Why rafter length uses a slope multiplier, not a tape on the attic floor
Why the multiplier is
A common rafter is the hypotenuse of a right triangle whose run is half the building span and whose rise is that run times (pitch rise ÷ 12). Dividing the sloped length by the run gives the same number for every pitch: . You multiply run by that factor instead of walking a tape up the attic floor and guessing the ridge.
Run is span ÷ 2 only on a centered gable. A shed uses the full span. Hips and jacks are longer than the common. Angle is ; plumb is 90° minus that angle; seat is the pitch angle. Full squares and valleys belong on the squares tool. The pitch table on the right already lists multipliers — this guide does not reprint it.
Worked field example
28-foot span, 7:12 pitch, 16-inch eave, 42-foot building length. Not the 24-foot / 6:12 / 12-inch default on the form.
Run is 14 feet. Multiplier for 7:12 is . Common rafter to the plate is 14 × 1.1577 = 16.21 feet (194.5 inches). The 16-inch eave adds 16 × 1.1577 = 18.5 inches on the slope, so stock to the fascia is about 17.75 feet. Ridge rise from the plate is 14 × 7 = 98 inches. Plumb is 90 − 30.26 = 59.74°; seat is 30.26°.
Order commons from that line length plus cutoff, not from the 42-foot ridge. Hip and valley squares are a different takeoff — use the squares calculator.
What IRC R905 actually limits
R905 is a covering chapter, not a rafter-span table. It sets the lowest pitch a given product may see. Framing spans, snow, and wind live in the lumber tables and the engineer's drawing. This tool does not size those.
Covering minimums — not rafter design
- Provision
- IRC R905.2
- Limit
- Asphalt shingles generally 2:12 min; many makers want 4:12 without extra underlayment
- Failure mode
- Shingles on a 2:12 without the ice-and-water the label requires
- Provision
- IRC R905.3–.4
- Limit
- Clay/concrete tile and metal have their own min slopes
- Failure mode
- Using the shingle 2:12 number on tile
- Provision
- IRC R802 (not computed)
- Limit
- Rafter span, species, snow, ridge connection
- Failure mode
- Treating a line length as a span rating
| Provision | Limit | Failure mode |
|---|---|---|
| IRC R905.2 | Asphalt shingles generally 2:12 min; many makers want 4:12 without extra underlayment | Shingles on a 2:12 without the ice-and-water the label requires |
| IRC R905.3–.4 | Clay/concrete tile and metal have their own min slopes | Using the shingle 2:12 number on tile |
| IRC R802 (not computed) | Rafter span, species, snow, ridge connection | Treating a line length as a span rating |
Where the field usually goes wrong
Measuring rise in the attic from the joist to a collar, then treating that as the 12-inch-run pitch, mixes two different triangles. The collar is not 12 inches of run from the plate. Use a level and a 12-inch square on the rafter itself, or compute from span and ridge height.
Cutting hips to the common length is the next miss. A regular hip runs 17 inches on the level for every 12 of common run. Valley steel is a squares problem, not a 10 percent fudge on a common. An offset ridge needs two runs, not span ÷ 2. Heel height has to match; a deeper seat on one common drops the fascia.
Frequently asked questions
What is the difference between pitch and slope?
On a modern job they mean inches of rise per 12 of run. Older texts used pitch as rise over full span. If a drawing says 1/4 pitch it may mean 6:12.
Why is run half the span?
Only on a centered gable. A shed, saltbox, or offset ridge uses a different run. Punch the actual run.
Do I include the overhang in the common length?
Line length to the plate does not. Stock to the fascia is line length plus (overhang × multiplier).
Can I use this length for hip and jack rafters?
No. Commons only. Hips, valleys, and jacks use different triangles.
Where do I convert pitch to roofing squares?
On the roofing-squares page. This tool’s square figure is a gable estimate only.
Does a 2:12 roof take asphalt shingles?
R905.2 allows some products at 2:12 with the listed underlayment. Many architectural shingles still want 4:12. Read the wrapper.
What are plumb and seat cuts?
Plumb is the ridge cut at 90° minus pitch. Seat is the birdsmouth level cut, equal to the pitch angle.