TradesHow this works
A common rafter runs from the top plate up to the ridge. Its length along the slope is just the horizontal run scaled by the pitch, so a steeper roof gives a longer rafter for the same run. The run is measured to the center of the ridge, then shortened by half the ridge board so the two rafters meet cleanly at the peak.
The two cuts follow the same angle. The plumb cut at the ridge sits at the slope angle off level, and the level seat cut of the birdsmouth is its complement. Set the rise and 12 on a framing square and both cuts come straight off it. This tool gives you the length, the cuts, and the stock board length that covers a rafter with the least waste.
Common questions
How do you find rafter length from run and pitch?
Multiply the horizontal run by the slope multiplier for the pitch, which is the square root of the rise squared plus twelve squared, divided by twelve. A 12 ft run at a 6 in 12 pitch gives a rafter about 13 ft 5 in along the slope before the overhang.
What are the plumb cut and the seat cut?
The plumb cut is the vertical cut where the rafter meets the ridge, and it sits at the slope angle off level. The seat cut is the level cut of the birdsmouth that rests on the top plate, and it is the complement, ninety degrees minus the slope angle. On a framing square you mark the rise on the tongue and twelve on the body.
Does this size the rafter for the load?
No. This gives the length and the cut angles so you can lay out and buy the boards. Whether a given rafter depth and species actually carries the roof load is a span-table or engineering question, separate from the geometry here.
Sources: Common-rafter trigonometry (evergreen geometry) · Stock lumber lengths: standard even 2 ft framing increments. Engine version 1.0.0. Risk tier 1.