Rafter Calculator
This free rafter calculator finds your common rafter length and cut angle from a rise-and-run measurement or a standard roofing pitch — including an overhang for the tail beyond the wall plate — so you can mark and cut with confidence before the first board goes up.
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Rafter Length = √(Run² + Rise²)Interactive step-by-step proof
Enter your details above to see the calculation unfold step by step.
Why Use a Roof Rafter Calculator Before You Cut
A rafter is the hypotenuse of a right triangle formed by the horizontal run and the vertical rise, so getting the length right is ultimately a Pythagorean-theorem problem — but doing that math by hand for every pitch, run, and overhang combination invites small errors that compound across a whole roof. A rafter calculator applies the same formula a framing square or speed square encodes, instantly, so the length and cut angle you get match what a carpenter would lay out on the board.
Because roofs are described two different ways on site — sometimes as a measured rise and run, sometimes as a pitch notation like “6/12” — this rafter design calculator accepts either input. Entering a pitch converts it to the equivalent rise automatically, so a common rafter calculator built this way works whether you’re reading plans that specify degrees, a ratio, or actual feet and inches on the ground.
The overhang field matters just as much as the main span: the rafter tail beyond the wall plate continues at the exact same slope, so it has to be added to both the run and the rise before the final hypotenuse is calculated — not tacked on afterward as a flat measurement. Getting that step right the first time avoids a short rafter tail or an eave line that doesn’t sit flush. For the pitch itself, our Roof Pitch Calculator works out the rise-to-run ratio directly from a measured slope, and for the lumber sizing and span limits that go with the length this tool returns, pair both with the American Wood Council’s span table guidance.
How This Rafter Cut Calculator Works
A rafter forms the hypotenuse of a right triangle where the run is the horizontal leg and the rise is the vertical leg — so its length comes straight from the Pythagorean theorem.
The formula
Rafter Length = √(Run² + Rise²), where Run includes any overhang and Rise is scaled to match so the slope stays constant along the whole rafter.
Rise & run vs. pitch notation
Roofing pitch is usually written as “6/12,” meaning 6 inches of rise for every 12 inches of run — mathematically the same ratio as rise ÷ run, just expressed as a fraction of 12.
Common roof pitches
| Pitch | Angle |
|---|---|
| 4/12 | 18.4° |
| 6/12 | 26.6° |
| 9/12 | 36.9° |
| 12/12 | 45.0° |
What this doesn’t include
The ridge board thickness deduction, birdsmouth seat cut depth, or plumb-cut fascia trim — those adjustments are made on the actual board after this rafter calculator’s theoretical length is established.
Rafter Calculator: Worked Examples
Three common framing scenarios worked end-to-end using the same math as the calculator above.
Standard 6/12 common rafter with overhang
A gable roof has a 6/12 pitch and a 12-foot run to the ridge centerline, with a 12-inch overhang for the eave. What’s the rafter length and angle?
Given inputs
- Pitch: 6/12
- Run: 12 ft
- Overhang: 12 in (1 ft)
Computed outputs
- Pitch angle:
atan(6/12) = 26.6° - Total run: 12 + 1 = 13 ft
- Total rise: 13 × 0.5 = 6.5 ft
- Rafter length:
√(13² + 6.5²) ≈ 14.53 ft(≈174.3 in)
Low-slope shed roof from a measured rise and run
A shed addition rises 3 feet over a 9-foot run, measured directly on site rather than read from a plan. No overhang is needed. What’s the rafter length?
Given inputs
- Rise: 3 ft
- Run: 9 ft
- Overhang: 0 in
Computed outputs
- Pitch ratio: 3 ÷ 9 = 0.333 (≈4/12)
- Pitch angle:
atan(0.333) ≈ 18.4° - Rafter length:
√(9² + 3²) ≈ 9.49 ft(≈113.8 in)
Steep 9/12 pitch with a deep overhang
A steep-roofed cabin uses a 9/12 pitch with an 8-foot run and an 18-inch overhang for extra weather protection. How long is the rafter, and at what angle is it cut?
Given inputs
- Pitch: 9/12
- Run: 8 ft
- Overhang: 18 in (1.5 ft)
Computed outputs
- Pitch angle:
atan(9/12) ≈ 36.9° - Total run: 8 + 1.5 = 9.5 ft
- Total rise: 9.5 × 0.75 = 7.125 ft
- Rafter length:
√(9.5² + 7.125²) ≈ 11.88 ft(≈142.5 in)
Rafter Calculator Mistakes to Avoid
Forgetting to subtract the ridge board thickness
This calculator returns the theoretical length to the ridge centerline. In practice, half the ridge board’s thickness (measured along the slope) is subtracted from the run so paired rafters meet flush at the peak.
Skipping the birdsmouth seat-cut allowance
The notch cut where a rafter rests on the wall plate — the birdsmouth — shortens the effective bearing length. Mark and cut it after establishing the theoretical rafter length, not before, so the layout marks stay accurate.
Adding overhang as a flat length instead of along the slope
The rafter tail continues at the same pitch as the rest of the board, so overhang has to be converted into extra run and extra rise together — simply adding the overhang inches to the final rafter length undershoots the true measurement.
Using common-rafter math for hip or valley rafters
Hip and valley rafters run diagonally at roughly 45° in plan view and use a different run measurement (multiplied by about 1.414), so this calculator’s straightforward rise-and-run math is best suited to common rafters only.
Underestimating fall risk while marking and setting rafters
Falls remain a leading cause of injury in residential roof framing. Follow OSHA’s fall-protection guidance for residential construction whenever work happens six feet or more above a lower level, regardless of how confident the layout math is.