Rafter Calculator
| Span | Pitch | Rafter | Roof area (40 ft bldg) |
|---|---|---|---|
| 24 ft | 6/12 | 13.42 ft | 1,073 sq ft |
| 28 ft | 8/12 | 16.83 ft | 1,346 sq ft |
| 32 ft | 6/12 | 17.89 ft | 1,431 sq ft |
| 40 ft | 10/12 | 26.03 ft | 2,083 sq ft |
A rafter is just the hypotenuse of a right triangle the building hands you: half the span is the run, the pitch sets the rise, and the rafter is the slope between them. That geometry compresses into one handy number per pitch - the multiplier. A 6/12 roof multiplies the run by 1.118, an 8/12 by 1.202, a 12/12 by 1.414 (Pythagoras himself: a 45-degree roof makes the rafter root-two times the run). Half the span times the multiplier is the rafter length, no table lookup needed.
Two things live outside that number. Overhang is the rafter's tail past the wall - 12 to 24 inches of it - so the board you order is rafter length plus the tail, and birdsmouth cuts (the seat and heel notches that sit the rafter on the wall plate) shave depth, not length. And the multiplier is also your area machine: rafter length times building length times two slopes is the roof surface, which is exactly the number the shingle order wants.
How to use
- Measure the building span wall-to-wall and take half of it as the run - the calculator does the halving.
- Pick the pitch from the roof pitch reading (rise per 12) so the multiplier is honest.
- Add the overhang tail on site: the rafter length is wall-plate to ridge, the eave tail is extra board.
Frequently asked questions
How do I calculate rafter length?
Rafter length = half the span times the pitch multiplier. A 24-foot span on a 6/12 pitch has a 12-foot run, and 12 × 1.118 = 13.4 feet per rafter. The multiplier is √(1 + (pitch/12)²) - the Pythagorean theorem folded into one number per pitch, which is what the old rafter tables printed along the top edge.
What is the pitch multiplier for common pitches?
4/12 is 1.054, 5/12 is 1.083, 6/12 is 1.118, 7/12 is 1.158, 8/12 is 1.202, 10/12 is 1.302, and 12/12 is 1.414. Steeper gets closer to 1.5 (a 24/12 pitch would be 2.06). The multiplier converts horizontal run to slope length directly - no angle finding, no trig on site.
Does rafter length include the overhang?
No - the calculated length runs from the wall plate to the ridge line. The overhang tail (typically 12 to 24 inches past the wall for eaves) is added as extra board, so order rafter stock at rafter length plus tail plus a cut margin. The birdsmouth notches that seat the rafter on the plate reduce effective depth, not length.
How do I get roof area from rafter length?
Rafter length times building length is one slope; times two is the whole roof. A 24-by-40-foot building at 6/12 gives 13.42-foot rafters, so 13.42 × 40 × 2 ≈ 1,074 square feet of roof surface - the number the shingle calculator turns into squares and bundles. Hip roofs differ: their rafters run at varying lengths to the corners, so this rectangle math is a gable-roof tool.
What size rafters do I need?
Length is geometry; size is engineering. Span, spacing, species grade and snow load set the board depth - a 24-foot span typically wants 2x10 or deeper rafters at 16-inch centers, but the roof snow load calculator and local code tables make that call, not the tape measure. This page gives the length; the lumber yard and the code book give the 2x.
Why does my rafter table show a slightly different length?
Books round the multiplier to three decimals and this page does not, and classic tables measure to the ridge centerline while some layouts measure to the far face. Expect agreement within about a quarter inch on a 14-foot rafter - cut one test rafter before batch-cutting, and let the first one be the expensive lesson.