The Basic Geometry
A common rafter forms a right triangle. The run is the horizontal leg (half the building span minus half the ridge thickness). The rise is the vertical leg (determined by the pitch). The rafter itself is the hypotenuse.
Step 1: Find the Run
The run for a common rafter is half the building span minus half the ridge board thickness:
Step 2: Find the Rise
Multiply the run by the pitch ratio. For a 6/12 pitch, the ratio is 6/12 = 0.5:
This is also the ridge height above the wall plate.
Step 3: Calculate Rafter Length
The rafter length along the slope is the run divided by the cosine of the roof angle (or equivalently, the hypotenuse of the rise/run triangle):
Step 4: Add the Overhang
The overhang extends past the wall. Its length along the slope is the horizontal overhang divided by the cosine of the roof angle:
Step 5: The Birdsmouth
The birdsmouth is a notch cut into the rafter where it sits on the wall plate. It has a horizontal seat cut (bearing on the plate) and a vertical plumb cut. The HAP (height above plate) is the material remaining above the seat cut — typically 3-1/2" for a 2x6 rafter to maintain at least 2/3 of the rafter depth.
Cutting Angles
- Plumb cut (at ridge) — Set your speed square to the roof pitch. For 6/12, mark at 26.6° from the rafter edge.
- Seat cut (birdsmouth horizontal) — Perpendicular to the plumb cut. This is the level line at the plate.
- Tail cut — Another plumb cut at the end of the overhang (can be plumb or square depending on fascia detail).
Use the Calculator
The rafter calculator computes all of this from just two inputs: building span and pitch. It shows a real-time roof cross-section diagram with all dimensions labeled.