S L B H α
Common Pitches
inches per 12" run
usually 12
full width
eave extension
Results
Pitch 6:12
Pitch Angle (α) 26.6°
Line Length (L)
Total w/ Overhang
Plumb Cut Angle 26.6°
Level Cut Angle 63.4°
Total Rise

Common Pitch Reference Table

Pitch Angle Slope % Multiplier Plumb Cut Level Cut Type

How Rafter Length Is Calculated

The rafter line length (L) is the distance along the rafter from the ridge to the wall's top plate — not the full board length. It's found using the Pythagorean theorem: L = √(Run² + Rise²), or equivalently, run × the pitch multiplier.

Pitch Multiplier

Each pitch has a multiplier (√(1 + (rise/run)²)) that converts horizontal run into rafter length. For a 6:12 pitch the multiplier is 1.118 — meaning for every 12" of run, the rafter is 13.42" long. Multiply the building's half-span by the multiplier to get the line length.

Overhang

The overhang (S) extends the rafter past the plate. The along-rafter overhang length = horizontal overhang × pitch multiplier. This is added to the line length to get the full board cut length before the plumb (tail) cut is made.

Plumb and Level Cuts

The plumb cut (at the ridge) is vertical — its angle from vertical equals the pitch angle. The level (seat) cut at the birdsmouth is horizontal. Both angles are derived from the same pitch ratio: plumb cut = atan(rise/run), level cut = 90° minus plumb cut.