Birdsmouth cut calculator

What a birdsmouth cut is and what the response contains

A birdsmouth cut, also called a birds-mouth joint, is the right-angled notch cut into the underside of a rafter so the member sits flat on the wall plate while the tail continues past the eave. The notch has a level seat that bears on the top of the plate and a plumb heel that meets the outer face of the plate. There is no lumber SKU catalogue, no common-rafter length, and no code span table baked into the core number: you get geometric cut dimensions so you can mark the square, add waste, and check the one-third depth rule of thumb after the pure notch is known. This calculator takes rafter_width as the stock depth measured square across the board, roof_pitch as the rise component of an X-over-twelve pitch, and wall_plate_width as the horizontal plate bearing width. It returns the parsed inputs, a pitch_label such as six slash twelve, the pitch angle in degrees, the unit rise and pitch factor, the horizontal_seat equal to the plate width, the heel_height of the plumb cut, the along-rafter seat_length, the cut_depth measured perpendicular into the rafter from the bottom edge, the remaining_depth of stock after the notch, a depth_ratio of cut to rafter width, a unit tag, the precision used, a method tag, and a short formula string you can audit. Rejected cases include missing fields, non-finite values, magnitudes above the supported ceiling, a non-positive rafter width, a roof pitch that is not a positive number, a non-positive plate width, and a combination that would cut through the entire rafter depth.

How pitch, plate width, and precision stay reproducible

Prefer rafter_width for the stock depth, with aliases rafter_depth, depth, stock_width, and D so forms and query strings can reuse the same contract. Roof_pitch accepts roof_pitch plus aliases pitch, rise, pitch_rise, and X, always as the rise component of an X-over-twelve pitch, never as degrees alone and never as a unitless slope without the twelve base. Wall_plate_width accepts wall_plate_width plus plate_width, plate, top_plate, and W; it must be strictly positive so a real seat can be defined. Optional precision, with aliases decimals and dp, chooses decimal places for every numeric field in the response, defaulting to four and capped at fifteen so JSON goldens stay stable. Computation forms unit_rise as pitch divided by twelve, builds pitch_factor as the square root of one plus unit-rise squared, takes sine as unit_rise over that factor and cosine as one over that factor, sets seat_length to plate width divided by cosine, and sets cut_depth to plate width times sine. Remaining depth is rafter width minus cut depth, and depth_ratio is cut depth over rafter width so you can compare against a site rule of thumb without re-deriving trigonometry. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline.

Where birdsmouth layout fits in DIY, trade quotes, and software

Framers and small contractors use the same numbers to mark the framing square on site, then compare remaining_depth against local practice and the common one-third rule before they commit the saw. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a phone check on the plate to an automated pipeline without changing the mathematical result.