided by sin A, so a 1.5-inch seat on a 6/12 roof at 26.57 degrees yields a 1.677-inch plumb face and a 3.354-inch seat. The governing limitation is how much wood the notch removes. The remaining depth above the notch carries the bending stress in the rafter, and the notch corner is where splits start. Standard practice, reflected in the residential code provisions on notching rafters, is to keep the seat cut to no more than one third of the rafter depth: about 1.83 inches on a 2x6 at 5.5 inches actual, and 2.42 inches on a 2x8 at 7.25 inches. Full bearing on the plate is the other constraint, since a seat cut shorter than the plate width leaves the rafter perched on an edge. Engineered members such as LVL, LSL, and I-joists must never be notched this way without the manufacturer's written approval.

The birdsmouth predates modern framing by centuries; European and Asian timber-frame roofs used seated bearing notches where common rafters met a wall plate long before dimensional lumber existed, and the joint appears in traditional carpentry alongside mortise-and-tenon and lap connections. What changed in North America was the layout method rather than the joint. When balloon and later platform framing displaced heavy timber work in the nineteenth century, roofs came to be built from repetitive sawn rafters that had to be laid out quickly and identically, and that job fell to the steel framing square. The carpenter's steel square is generally credited to Silas Hawes, a blacksmith in South Shaftsbury, Vermont, who patented a version around 1819; later manufacturers stamped rafter tables directly onto the blade so a framer could read common, hip, and jack rafter lengths per foot of run without computing anything. Instructional literature followed, most notably Frederick T. Hodgson's widely reprinted nineteenth-century books on the steel square and its uses, which taught stepping the square along the rafter with the rise on the tongue and 12 on the blade to scribe plumb and seat lines. Albert Swanson's Speed Square, introduced in the 1920s, compressed the same pitch geometry into a triangular tool that stayed in a carpenter's pouch. The one-third depth limit is the newer element, arriving with codified notching and span rules in the model residential codes of the twentieth century.