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 stiffness of your selected material and I is the shelf's moment of inertia, calculated as depth × thickness³ ÷ 12. That sag figure is compared against span ÷ 360.
Span ÷ 360 is a long-standing rule of thumb in furniture and cabinetry design for the point where sag becomes visible to the eye on an otherwise sound shelf — it's a cosmetic threshold, not a failure point. Because moment of inertia scales with thickness cubed, small increases in shelf thickness cut sag far more than switching to a stiffer material: doubling thickness reduces sag roughly eightfold, while doubling stiffness only cuts it in half.
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.