How to calculate rafter length
A common rafter is the hypotenuse of a right triangle. The run is half the span, less half the ridge board thickness. The calculator multiplies that run by the pitch multiplier, then adds the tail for the overhang:
Run = span ÷ 2 − ridge thickness ÷ 2
Rafter (ridge to plate) = run × √(1 + (pitch ÷ 12)²)
Tail = level overhang × same multiplier
For a 24 ft span at 6/12 with a 1.5 in ridge and 12 in overhang: run is 11.94 ft, ridge to plate is 13.35 ft, and the total is 14.46 ft (14' 5-9/16"), so you buy 16 ft stock.
Need the pitch first? Use the roof pitch calculator. Rafter size and spacing depend on span, snow load and lumber grade, so check IRC Table R802.4 or your engineer.
Common rafter lengths before overhang
Half the span times the pitch multiplier. Add the overhang along the slope, and subtract half the ridge board.
| Span | 4/12 | 6/12 | 8/12 | 10/12 | 12/12 |
|---|---|---|---|---|---|
| 12 ft | 6.32 ft | 6.71 ft | 7.21 ft | 7.81 ft | 8.49 ft |
| 16 ft | 8.43 ft | 8.94 ft | 9.61 ft | 10.41 ft | 11.31 ft |
| 20 ft | 10.54 ft | 11.18 ft | 12.02 ft | 13.02 ft | 14.14 ft |
| 24 ft | 12.65 ft | 13.42 ft | 14.42 ft | 15.62 ft | 16.97 ft |
| 28 ft | 14.76 ft | 15.65 ft | 16.83 ft | 18.22 ft | 19.80 ft |
| 32 ft | 16.87 ft | 17.89 ft | 19.23 ft | 20.83 ft | 22.63 ft |
For a worked cut, a shed roof uses the whole width as the run, not half. The roof pitch calculator gives the multiplier for any pitch.
Frequently asked questions
How long is a rafter for a 24 ft span at 6/12?
About 13.35 ft from ridge to plate with a 1.5 in ridge board, plus the tail for your overhang.
Why subtract the ridge board?
Rafters butt against each side of the ridge board, so each run is shortened by half the board's thickness.
What is the plumb cut angle?
It equals the roof angle. For 6/12 that is 26.57 degrees, set on a speed square using the 6 on the common scale.
How do I calculate rafter length?
Take half the building span as the run, then multiply by the pitch multiplier. For a 24 ft span at 6/12 the run is 12 ft and the rafter is 12 × 1.118 = 13.42 ft before overhang and ridge adjustments.
How long is a rafter for a 28 ft wide house at 8/12?
The run is 14 ft, and the multiplier is 1.202, so the rafter is 16.83 ft before the overhang.