Find how much weight a roof can hold per square foot from its rafter size, spacing, span and lumber grade, or the longest span for a snow or live load.
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- Roof Weight Calculator
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Calculator Functions
The calculator checks one rafter the way the American Wood Council span tables do: for bending strength under the total roof load, and for stiffness under the snow or live load. Select a function to open it in the calculator.
| Function | Use it when | You enter |
|---|---|---|
| Load the roof can hold | You know the rafters and how far they span | Rafter size and spacing, the level span and the lumber grade |
| Maximum rafter span | You know the snow or live load the roof must carry | Rafter size and spacing, the load and the lumber grade |
Each lumber grade fills in its design values from the AWC tables. Choose Custom Fb and E to use values from a grade stamp or another table. The roof’s own weight, its dead load, is 10 psf unless you change it under the optional settings.
Roof Load Formulas
qΔ = 144 × 384EI ÷ (5DsL³) [3]
| qb | Snow or live load bending strength allows, psf |
| qΔ | Snow or live load the deflection limit allows, psf |
| qd | Dead load, the roof’s own weight, psf |
| Fb, E | Bending design value and modulus of elasticity of the lumber, psi |
| S, I | Section modulus b × d² ÷ 6 (in³) and moment of inertia b × d³ ÷ 12 (in⁴), with b = 1.5 in and d the actual depth |
| s, L | Rafter spacing and horizontal span, both in inches |
| D | Deflection limit: 240 for L/240 or 180 for L/180 |
Both come from the formulas for a simple beam with a uniform load: the largest bending moment is wL²/8 and the largest deflection is 5wL⁴/384EI [3]. Here w is the load on each inch of rafter, the roof load in psf times the spacing ÷ 144. As in the AWC rafter tables, bending is checked under the snow or live load plus the dead load, deflection under the snow or live load alone, and the span is measured on the horizontal projection [1]. The smaller of qb and qΔ is the load the roof can hold.
Lumber design values
The calculator uses the snow-loading bending values from AWC Table W-1. They already include the adjustment for repetitive members spaced 24 in or less, and they change with the size of the lumber [2].
| Size | Douglas fir-larch No. 2 | Douglas fir-larch No. 1 | Southern pine No. 2 | Spruce-pine-fir No. 1/No. 2 |
|---|---|---|---|---|
| 2×4 | 1,785 | 1,985 | 1,455 | 1,735 |
| 2×6 | 1,545 | 1,720 | 1,325 | 1,505 |
| 2×8 | 1,430 | 1,585 | 1,225 | 1,390 |
| 2×10 | 1,310 | 1,455 | 1,060 | 1,275 |
| 2×12 | 1,190 | 1,325 | 990 | 1,155 |
| E, all sizes | 1,600,000 | 1,700,000 | 1,400,000 | 1,400,000 |
Deflection limits and minimum roof loads
The International Residential Code limits deflection under live load to L/180 for rafters steeper than 3:12 with no finished ceiling attached, and to L/240 under gypsum board ceilings and for most other members [4]. A roof must be designed for the code’s minimum roof live load or the ground snow load, whichever is greater. The minimum is 20 psf for a flat roof or one with less than 4 in of rise per foot, when a member carries 200 ft² of roof or less; it falls to 16 or 12 psf on steeper roofs and larger areas [4].
Worked example
Take Douglas fir-larch No. 2 2×8 rafters at 16 in on center, spanning 14 ft (168 in) measured level, with a 10 psf roof and a ceiling attached (L/240). A 2×8 has S = 13.141 in³ and I = 47.635 in⁴. Bending allows 8 × 1,430 × 13.141 × 144 ÷ (16 × 168²) = 47.9 psf in total, or 37.9 psf once the 10 psf dead load is taken off. Deflection allows 384 × 1,600,000 × 47.635 × 144 ÷ (5 × 240 × 16 × 168³) = 46.3 psf. Bending governs, so the roof can hold about 37.9 psf of snow or other live load, or 50.6 lb on each foot of rafter.
As a check against the published tables: AWC Table R-1 (20 psf live load, 10 psf dead load, L/240) lists a 14 ft 10 in span for 2×8 rafters at 16 in with Fb = 1,000 psi, which needs E = 820,000 psi [1]. The Maximum rafter span function gives 14 ft 9.6 in for the same values, within half an inch of the table.
Limits of This Estimate
- Like the AWC tables, it checks bending and deflection of sound rafters under an even load on a single span. Notches, rot, splices, heavy point loads such as equipment, and the bearing, connections and ridge are not checked.
- Manufactured trusses and I-joists are designed by their makers and cannot be checked with lumber design values.
- Snow does not always settle evenly. Where it drifts against a higher wall or slides from an upper roof, part of the roof carries more than the average load.
- Local building departments set the design snow load. Before adding weight to a roof or repairing damaged framing, have a structural engineer or the building department confirm the framing.
Sources
- American Wood Council, Span Tables for Joists and Rafters, 2024 Edition: how rafter spans are calculated and measured, the loads and deflection limits of the rafter tables, and Table R-1
- American Wood Council, Design Values for Joists and Rafters, 2024 Edition: Table W-1 bending design values for snow loading and modulus of elasticity by species, grade and size
- American Wood Council, Design Aid No. 6, Beam Design Formulas with Shear and Moment Diagrams: maximum moment and deflection of a simple beam with a uniformly distributed load
- International Code Council, 2021 International Residential Code, Chapter 3: Section R301.6 and Table R301.6 minimum roof live loads, Table R301.7 allowable deflection
