calcs.homes
calcs.homes
Estimate how much a shelf will sag under load, based on material, thickness, span, and weight — so you can catch a problem before you mount it.
Estimate only — real deflection also depends on grain direction, moisture, and edge support.
We use the standard engineering beam deflection formula for a uniformly loaded, simply supported beam: sag = (5 × load × span³) ÷ (384 × E × I), where E is the material's stiffness and I is the shelf's moment of inertia (depth × thickness³ ÷ 12). We compare that against span ÷ 360, a common rule-of-thumb limit for barely-noticeable sag.
Shorten the span with an added support bracket, increase thickness (deflection drops with the cube of thickness, so even a small increase helps a lot), or switch to a stiffer material like plywood or hardwood instead of particleboard.
Deflection scales with the cube of thickness but only linearly with material stiffness — doubling thickness cuts sag by 8×, while doubling stiffness only cuts it by half. When in doubt, add thickness or a mid-span support.