Rafter Length Calculator
Common rafter length, rise, tail, and cut angles for a symmetric gable roof. Enter span (or run), pitch, and overhang. Output in feet and inches to the nearest 1/16".
Results
Estimates assume a symmetric gable roof and standard framing geometry. For hip rafters, valley rafters, irregular pitches, or spans that need engineered lumber, work from the IRC R802.5.1 span tables and local building code. A framing inspector or structural engineer should review anything past standard residential geometry.
How to use this calculator
- 01Pick which input you have and toggle Span or Run. Span is the full width of the building wall to wall. Run is half of that, the horizontal distance from the wall to the ridge on a symmetric gable.
- 02Enter pitch as the rise over 12. A roof that climbs 6 inches for every foot of horizontal run is 6/12. Whole numbers 1 through 12.
- 03Overhang is optional. Enter the horizontal distance from the wall to the rafter tail’s outer edge, or 0 for none. The calculator returns the sloped tail length, not the horizontal overhang.
- 04Read the common rafter length first. That’s the board you cut. Add the tail to get total length, then order one standard lumber length up to allow for the plumb cut and birdsmouth.
- 05Plumb cut and seat cut angles drive your saw setup. Set your speed square or miter saw to the plumb cut for the ridge end and the seat cut for the wall plate.
Understanding the math
A common rafter is the hypotenuse of a right triangle. The run is the horizontal distance from the wall to the ridge, half the span on a symmetric gable. The rise is how high the ridge sits above the wall plate. Pitch is rise over run expressed as X/12, so a 6/12 pitch climbs 6 inches for every 12 inches of run.
Run gives us one leg. Rise comes from run times pitch divided by 12. Rafter length is the square root of run squared plus rise squared. That’s it.
run = span / 2 · rise = run × pitch / 12 · rafter = √(run² + rise²)
Worked example. 24-ft span, 6/12 pitch, 18-in overhang.
Run = 12 ft. Rise = 12 × 6 / 12 = 6 ft. Rafter = √(12² + 6²) = √180 = 13.42 ft. Tail = 1.5 × √(1 + (6/12)²) = 1.5 × 1.118 = 1.68 ft. Total rafter with tail = 15.10 ft. Order a 16-ft board.
Plumb cut and seat cut come from pitch directly. Plumb cut angle = arctan(6/12) = 26.57°. Seat cut = 90 − 26.57 = 63.43°.
Rafter line factor reference
Multiply run by the factor for your pitch to get the sloped rafter length. Same answer as the Pythagorean formula, faster in the field. Source: standard framing square reference. Matches Stanley Quick Square and Swanson Speed Square documentation.
| Pitch | Factor | Rafter per Foot of Run |
|---|---|---|
| 1/12 | 1.003 | 12.04 in |
| 2/12 | 1.014 | 12.17 in |
| 3/12 | 1.031 | 12.37 in |
| 4/12 | 1.054 | 12.65 in |
| 5/12 | 1.083 | 13.00 in |
| 6/12 | 1.118 | 13.42 in |
| 7/12 | 1.158 | 13.90 in |
| 8/12 | 1.202 | 14.42 in |
| 9/12 | 1.250 | 15.00 in |
| 10/12 | 1.302 | 15.62 in |
| 11/12 | 1.357 | 16.28 in |
| 12/12 | 1.414 | 16.97 in |
Frequently asked questions
How to calculate rafter length?
Square the run, square the rise, add them, take the square root. That's your rafter length. Run is half the building's span on a symmetric gable. Rise is run times pitch over 12. A 12-ft run on a 6/12 pitch gives 6 ft of rise. Plug into √(12² + 6²) and you get 13.42 ft. Add overhang on top of that for the tail.
For quick field work, framers use the rafter line factor table. Multiply your run by the factor for your pitch and skip the square root. A 6/12 has a factor of 1.118, so 12 × 1.118 = 13.42 ft. Same answer, faster.
How far can a 2x6 span as a rafter?
Depends on species, grade, spacing, and load. IRC R802.5.1 span tables are the authority. For SPF #2 at 16" on center carrying a 30 psf ground snow load, a 2x6 rafter spans roughly 12 ft. Bump it to 24" on center or higher snow load and the span drops. Drop to 12" on center or use a stronger species like Douglas fir #1 and it goes up.
Use the published tables for your local conditions. A framing inspector will check them, and the numbers shift with snow load zones, dead load, and live load assumptions. Never eyeball this off a single online number.
What length do roof rafters come in?
Dimensional lumber comes in 8, 10, 12, 14, 16, 18, 20, and 24 ft lengths at most yards. Anything past 20 ft is usually special order. For longer spans, framers either splice over a bearing wall, use engineered I-joists, or switch to manufactured trusses.
Order one length up from your calculated rafter to give yourself room for the plumb cut, the birdsmouth, and the tail. A 13.42-ft calculated rafter wants a 14-ft board.
What is the rafter length for a 4x12 pitch?
Depends on the run. A 4/12 pitch has a rafter line factor of 1.054. Multiply your run by 1.054 and you have the sloped rafter length, not counting overhang.
For a 24-ft span (12-ft run), rafter = 12 × 1.054 = 12.65 ft. For a 30-ft span (15-ft run), rafter = 15 × 1.054 = 15.81 ft. Add overhang times 1.054 for the tail.
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