Rafter length math is a 30-second job once you know the pitch factor — and a confusing mess if you don't. A 6/12-pitch rafter on a 24-ft-wide building is not 12 feet long. It is 13.4 feet, plus an overhang. Here is where the number comes from and how to lay out the cuts.

Pitch is rise per 12 inches of run

A 6/12 pitch means the roof rises 6 inches for every 12 inches of horizontal run. 4/12 is a low slope; 6/12 is the conventional residential pitch; 9/12 and steeper require roof jacks or scaffolding to walk safely; 12/12 is a 45° cathedral pitch.

Run, rise, and the diagonal

For a gable roof, the run of one rafter is half the building width. A 24-ft-wide building gives 12 ft of run per rafter. The rise at the ridge is run × pitch/12 — for 6/12, that is 12 × 0.5 = 6 ft of rise.

The diagonal length, ridge to wall plate, is the Pythagorean √(run² + rise²). Or, more practically, you multiply run by the pitch factor:

  • 3/12 → factor 1.031
  • 4/12 → factor 1.054
  • 6/12 → factor 1.118
  • 8/12 → factor 1.202
  • 9/12 → factor 1.250
  • 12/12 → factor 1.414 (45°)

The factor comes from √(pitch² + 144) ÷ 12. The rafter length calculator runs all this and includes the eave overhang along the slope.

Don't forget the overhang

The eave overhang is the horizontal projection of the rafter past the wall plate. 12 inches is conventional; 18–24 inches gives more weather protection. The overhang is also multiplied by the pitch factor to get its along- slope length, because the rafter slopes down past the wall at the same angle.

For a 6/12 pitch with a 12-inch overhang, the overhang contributes 12 × 1.118 = 13.4 inches of additional rafter length along the slope. Add that to the run-to-ridge slope length to get total cut length.

The ridge correction

At the upper end of the rafter, you cut a plumb cut that lands flush against the ridge board. Most ridges are 2x stock (1-1/2" thick), so you subtract half the ridge thickness — 3/4" — from the horizontal run before multiplying by the pitch factor. For a 6/12 pitch, that is 0.84" off the slope length. Small, but real for a precise cut. The calculator does not include this offset; subtract it manually before final cut.

The bird's-mouth seat cut

The rafter sits on the wall plate via a bird's-mouth cut — a level seat cut where the rafter rests on top of the plate, plus a plumb cut that runs flat against the outside face of the wall. The seat cut depth must leave at least enough wood above the plate for the rafter to actually transfer load (rule of thumb: at least 2/3 of the rafter depth remains above the seat). For a 2x10 rafter, that is ~6" above the seat cut.

Plumb-cut angle

The plumb-cut angle (used at both the ridge and the bird's-mouth) is arctangent of pitch ÷ 12. A 6/12 rafter cuts at 26.6° off vertical; a 9/12 rafter cuts at 36.9°. Set your circular saw or use a Speed Square at the pitch number printed on it for the matching plumb cut.

Hip and valley rafters

Hip and valley rafters run on a 17:12 effective slope (not 12:12 like commons), because they travel diagonally across a 12×12 horizontal grid. A 6/12 hip rafter has a pitch factor of √(36 + 17²) ÷ 17 ≈ 1.10, applied to a longer hip run = √(run² + run²) = run × √2 = run × 1.414. Hip rafter length math is a separate calculation; this calculator handles common rafters only.

Common errors

Using run instead of slope length. A 24-ft-wide gable roof needs 13.4-ft rafters (per 6/12 pitch), not 12-ft. Running with 12-ft stock leaves you short at the eave. Always buy stock 1–2 ft longer than the calculated slope length.

Measuring overhang horizontally instead of along the slope. A 12-inch horizontal overhang is 13.4 inches of rafter material at 6/12 pitch. Mark the cut along the slope, not horizontally.

Skipping the ridge correction. Half the ridge board (3/4" for 2x stock) needs to come out of the run. Forget it and your rafters jam against each other at the peak.

Quick FAQ

What is the pitch factor for a 6/12 roof? 1.118. Multiply run by this to get rafter slope length.

How long should the eave overhang be? 12" is the most common; 18–24" gives more protection from rain and sun, but adds load and material cost.

Does this calculator size rafters? No — it gives length only. Rafter size depends on snow load, species/grade, spacing, and ceiling-joist tie. AWC and IRC R802.5 span tables are the right reference.

Estimate only. The rafter length calculator returns cut length, not structural rafter size. Verify sizing against engineered roof plans, IRC R802.5 span tables, or a licensed engineer for snow-region or cathedral-ceiling work.