Rafter Calculator

Enter the building span and roof pitch, and this free rafter calculator gives the rafter length to cut, the lumber length to buy, every cut angle and the birdsmouth. Type sizes the way they're written on a plan, like 24' or 23' 7-1/2".

Building span (outside of wall to outside of wall) Roof pitch (rise per 12" of run) Overhang (level, past the wall) Ridge board thickness Rafter size Birdsmouth seat (wall plate width)

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How the rafter calculator works

A common rafter is the long side of a right triangle. The run is half the span (for a ridge in the middle), the rise is the run times the pitch over 12, and the rafter runs along the slope between them. Every foot of run needs √(1 + (pitch/12)²) feet of rafter. That number is the pitch multiplier, and it turns any level measurement into a length along the slope.

Line length = run × pitch multiplier (wall plate to the center of the ridge)
Ridge deduction = half the ridge thickness × multiplier, taken off the top so the rafter stops at the face of the ridge board
Tail length = level overhang × multiplier, added past the birdsmouth
Plumb cut angle = arctan(pitch / 12); the seat cut is 90° minus that
Height above plate (HAP) = rafter depth × multiplier − birdsmouth heel height

Worked example: 24' span, 8/12 pitch, 2x8 rafters

The run is 12'. The multiplier for 8/12 is 1.2019, so the line length is 144" × 1.2019 = 173.07", or 14' 5-1/16". A 1-1/2" ridge takes off 3/4" × 1.2019 = 7/8". A 12" overhang adds 14-7/16" of tail. The rafter to cut is 173.07 − 0.90 + 14.42 = 186.59", or 15' 6-9/16", so buy 16-footers. The plumb cut is 33.7°. With a 3-1/2" seat the heel is 2-5/16" high, which leaves 6-3/8" of rafter above the plate.

Laying out the rafter

Pick the straightest board and sight it for crown. The crown goes up.
Mark the plumb cut at the top with a speed square set to the pitch (8 on the common scale for 8/12).
Measure the rafter length to cut along the top edge and mark the plumb line of the tail.
Measure back the tail length and mark the birdsmouth heel, then square the seat cut off it to the seat width.
Cut this one pattern rafter, test it at both ends of the building, then trace it for the rest.

FAQ

What does 8/12 pitch mean?

The roof rises 8 inches for every 12 inches it runs level. You can type it as 8/12, as 8, or as an angle like 33.7°.

Is span measured to the outside of the walls?

Use the outside of the top plates, which is where the birdsmouth heel sits. If your plan gives the run to the ridge instead, double it.

How deep can the birdsmouth be?

A common rule is to cut no more than one third of the rafter depth, while keeping at least 1-1/2" of bearing on the plate. The calculator warns you when the seat you entered cuts deeper than a third. Your local code has the final say.

Does this size the rafter for my span?

No. This page works out lengths and cuts. Whether a 2x8 can carry your span depends on species, grade, spacing and snow load. Check the rafter span tables in your local building code (in the US, the IRC span tables in section R802).