Shelf Sag Calculator

How it works

I = b·h³ ÷ 12 · Deflection δ = 5·W·L³ ÷ (384·E·I) for a uniform load on a simply supported shelf

A shelf carrying an even load behaves like a simply supported beam: it sags most in the middle, and the sag grows with the cube of the span but shrinks with the cube of the thickness. That h³ term is why doubling a shelf’s thickness makes it eight times stiffer while adding depth (width) only helps in proportion. Deflection also depends on the material’s stiffness (modulus of elasticity, E) — particleboard sags roughly three times as much as plywood of the same size. Woodworkers judge the result against the L/360 rule of thumb: sag under 1/360 of the span reads as flat; more than that looks like a sagging shelf even if it never breaks.

Worked example

A 36″ span of 3/4″ plywood, 10″ deep (E ≈ 1.6M psi), carrying 30 lb: I = 10 × 0.75³ ÷ 12 = 0.352 in⁴; δ = 5 × 30 × 36³ ÷ (384 × 1,600,000 × 0.352) ≈ 0.032″. That is L/1111 — comfortably inside the L/360 limit (0.10″), so it will look flat.

Sources: Beam deflection — Wikipedia

Frequently asked questions