Rafter Length Formula
Rafter length is just the Pythagorean theorem applied to the roof triangle: rafter² = run² + rise². The run is the horizontal distance from the outside wall to the center of the ridge — exactly half the building width for a symmetrical gable roof. The rise is the vertical distance from the top of the wall plate to the top of the ridge board. Once you know both, take the square root of their squares to get the length of lumber you need for the rafter body, plus any overhang at the eave.
Roof Pitch Notation
North American builders describe pitch as rise over 12 inches of run — for example, 6/12 means the roof rises 6 inches for every 12 inches horizontally. A 4/12 pitch is considered low-slope but still suitable for asphalt shingles. 6/12 is the most common pitch for traditional homes. 8/12 and 12/12 are steep slopes used for colonial revival, snow country, and attics you plan to finish later. Below 3/12 you need a waterproof membrane instead of shingles.
How Pitch Relates to Angle
Convert pitch to degrees with arctangent: angle = atan(pitch ÷ 12). A 12/12 pitch is exactly 45 degrees. 6/12 is 26.6 degrees. 4/12 is 18.4 degrees. The calculator shows both degrees and grade percentage (pitch × 8.33) so you can cross-check against framing squares and digital angle finders.
Ordering Rafter Stock
Always order rafters slightly longer than the calculated length. A good rule is to round up to the next even length (8, 10, 12, 14, 16 ft), which covers the bird's mouth cut at the wall plate and leaves room for the plumb cut at the ridge. For example, a calculated rafter length of 13.42 ft should be cut from 16 ft stock; 14 ft is marginal once cuts are made.
Rafter Length Quick Reference
Rafter lengths (ft) for common runs and pitches, calculated from the Pythagorean theorem (no overhang):
| Run | 4/12 (18.4°) | 6/12 (26.6°) | 8/12 (33.7°) | 12/12 (45°) |
|---|---|---|---|---|
| 8 ft (16 ft span) | 8.43 ft | 8.94 ft | 9.61 ft | 11.31 ft |
| 10 ft (20 ft span) | 10.54 | 11.18 | 12.02 | 14.14 |
| 12 ft (24 ft span) | 12.65 | 13.42 | 14.42 | 16.97 |
| 14 ft (28 ft span) | 14.76 | 15.65 | 16.82 | 19.80 |
| 16 ft (32 ft span) | 16.87 | 17.89 | 19.23 | 22.63 |
Multiplier shortcut: rafter length = run × √(1 + (pitch/12)²). Multipliers for common pitches: 4/12 → 1.054, 6/12 → 1.118, 8/12 → 1.202, 10/12 → 1.302, 12/12 → 1.414. So for a 12 ft run at 6/12, rafter = 12 × 1.118 = 13.42 ft. Add 1-2 ft for the overhang and bird's mouth allowance when ordering stock.
Frequently Asked Questions
Is span the same as run?
No. Span is the full building width; run is half the span (for symmetrical gable roofs).
What is a bird's mouth cut?
The notch cut in the bottom of a rafter that sits over the top plate of the wall. It has a seat cut (horizontal) and a heel cut (vertical).
How do I cut the ridge plumb cut?
Set a framing square with 12 on the blade and the pitch number on the tongue, then mark along the tongue for the plumb cut.
What is the maximum rafter span without support?
Depends on lumber size, grade, spacing, and load. A 2×8 SPF rafter at 16" OC with 20 psf live load spans about 14-15 ft. Consult IRC Table R802.4 for your specific load.
Do hip rafters use the same formula?
No — hip rafters run diagonally at 45 degrees in plan, so their run is √2 × the gable run. Use a hip-rafter calculator for that.
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