Rafter Length Calculator
Calculate rafter length, plumb cut and bird's-mouth cut from run, rise or roof pitch.
The rafter length calculator returns rafter length, plumb cut and bird's-mouth cut angles for any gable or shed roof rafter. Rafter length is the diagonal from the ridge board down to where the rafter sits on the wall top plate - calculated as sqrt(run^2 + rise^2). The ridge board takes up some of the run (typically 3/4 inch on each side for a 1.5 inch ridge), so the calculator subtracts half the ridge thickness before calculating. The tail or overhang length is the extra rafter material extending past the wall to form the eave - measured along the slope, not horizontally. The plumb cut at the ridge end and the seat cut (bird's-mouth) where the rafter meets the wall both follow from the pitch.
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Frequently asked questions
Rafter length = sqrt(run^2 + rise^2), where run is the horizontal distance from the ridge to the wall (half the building width minus ridge board thickness) and rise is the vertical distance from the wall top to the ridge. For a 12 ft run with 6/12 pitch (6 ft rise): rafter = sqrt(144 + 36) = sqrt(180) = 13.42 ft. Add tail length for the overhang, which is overhang_in / 12 x pitch_multiplier.
The plumb cut angle is the angle measured from vertical at the ridge end of the rafter. For a 6/12 pitch, plumb cut = arctan(6/12) = 26.57 degrees from vertical. On a framing square, this is the same as the angle of the rafter from horizontal. The plumb cut leaves the cut face perfectly vertical when the rafter is installed in place - it meets the ridge board flush.
The bird's-mouth is a notch cut into the rafter where it sits on the top plate of the wall - one cut horizontal (the seat cut, parallel to the top plate) and one cut vertical (the heel cut, parallel to the wall). The notch lets the rafter rest flat on the wall with the rafter extending past as the eave overhang. Standard depth is no more than 1/3 of the rafter depth to maintain structural integrity.
Half the ridge board thickness. A 2x ridge (1.5 inches actual) means subtracting 0.75 in from the run on each side. So a 24 ft wide building with 12 ft of run per side actually has 11 ft 11.25 in of run per rafter. For thicker LVL ridge beams (3.5 in or more), the adjustment matters - skip it and your rafters won't meet at the ridge correctly.
Standard residential rafters are 2x6 or 2x8 for spans up to 12-16 ft, 2x10 for longer spans, 2x12 for major spans. Just like joists, rafter size depends on span, snow/wind load and lumber species - consult IRC R802.5 for the rafter span tables. For a typical 12 ft run with 6/12 pitch (about 13.5 ft rafter length), 2x8 Doug fir at 16 in OC handles most snow loads up to 50 psf.