Shelf Sag Calculator
Estimate how far a shelf will bow under a load before you build it. Enter the span, depth, thickness, total weight and material to see the sag and whether it stays within the usual 1/32 inch per foot guideline.
How to calculate shelf sag
- Enter the clear span between supports and the shelf depth and thickness in inches.
- Enter the total weight the shelf will carry and pick the material.
- Read the sag and sag per foot, then thicken the shelf or shorten the span if it is too much.
Examples
A 36 in pine shelf holding 40 lb
Span 36 in, depth 10 in, thickness 0.75 in, load 40 lb, pine
Sag about 0.063 in (0.021 in per foot), within the guideline
Frequently asked questions
How much shelf sag is acceptable?
A common rule of thumb is no more than 1/32 inch of sag per foot of span. At that level the bow is barely visible and the shelf still looks flat with a row of books on it.
What formula does this use?
It models the shelf as a simply supported beam under a uniformly distributed load: sag equals 5 times load times span cubed, divided by 384 times the modulus of elasticity times the moment of inertia.
Does it assume fixed or simply supported ends?
It assumes simply supported ends, where the shelf rests on supports and is free to rotate. Shelves fixed in dados or screwed to cleats sag less, so this gives a safe worst case.
Why does thickness matter so much more than depth?
Stiffness depends on thickness cubed but only on depth to the first power. Doubling the thickness cuts sag to one eighth, while doubling the depth only halves it.
How do I reduce a shelf that sags too much?
Shorten the span by adding a support, use a thicker or stiffer board, add a front edge stiffener, or switch to a higher modulus material such as oak or plywood.
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