Rafter Calculator
Common rafter length with overhang, the plumb and seat cut angles, a birdsmouth that keeps the roof plane true, ridge height, hip and valley length and how many rafters to order.
Common rafter, with overhang
14′ 5 9/16"
- Ridge to wall (line)
- 13′ 4 3/16"
- Tail (overhang)
- 13 7/16"
- Plumb cut angle
- 26.6°
- Seat cut angle
- 63.4°
- Birdsmouth heel
- 1 3/4"
- HAP
- 6 3/8"
- Ridge top above plate
- 6′ 6 3/8"
- Rafters
- 69 × 16 ft
- Board feet
- 1,472 bf
- Valley (if any)
- 19′ 4 7/8"
Lengths are measured along the top edge. Subtract nothing more for the ridge; half its thickness is already taken out of the run.
Rafter length chart (24 ft span)
Gable roof, 1½″ ridge, 12″ level overhang; length along the top edge. Click a pitch for spans from 12 to 40 ft.
| Pitch | Angle | Rafter factor | Ridge to wall | With overhang | Buy |
|---|---|---|---|---|---|
| 3/12 | 14° | 1.031 | 12′ 3 11/16" | 13′ 4" | 14 ft |
| 4/12 | 18.4° | 1.054 | 12′ 7" | 13′ 7 5/8" | 16 ft |
| 5/12 | 22.6° | 1.083 | 12′ 11 3/16" | 14′ 3/16" | 16 ft |
| 6/12 | 26.6° | 1.118 | 13′ 4 3/16" | 14′ 5 9/16" | 16 ft |
| 7/12 | 30.3° | 1.158 | 13′ 9 13/16" | 14′ 11 3/4" | 16 ft |
| 8/12 | 33.7° | 1.202 | 14′ 4 3/16" | 15′ 6 9/16" | 18 ft |
| 9/12 | 36.9° | 1.25 | 14′ 11 1/16" | 16′ 2 1/16" | 18 ft |
| 10/12 | 39.8° | 1.302 | 15′ 6 1/2" | 16′ 10 1/16" | 18 ft |
| 12/12 | 45° | 1.414 | 16′ 10 9/16" | 18′ 3 9/16" | 20 ft |
How rafter length is worked out
Every common rafter is the hypotenuse of a right triangle. The run is half the span, less half the ridge board. The rise is run × pitch ÷ 12. Instead of taking a square root every time, framers multiply the run by the rafter factor √(1 + (pitch/12)²), the "length per foot of run" row stamped on a framing square's rafter table (13.42" per foot for 6/12 means a factor of 1.118).
Cutting sequence
- Mark the plumb cut at the ridge end at 26.6° (a speed square's 6 mark on the common scale).
- Measure 13′ 4 3/16" along the top edge and mark a parallel plumb line: that is the outside face of the wall.
- From that line, lay out the heel (1 3/4") and the seat (3.5") so 6 3/8" of rafter stays above the plate.
- Measure the tail (13 7/16" along the top edge) and cut the fascia plumb cut.
- Cut one pattern rafter, test it on both walls, then use it to mark the rest.
Shed and hip roofs
On a shed (lean-to) roof the rafter runs the full building width from the low wall to the high wall, and both ends overhang, so run = span, not half the span. On a hip roof the four hips run diagonally at 45° in plan: hip run = common run × 1.4142, so the hip slope is pitch ÷ 1.4142 (a 6/12 roof has 4.24/12 hips). Jack rafters fill between the hip and the wall plate, each one shorter than the last by spacing × rafter factor.
Choosing a rafter size
Size comes from the IRC rafter span tables R802.4.1(1)–(8), read for your species and grade, snow or live load, dead load, spacing and whether a ceiling is attached. Longer spans, heavier snow or heavy roofing (tile, slate) push you to deeper rafters or closer spacing. Engineered trusses avoid the question on most new houses. Check the table that matches your load and ask your building department if you're unsure.
Need the pitch first? Use the roof pitch calculator, or go straight to a common pitch: 4/12, 6/12, 8/12, 12/12.
Ask the shop
Stuck on a detail? Ask a question about this job. Your current inputs and results are sent along so the answer fits your numbers. AI answers can be wrong, so double-check anything structural with your building department.