How to Calculate Rafter Length
Work out common rafter length from span and pitch or rise and run.
Quick answer
Half the building span is the run (after ridge deduction). Rise = run × (pitch rise ÷ 12). Common rafter length = √(run² + rise²). Add overhang along the slope separately.
Formula
Run = (span − ridge thickness) ÷ 2. Rise = run × (pitchRise ÷ 12). Length = √(run² + rise²). Overhang along slope = overhang projection ÷ cos(roof angle).
Units
Keep span, ridge, and overhang in the same length unit (feet or inches). Pitch is rise inches per 12 inches of run. Convert to feet-inches only for the final cut mark.
Step-by-step
- Measure outside-to-outside building span and the ridge board thickness.
- Compute run = (span − ridge) ÷ 2 for a centered ridge.
- From pitch X/12, rise = run × (X ÷ 12).
- Length = √(run² + rise²). That is the common rafter before overhang.
- If you need eave overhang, convert horizontal projection to length along the slope and add it.
- Mark plumb cut (roof angle) and level seat cut; check birdsmouth depth against stock size.
Example 1 — 24 ft span at 6/12
Ignore ridge for a moment: run = 12 ft. Rise = 12 × 6/12 = 6 ft. Length = √(144 + 36) = √180 ≈ 13.416 ft ≈ 13′ 5″. With a 1½″ ridge, run becomes 11.9375 ft and length ≈ 13.35 ft before overhang.
Example 2 — 16 ft span at 8/12 with 12″ overhang
Run = 8 ft. Rise = 8 × 8/12 ≈ 5.333 ft. Common length ≈ √(64 + 28.44) ≈ 9.61 ft. Roof angle ≈ 33.69°. Overhang along slope ≈ 1 ÷ cos(33.69°) ≈ 1.20 ft. Total stock to order ≈ 10.81 ft ≈ 10′ 9¾″ before waste.
Common pitches — length factor per foot of run
| Pitch | Angle (approx.) | Factor (× run) |
|---|---|---|
| 4/12 | 18.4° | 1.054 |
| 6/12 | 26.6° | 1.118 |
| 8/12 | 33.7° | 1.202 |
| 10/12 | 39.8° | 1.302 |
| 12/12 | 45.0° | 1.414 |
Common mistakes
- Using full span as run instead of half-span to the ridge.
- Forgetting ridge thickness deduction before Pythagorean length.
- Adding overhang as horizontal inches instead of along the slope.
- Mixing feet and inches in the same √(run² + rise²) step.
Practical notes
- Engineered trusses replace this math — use manufacturer layout.
- Seat cut / birdsmouth must leave enough depth in the rafter stock.
- Verify local framing practices; this is layout geometry, not a structural design.
Related calculator
Use the free Rafter Calculator to run the same math with your field numbers.
Related tools
- Rafter Calculator — Common rafter length, plumb cut, and seat cut from span or rise/run.
- Roof Pitch Calculator — Convert pitch, angle, and slope percent with rafter factors.
Related guides
- Roof Pitch to Rafter Length — Convert an X/12 pitch into rafter length for a known run.
- Common Rafter Formula — The core formula carpenters use for common rafter layout.
- Roof Pitch Explained — What X/12 pitch means and how it relates to angle.
FAQ
Is rafter length the same as stock length to buy?
Not always. Add overhang along the slope, ridge plumb cut waste, and a little for square ends. Round up to available lumber lengths.
Can I use the pitch factor instead of square root?
Yes for planning: length ≈ run × factor. Confirm critical cuts with √(run² + rise²) or the free rafter calculator.
Updated 2026-09-17. Planning aid only — verify against local codes and professional judgment.