Figuring rafters — both their length and the angle of each cut — is the basic math problem of stick-frame roof construction. Every rafter has three angled cuts: plumb at the ridge, seat at the wall plate (part of the bird's mouth), and tail at the eave. Each angle is determined by the roof pitch, and the math is the same for all three. The same math also serves as a birdsmouth cut calculator (or birdsmouth calculator, also written birds mouth cut calculator in some references) — the bird's mouth notch combines the seat cut angle and the heel cut angle on the rafter's underside, both of which are derived from the pitch.
A rafter calculator with birdsmouth functionality (sometimes searched as a rafter length calculator with birdsmouth) gives you both the rafter length and the bird's mouth dimensions in one calculation. The figuring rafter angles question reduces to: plumb cut = 90° minus pitch angle; seat cut = pitch angle; tail cut = whichever you pick (usually plumb to match the ridge). For an angle rafter on a 6/12 pitch (26.57°): plumb cut at 63.43°, seat cut at 26.57°, tail cut at 63.43° if plumb.
The plumb cut is 90° minus the pitch angle. The seat cut equals the pitch angle. The tail cut is whichever you pick — usually plumb to match the ridge.
Plumb cut at the ridge
The plumb cut at the upper end of the rafter is the angle that produces a vertical face when the rafter is in place. Mathematically, it is 90° minus the pitch angle measured from the rafter's long axis.
For a 6/12 pitch (26.57°), the plumb cut is 63.43° from the rafter's long axis. For a 4/12 (18.43°) it is 71.57°. For a 12/12 (45°) it is 45°.
Seat cut at the wall plate
The seat cut is the horizontal surface of the bird's mouth — the part that bears on the wall plate. Its angle is the pitch angle itself: 26.57° for 6/12, 18.43° for 4/12, 45° for 12/12.
In framing-square shorthand, the seat cut is laid out by holding the square with the rise on the tongue and 12 on the blade, lining up against the rafter's top edge.
Tail cut at the eave
The tail cut at the lower end of the rafter is whichever angle you choose for the eave detail. The two common options:
Plumb tail — same angle as the ridge plumb cut. Produces a vertical face at the rafter end, ideal for fascia attachment.
Square tail — perpendicular to the rafter's long axis. Used for exposed-tail Craftsman-style overhangs or where the rafter ends are decoratively shaped.
Need to run the numbers?Use the free roof pitch calculator on the home page to convert pitch to angle, calculate rafter length, or estimate roof area in any unit.