Shelf sag calculator

Limits of this estimate

• This is an estimate. Real boards vary, and knots or cross grain make a shelf less stiff than the clear-wood test values.
• Wood keeps sagging under a load that stays put (creep). The Wood Handbook says that after several years the extra sag can roughly equal the first sag, and more in heat or humidity. Plan for a long-loaded shelf to sag about twice as much as shown.
• This does not check brackets, pins, cleats, screws, or the wall. It does not tell you how much weight a shelf can safely hold.
• Plywood and MDF are not included because we could not find a single reliable stiffness value to cite.
• Don't use this for anything where a sagging or failed shelf could hurt someone, such as shelves over beds or seating, children's furniture or overhead storage. Get proper hardware and, if in doubt, a qualified pro.

The formula

Sag = 5 × w × L⁴ ÷ (384 × E × I), where w is the load per inch of span, L is the span, E is the wood’s modulus of elasticity (MOE), and I = depth × thickness³ ÷ 12. This treats the shelf as resting on two supports with the load spread evenly.

Worked example

A ¾″ × 10″ red oak shelf spanning 36″ with 50 pounds spread along it: I = 10 × 0.75³ ÷ 12 ≈ 0.352 in⁴, w = 50 ÷ 36 ≈ 1.39 lb/in, E = 1,820,000 psi. Sag ≈ 0.047″ (1.2 mm). The rule-of-thumb limit for a 3-foot span is 3/32″ (0.094″), so this shelf is within it.

The 1/32″ per foot guideline

Many woodworkers aim for no more than 1/32″ of sag per foot of span, because more than that tends to be visible. This is a common woodworking rule of thumb, not a building code or engineering standard, and we did not find an authoritative source for it.

Species stiffness

Sources

• Modulus of elasticity values: Wood Handbook: Wood as an Engineering Material, FPL–GTR–282 (2021), chapter 5, Table 5–3b (inch–pound; metric in Table 5–3a), static bending, 12% moisture content. Forest Products Laboratory, USDA Forest Service. Wood Handbook, chapter 5 (PDF, USDA Forest Service)↗ (external site, opens in a new tab)
• Creep: same chapter, “Time Under Load,” section “Creep and Relaxation” (page 5–38 onward).
• Beam formula: standard result for a simply supported beam under a uniform load, Wood Handbook, FPL–GTR–282 (2021), chapter 9 (Structural Analysis Equations), Table 9–1 (deflection coefficient 5/384 for a uniformly loaded beam on two simple supports). Wood Handbook, chapter 9 (PDF, USDA Forest Service)↗ (external site, opens in a new tab)
• 1/32″ per foot: common woodworking rule of thumb; no authoritative source found.