How this shelf sag calculator works
It applies the standard simply-supported beam deflection formulas: for a load spread evenly across the shelf, sag = 5WL³ / (384EI); for a load concentrated at the center, sag = WL³ / (48EI). W is the total load in pounds, L the span in inches, E the species' modulus of elasticity, and I = (depth × thickness³) / 12 the moment of inertia of the shelf's rectangular cross-section — which is why thickness matters so much more than depth.
This estimates the shelf itself, not the wall brackets, cleats, or dado joints holding its ends — those can sag or pull loose independently of the wood's own stiffness.
Sources
Modulus of elasticity for solid species: USDA Forest Products Laboratory, Wood Handbook: Wood as an Engineering Material (FPL-GTR-190), Chapter 5, Table 5-3b (12% moisture content, static bending). Sheet-good figures: Engineering ToolBox, timber & panel mechanical properties. Deflection formulas, the 0.02 in./ft guideline, and the "+50% over time" creep rule of thumb: Fine Woodworking, "Engineer Shelves With the Sagulator" and the WoodBin Sagulator.
Questions
How much shelf sag is acceptable?
A common engineering guideline is 0.02 in. of sag per foot of span or less. Beyond that, sag around 1/32 in. (0.03 in.) per foot starts to look visibly crooked to the eye.
Does shelf sag get worse over time?
Yes — wood creeps under sustained load, so a shelf that measures fine on day one typically sags further afterward. A widely used rule of thumb is roughly 50% more sag than the initial elastic deflection this calculator computes.
Is plywood or solid wood stiffer for a shelf?
It depends on species and grain direction more than on plywood-vs-solid as a category. This calculator's plywood figure assumes the face grain runs parallel to the span (the stiffest orientation) — grain running across the span is much weaker.
What's the fastest way to stop a shelf from sagging?
Shorten the span (add a support) or add thickness — thickness matters a lot, since stiffness scales with thickness cubed. Doubling thickness cuts sag to about an eighth, all else equal.
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