Shelf sag calculator, will it hold the books?

What counts as flat

A shelf that sags less than 1/32 inch per foot of span reads as straight to the eye; a 3-foot shelf may dip 3/32 inch in the middle and nobody notices. Between 1/32 and 1/16 inch per foot the curve shows along the front edge in raking light. Beyond that the shelf looks loaded, and because wood creeps, a sag you can see in the first month will roughly double over the years.

How it is worked out

The shelf is treated as a beam. For a load spread along a shelf that rests on its supports, the sag in the middle is 5 W L³ / (384 E I), where W is the total weight, L the span, E the stiffness of the wood and I the second moment of the cross-section, b t³ / 12 for a plain board of depth b and thickness t. A single weight in the middle sags more, P L³ / (48 E I). Ends glued or screwed into the sides of a cabinet are stiffer; the calculator treats them as fixed, which cuts the sag by about four to five times. Real joints are somewhere between, so treat the fixed figure as the best case.

Because thickness enters as a cube, a little more wood does a lot: going from 3/4 to 1 inch cuts the sag by more than half. Span enters as a cube too, so a shelf twice as long sags eight times as much under the same total load. Depth only helps in proportion.

Loads to expect

• Paperbacks: about 15 lb per foot of shelf. Hardcovers and textbooks: 20 to 25 lb. Oversized art books: 30 lb and up.
• Vinyl records stood on edge: about 35 lb per foot.
• A rock collection on a shelf is heavier than it looks: a flat of specimens runs 10 to 20 lb per foot.

Stiffness values come from the USDA Forest Products Laboratory Wood Handbook (2010, chapter 5) at 12 percent moisture; sheet goods are typical figures and vary by brand. The result is a design estimate, not a guarantee: knots, grain run-out and a board that was wetter than you thought all add sag.