Rafter calculator

How the rafter length is worked out

The run is half the building's width, outside of wall to outside of wall. Along the measuring line, which runs through the outside corner of the seat cut, the rafter is the run times √(12² + rise²) ÷ 12. Half the ridge board's thickness comes off at the top, measured level and then along the slope; the overhang, measured level from the wall, goes on at the tail the same way. Cut the ridge end plumb, step the length down the board, and cut the seat and tail. The board must be longer than the measuring-line length by the rafter's depth times the tangent of the roof angle, because the plumb cuts lean across it.

The birdsmouth

The IRC never names the birdsmouth. Section R802.7.1 sends rafter notches to R502.8.1, where a notch at the end of a member may take no more than a quarter of its depth, and R802.6 asks for at least 1 1/2 inches of bearing on wood. The seat cut is level; it notches the rafter by its length times the sine of the roof angle. Where a full seat on the wall plate would cut deeper than a quarter, the calculator shortens the seat to fit, to the 1/16 inch below. A 3 1/2 inch seat on a 2x6 at 6/12 notches 1.57 inches, more than a quarter of 5 1/2, so the seat becomes 3 1/16 inches. Where the rafter overhangs the wall, R802.7.1.1 permits notches on the tail when 3 1/2 inches of rafter remain and the tail is no longer than 24 inches. Rules of thumb that allow a third of the depth are looser than the code.

The allowed span

Tables R802.4.1(1) to (8) of the 2024 and 2021 IRC give the most a rafter may span, measured level, for Douglas Fir-Larch, Hem-Fir, Southern Pine and Spruce-Pine-Fir in four grades, 2x4 to 2x12, at 12, 16, 19.2 and 24 inches on centre. There is one table for each load and ceiling: a 20 psf roof live load where no snow load applies, or 30, 50 and 70 psf of ground snow, each with the ceiling not attached to the rafters (deflection limit L/180) or attached to them (L/240), and each for a 10 or 20 psf dead load. The calculator reads the table at or above your snow load. The span is counted from the outside of the wall to the ridge's face, which errs long. The tables assume the ceiling joists or rafter ties are at the wall top; higher ties shorten the span by Table R802.4.1(9), down to ties a third of the way to the ridge.

The printed tables have a few cells that break their own pattern, such as a span of 12 feet 12 inches or a 2x10 that spans less than a 2x8. The 2018, 2021 and 2024 editions print them the same way. Where two cells contradict, the calculator uses the shorter and refuses the longer, and it never uses a cell that cannot be a span:

• Table R802.4.1(1), 16 in, Douglas Fir-Larch #3, 2x8 at 20 psf: printed 12-12; 12 inches is not a feet-and-inches value.
• Table R802.4.1(2), 19.2 in, Douglas Fir-Larch #3, 2x10 at 20 psf: printed 13-7; it is longer than the same rafter’s 12-7 in Table R802.4.1(1), and an attached ceiling cannot span farther.
• Table R802.4.1(3), 16 in, Southern Pine SS, 2x10 at 20 psf: printed 1-11; it is shorter than the 2x8’s 18-5 beside it.
• Table R802.4.1(4), 19.2 in, Hem-Fir #1, 2x6 at 20 psf: printed 16-3; it is longer than the 2x8’s 13-0 beside it.
• Table R802.4.1(5), 19.2 in, Hem-Fir #1, 2x4 at 20 psf: printed 8-11; it is longer than the 2x6’s 8-8 beside it and the same rafter’s 6-5 at 10 psf.
• Table R802.4.1(5), 24 in, Hem-Fir #1, 2x4 at 20 psf: printed 8-4; it is longer than the 2x6’s 7-9 beside it and the same rafter’s 5-9 at 10 psf.
• Table R802.4.1(6), 16 in, Spruce-Pine-Fir SS, 2x10 at 20 psf: printed 16-8; it is longer than the same rafter’s 15-11 in Table R802.4.1(5), and an attached ceiling cannot span farther.
• Table R802.4.1(7), 24 in, Douglas Fir-Larch #3, 2x12 at 20 psf: printed 9-10; it is longer than the same rafter’s 9-7 at 10 psf dead load.

What the calculator will not do

It covers common rafters on a gable roof. Hips, valleys and jacks, trusses, I-joists and engineered lumber, ground snow over 70 psf, dead loads over 20 psf, spans past 26 feet and wind uplift connections all need their own tables or a design. Your building department sets the snow load and the code edition in force, so check your local building code before you cut.

Need the pitch first? The roof pitch calculator turns a rise and run, an angle or a slope into every form, with a pitch chart. The 2x6 actual size page shows why a 2x6 rafter is 5 1/2 inches deep.