Rafter framing starts with geometry, but geometry alone does not approve a roof. Pitch, span, ridge thickness, overhang, and a centered-ridge assumption can produce useful common and hip rafter prompts, while adopted code, span tables, roof loads, species, grade, ties, bearing, bracing, uplift, roof assembly, permits, and jobsite safety remain separate source gaps.
This guide explains the local math behind common, hip, and valley rafter prompts, the bird's mouth source boundary, and overhang geometry. Treat it as context for review with current IRC/AWC references, field layout, manufacturer instructions, and qualified structural and safety reviewers before ordering, cutting, installing, or accessing a roof.
Unit Run and Unit Rise
Roof pitch is expressed as inches of rise per 12 inches of horizontal run. A 6/12 pitch rises 6 inches for every 12 inches of run. The unit run is always 12 inches for a common rafter. The unit rise is the pitch number (4, 6, 8, etc.). The unit rafter length (the hypotenuse) is the square root of (12² + rise²). For a 6/12 pitch: sqrt(144 + 36) = sqrt(180) = 13.416 inches per foot of run.
Total rafter length prompt equals the unit rafter length times the number of feet of run. For a 24-foot wide building with a centered ridge, each common rafter has a run near 12 feet before ridge-board thickness and field layout adjustments. At 6/12 pitch, the rafter length prompt is about 13.416 times the run in feet. Add the overhang prompt separately after converting horizontal overhang to slope length.
Rafter Length Calculator
Calculate common, hip, and valley rafter lengths with bird's mouth cuts and roof area.
Bird's Mouth Layout
The bird's mouth is the notch where a rafter bears on the wall top plate. The app treats a one-third-depth comparison as a source-review prompt, not as code compliance, bearing approval, HAP approval, connection approval, ridge-system approval, or cutting authorization.
Actual acceptability depends on the adopted code edition and amendments, rafter species and grade, spacing, roof loads, ridge board or ridge beam condition, rafter ties, bracing, uplift connections, bearing, fasteners, and the approved plans. Use current IRC/AWC references and qualified review before relying on any notch or cut geometry.
Hip and Valley Rafters
Hip and valley rafters run diagonally from the ridge to the plate corner (hip) or from the plate intersection to the ridge (valley). Because they run at 45 degrees in plan view, their unit run is not 12 inches but rather the diagonal of a 12-inch square: sqrt(12² + 12²) = 16.97 inches. The unit hip/valley rafter length is sqrt(16.97² + rise²). For a 6/12 pitch: sqrt(288 + 36) = sqrt(324) = 18 inches per foot of common run.
Hip and valley prompts also hide source gaps. Compound cheek cuts, backing or drop, jack rafters, unequal pitches, overhang geometry, roof intersections, ridge and valley details, and product-specific installation requirements must be resolved from the actual roof plan and qualified field review.
Overhang and Tail Cuts
The rafter tail extends beyond the building line to form the eave overhang. Its length is calculated the same way as the main rafter: overhang run times the pitch multiplier. A 16-inch horizontal overhang at 6/12 pitch has a rafter tail length of (16/12) × 13.416 = 17.9 inches measured along the rafter. The tail cut at the end can be plumb (for a vertical fascia), square (perpendicular to the rafter), or a combination.
Fascia board thickness, subfascia, soffit plane, HAP, bearing, ridge height, and roof plan details must be reconciled in the field. A pattern-rafter review is a field quality step, but it is still not a substitute for adopted-code, structural, permit, manufacturer, or site-safety review.