How long is a rafter for a 24 foot span at 6/12 pitch?

The run is 12 feet, half the span. Times the 6/12 slope factor of 1.118, the line length is 13.416 feet. Taking off half of a 1-1/2 inch ridge board gives 13.346 feet (13 feet 4-3/16 inches), and a 12 inch level overhang adds 13-7/16 inches for a total of about 14.465 feet.

Rafter Length Calculator with Cut Angles

Common rafter

Total length (line + overhang)–

Line length–

Overhang length–

Run–

Rise to ridge–

Plumb cut–

Seat cut–

Birdsmouth

Seat (level) cut–

Heel (plumb) cut–

Height above plate–

Notch depth–

Hip or valley (equal pitches)

Hip/valley line length–

Hip pitch / angle–

Estimate only. Line length is geometry, not board length, and not a span or load check. Rafter size and spacing must meet local code (IRC R802) or an engineer's design.

Rafter diagram

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How rafter length is worked out

Run = span ÷ 2 − ridge thickness ÷ 2. The span is measured outside wall to outside wall, so the run ends at the face of the ridge board.

Line length = run × slope factor, where the slope factor is √(1 + (pitch ÷ 12)²): 1.118 for 6/12. It's measured along a line parallel to the rafter edge, from the heel of the birdsmouth (outside of the wall) to the ridge face, along the plumb cut.

Overhang length = level overhang × slope factor, added beyond the birdsmouth to the tail plumb cut.

Birdsmouth: the seat cut is the width of the wall plate, the heel cut is seat × pitch ÷ 12, and the height above plate (HAP) is what's left of the rafter measured plumb over the wall. Keep the same HAP on every rafter so the roof plane stays flat. Notch limits are set by code (IRC R802.7) and the engineer; check them before cutting deep seats on small rafters.

Hip and valley: with equal pitches, the hip runs at 45° in plan, so its run is the common run × √2 and its length uses √(2 + slope²). Before cutting, subtract the ridge and hip deductions, and work out side cuts.

Questions

How long is a rafter for a 24' span at 6/12?

Run 12', line length 13.416'. Subtract half a 1-1/2" ridge and it's 13.346' (13' 4-3/16"). A 12" overhang adds 13-7/16", so about 14.465' in total: buy 16' boards.

Why subtract half the ridge board thickness?

The run is measured to the centre of the ridge, but the rafter stops at the ridge face. Shorten the run by half the ridge thickness before multiplying.

Is rafter length the board length to buy?

No. The plumb cuts at each end make the long edge longer, so buy the next stock length up from the total length.

Need the pitch first? Use the roof pitch calculator. Ordering shingles? Try the roofing calculator.

Safety

Rafter length is geometry, not a span or load check. Size, grade and spacing must meet local code (IRC R802) or an engineer's design; consult a licensed professional. Roof work is a fall risk: use fall protection (OSHA guidance).