Common Rafter Formula

Formula

L = √(R² + H²) where R = run and H = rise. Plumb cut angle = arctan(H/R). Seat cut is typically level (90° − plumb for complementary framing marks depending on square use).

Units

Same length unit for R and H. Report L in feet and inches for cutting.

Step-by-step

1. Define run from the birdsmouth heel point (or outside of plate) to the ridge face after deduction.
2. Find rise from pitch or from a measured height difference.
3. Apply L = √(R² + H²).
4. Add overhang along the slope if the stock includes the eave.
5. Transfer plumb and seat cuts with a framing square or calculator angles.

Equal rise and run (12/12)

If run = 10 ft and pitch is 12/12, rise = 10 ft. L = √200 ≈ 14.14 ft ≈ 14′ 1¾″. Angle = 45°.

Shallow 4/12 on a 9 ft run

Rise = 9 × 4/12 = 3 ft. L = √(81 + 9) = √90 ≈ 9.49 ft ≈ 9′ 5⅞″.

Common mistakes

• Measuring run to ridge centerline without subtracting half ridge thickness for the cut length.
• Confusing theoretical length with board length after birdsmouth removal.

Practical notes

• Pattern rafter first; copy only after a dry fit.
• Steep pitches amplify small run errors into large length errors.

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

• How to Calculate Rafter Length — Work out common rafter length from span and pitch or rise and run.
• Roof Pitch to Rafter Length — Convert an X/12 pitch into rafter length for a known run.
• Roof Pitch Explained — What X/12 pitch means and how it relates to angle.