A 2x8 Douglas fir-larch No. 2 rafter at 16 inches on center, under a 30 psf snow load and 15 psf of roofing, can span 14 ft 5 in horizontally when no ceiling hangs from it. At 24 in spacing the same rafter reaches 11 ft 10 in; a 2x10 reaches 14 ft 5 in at 24 in. The calculator above gives the maximum span for any of four common species, three grades, five sizes and four spacings, checks your run against it and counts the rafters.
How the calculator works
Choose the lumber, the spacing and the loads, then enter the horizontal run of your rafter. The result is the maximum span, whether bending strength or stiffness limits it, the smallest size that works for your run, and a table of every size and spacing for the same lumber and loads.
The method
The spans come from the method the American Wood Council uses for its Span Tables for Joists and Rafters, the source of the rafter tables in the building codes. A rafter is treated as a single span with a uniform load. Bending limits the span to √(8·Fb·S ÷ w), where Fb is the bending design value, S the section modulus and w the dead plus snow load per inch of rafter. Deflection limits it so that the sag under the snow load, 5·w·L⁴ ÷ (384·E·I), stays under the span divided by 180 (no ceiling attached) or 240 (drywall ceiling attached, as in a cathedral ceiling). The shorter of the two governs. The calculator reproduces tabulated AWC spans to the inch.
Design values
Fb and E for each species and grade come from AWC's Design Values for Joists and Rafters (Table W-1). These values already include the size factor and the repetitive member factor that applies when rafters are spaced 24 in or less. Snow is a two-month load, so roofs use the snow-duration bending value, about 15 % higher than the normal value. Spaced wider than 24 in, rafters lose the repetitive member factor and Fb drops 13 %.
| 2x8 No. 2 @ 16 in, 30 + 15 psf, L/180 | Fb snow, psi | E, psi | Maximum span |
|---|---|---|---|
| Douglas fir-larch | 1,430 | 1,600,000 | 14' 5" |
| Southern pine | 1,225 | 1,400,000 | 13' 4" |
| Hem-fir | 1,350 | 1,300,000 | 14' 0" |
| Spruce-pine-fir (No. 1/No. 2) | 1,390 | 1,400,000 | 14' 3" |
Loads
Use the roof snow load your building department gives for your location; where snow is light, the minimum roof live load is 20 psf. Dead load is the weight of the roof itself: about 10 psf for light roofing on sheathing, 15 psf for asphalt shingles with sheathing and insulation, 20 psf for heavier coverings. Heavier tile or slate roofs need their actual weight.
Run, not rafter length
Rafter spans in the tables and here are horizontal: the run from the wall to the ridge support, not the sloped length of the board. The sloped length matters for buying lumber, and the calculator works it out from the pitch and the overhang: a 12 ft run at 6/12 is 13 ft 5 in along the slope, 14 ft 5 in with a 12 in overhang, so you buy 16 ft boards. Members per slope are the roof length divided by the spacing, plus one.
Common mistakes
- Using the sloped length as the span. The tables are horizontal; using the sloped length makes rafters look too short and oversizes them.
- Ignoring the ceiling. A drywall ceiling attached to the rafters needs L/240; at L/180 it cracks.
- Wide spacing with the same Fb. Beyond 24 in, rafters are not repetitive members and lose 13 % of their bending value.
- Rafters without ties. Span tables assume the outward thrust is resisted by ceiling joists, rafter ties or a structural ridge.
For the whole gable roof framing, use the Roof Pitch Calculator; for floors, the Joist Span Calculator.