Rafter Length Calculator

How rafter length is calculated

A common rafter is the hypotenuse of a right triangle. The horizontal leg is the run (half the building span, less half the ridge board), the vertical leg is the rise, and the pitch tells you how the two are related: a 6/12 roof rises 6 inches for every 12 inches of run. Everything else follows from the Pythagorean theorem.

The factor √(1 + (pitch ÷ 12)²) is the rafter multiplier: the length of rafter needed for each unit of run. It depends only on the pitch, which is why framers memorise it, or read it as "length per foot of run" from the table stamped on a framing square.

Worked example: 24 ft span, 6/12 pitch, 12 in overhang

1. Half the span is 12 ft = 144 in. With a 1½ in ridge board, run = 144 − 0.75 = 143.25 in.
2. Rise = 143.25 × 6 ÷ 12 = 71.63 in (5' 11-5/8").
3. Multiplier = √(1 + 0.5²) = √1.25 = 1.1180.
4. Rafter, ridge to building line = 143.25 × 1.1180 = 160.16 in (13' 4-3/16").
5. Tail = 12 × 1.1180 = 13.42 in (13-7/16").
6. Total = 160.16 + 13.42 = 173.57 in (14' 5-9/16"), so buy 16 ft boards.
7. Plumb cut = arctan(0.5) = 26.57°; the level seat cut is 90° − 26.57° = 63.43° from the rafter edge.

Rafter multipliers by pitch

Common multiplier = √(1 + (pitch/12)²). Hip and valley length per 12 in of common run = 12 × √(2 + (pitch/12)²).

Hip and valley rafters

A hip rafter crosses the corner of the building at 45° in plan, so its horizontal run is the common run × √2. It climbs the same rise as the common rafters, which makes its slope flatter: a 6/12 roof has 6/16.97 hips. The line length is run × √(2 + (pitch ÷ 12)²). Treat the calculator's hip figure as the theoretical length to the centre of the ridge; the actual cut is shortened for the ridge and for half the hip's own thickness measured at 45°.

Before you cut

• Measure the span at the top plates, in several places. Walls are rarely perfectly parallel, and the rafter follows the real span, not the drawing.
• The birdsmouth seat should not remove more than about one third of the rafter depth; deeper notches weaken the rafter at its most loaded point.
• Cut one pair, test it against the ridge, and use it as the pattern for the rest.
• Rafter size and spacing are structural. Use the span tables in your local building code (IRC R802 in the U.S.) or an engineer for snow and wind loads.

Need the pitch first? Use the roof pitch calculator to convert between rise/run, degrees and X/12, or read the roof pitch trigonometry guide.