Shelf Sag Calculator

Inputs

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Clear unsupported span between side panels, brackets or bearing points.
in
Shelf depth across the beam section. A deeper shelf has more area resisting bending.
in
Actual shelf thickness. Stiffness rises with thickness cubed for a rectangular shelf.
in
Total applied load on the shelf. Uniform mode spreads this across the span; point mode puts it at the center or cantilever end.
lbf
Uniform load is typical for books or stored goods. Point load is a concentrated object at midspan, or at the free end for cantilever mode.
Fixed ends are much stiffer in theory but only apply when the shelf ends are truly restrained. Brackets and fasteners still need separate checks.
Approximate modulus presets for a stiffness screen. Use manufacturer or species data for decisions that matter.
Allowable sag is span divided by this number. Example: L/240 allows 0.15 in over a 36 in span.
L/n

Results

Default result
Edit inputs
Max shelf sag(delta)
0.1241in
Pass

simply supported shelf, uniform total load.

Also computed

Allowed sag(L/n)0.15in

Allowable sag = L/240.

Sag margin(margin)Pass0.02589in

Positive margin means calculated sag is below the entered limit.

Span / sag(L/delta)Pass290.1

Compare against L/240.

Bending stress(stress)0.4ksi

Stress = M/S. Compare against material and grade design values separately.

Compare to material design values; no strength pass/fail is assumed.

Max bending moment(M)37.5lbf·ft

M = W*L/8

Equivalent line load(w)33.33lb/ft

Total shelf load divided by span.

Shelf stiffness screen span simply supported shelf uniform total load sag 3.15 mm limit L/240 = 3.81 mm stress 2.76 MPa
Method notes 3 notes
  • Deflection model: delta = 5*W*L^3/(384*E*I); maximum moment model: M = W*L/8.
  • The shelf is treated as a rectangular beam with width equal to shelf depth: I = b*t^3/12 and S = b*t^2/6.
  • Material E presets are approximate. Real sag can change with grade, grain direction, panel layup, moisture, long-term creep, edge banding, back rails, brackets, fasteners and connection restraint.

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