Roof Pitch to Rafter Length
Convert an X/12 pitch into rafter length for a known run.
Quick answer
Rise = run × (pitch ÷ 12). Length = √(run² + rise²), or length ≈ run × common-rafter factor for that pitch.
Formula
pitch_in_12 = rise ÷ run × 12. common_factor = √(1 + (pitch/12)²). length = run × common_factor.
Units
Run and rise share one length unit. Pitch is unitless as “inches of rise per 12 inches of run.”
Step-by-step
- Confirm horizontal run from wall to ridge (after ridge deduction if used).
- Read pitch as X/12 from plans or measure rise over a 12″ level run.
- Compute rise = run × X/12, or multiply run by the factor for that pitch.
- Check angle = arctan(X/12) if you need plumb-cut degrees.
Example — 10 ft run at 8/12
Rise = 10 × 8/12 ≈ 6.667 ft. Length = √(100 + 44.44) ≈ 12.02 ft ≈ 12′ ¼″. Factor check: 10 × 1.202 ≈ 12.02 ft.
Example — 14′ 6″ run at 5/12
Run = 14.5 ft. Rise = 14.5 × 5/12 ≈ 6.042 ft. Length ≈ √(210.25 + 36.50) ≈ 15.71 ft ≈ 15′ 8½″.
Pitch → common factor
| Pitch | Common factor | Hip/valley factor (square corner) |
|---|---|---|
| 3/12 | 1.031 | 1.436 |
| 6/12 | 1.118 | 1.500 |
| 9/12 | 1.250 | 1.601 |
| 12/12 | 1.414 | 1.732 |
Common mistakes
- Multiplying span (full width) by the factor instead of run (half span).
- Using hip/valley factor for a common rafter.
Practical notes
- Hip/valley factors assume a 45° plan corner — adjust for odd hips.
- After length, use the rafter calculator for plumb/seat angles and overhang.
Related calculator
Use the free Roof Pitch Calculator to run the same math with your field numbers.
Related tools
- Roof Pitch Calculator — Convert pitch, angle, and slope percent with rafter factors.
- Rafter Calculator — Common rafter length, plumb cut, and seat cut from span or rise/run.
Related guides
- How to Calculate Rafter Length — Work out common rafter length from span and pitch or rise and run.
- Roof Pitch Explained — What X/12 pitch means and how it relates to angle.
- Common Rafter Formula — The core formula carpenters use for common rafter layout.
FAQ
Where do I get the run if I only know span?
Run is typically half the span minus half the ridge thickness. See How to Calculate Rafter Length for the full sequence.
Updated 2026-09-17. Planning aid only — verify against local codes and professional judgment.