How the rafter calculator works
A common rafter is the hypotenuse of a right triangle. The level leg is the run, the vertical leg is the rise, and the pitch tells you how they relate: so many inches of rise for every 12 inches of run. Once you know the run, everything else follows.
run = span ÷ 2 − ridge thickness ÷ 2
multiplier = √(1 + (pitch ÷ 12)²)
line length = run × multiplier
tail = overhang × multiplier
rise = run × pitch ÷ 12
Take a 24′ garage with a 6/12 roof, a 2× ridge and a 12″ overhang. Half the span is 144″; take off half the ridge and the run is 143 1/4″. The multiplier for 6/12 is 1.118, so the line length is 160 3/16″ from the heel of the birdsmouth to the face of the ridge. The tail adds 13 7/16″. On a 2×8, with the extra wood at both plumb cuts, the rafter needs about 177″ of board, so you buy 16-footers.
Where the measuring line runs
Rafter lengths are measured along a line, not along an edge. Here it's the line that runs parallel to the rafter edges through the corner where the seat cut meets the heel cut, right at the outside face of the wall. The plate shows it as a dash-dot line. Measure along it from that corner to the ridge plumb cut and you get the line length.
Mixing up where you measure from is how rafters end up an inch long or short. If your layout method measures along the top edge instead, that's fine, but don't mix the two on one roof.
Laying out the cuts
- Crown up. Sight each board and mark the crown. It goes up, toward the sky, so the load straightens it out.
- Mark the ridge plumb cut. Pivot a speed square to your pitch on the common scale and draw the plumb line near the top end.
- Measure the line length. Along the measuring line, from the plumb cut down. The ridge is already allowed for: the run on this page is shortened by half the ridge thickness.
- Draw the birdsmouth. Mark a second plumb line there for the heel, then square off it for the seat. The seat should be as wide as the wall plate.
- Mark the tail. Measure the tail length past the heel and mark the fascia plumb cut.
- Cut one, test it, then copy it. Set the pattern rafter in place at both ends before you cut the rest.
Height above plate and the ridge height
Height above plate (HAP) is the vertical distance from the top of the wall plate, at the outside face of the wall, up to the top edge of the rafter. It's the length of the plumb cut minus the heel height of the birdsmouth. For the 2×8 example that's 8 1/8″ − 1 3/4″ = 6 3/8″.
Add the HAP to the rise and you have the top of the rafter at the ridge, measured from the top of the wall plate. That's the number to set your ridge board to: 71 5/8″ + 6 3/8″ = 78″ for the garage. The IRC asks for a ridge board at least as deep as the plumb cut, so a 2×8 rafter at 6/12 needs a 2×10 ridge.
What this page doesn't do
It doesn't tell you whether a 2×8 can span 12 feet under your snow load. That's a structural question answered by span tables for your species and grade, and by your building department. It also handles common rafters only, not hips, valleys or jacks. If you don't know the pitch yet, start by measuring your roof pitch.