How far can a 3/4 inch shelf span before it sags?

A 3/4" hardwood plywood shelf holding books runs to about 39" between supports before the sag shows. Maximum spans by material, thickness and load.

About 39 5/16" between supports, for 3/4" hardwood plywood carrying 25 lb of books per foot.

At a 36" span that shelf sags 1/16" — a ratio of L/469, comfortably inside the L/360 limit.

How that is worked out

  1. Sag goes with the *cube* of the span. Doubling the distance between supports does not double the sag, it multiplies it by eight — which is why the answer changes so fast as a shelf gets longer.
  2. It goes inversely with the cube of the thickness too, for the same reason. Doubling a shelf's thickness cuts its sag to an eighth.
  3. The limit used here is L/360, which is the IRC's floor deflection limit borrowed as a yardstick — it is not law about a bookshelf. The woodworker's rule is tighter: about 1/16" of sag per foot of span, which is roughly where the eye starts to notice.

Maximum span carrying 25 lb/ft, 11 1/4" deep, ends simply supported

Maximum span carrying 25 lb/ft, 11 1/4" deep, ends simply supported
Material3/4" thick1" thick1 1/2" thick
MDF27 1/4"36 5/16"54 1/2"
Melamine-faced particleboard25 5/16"33 3/4"50 5/8"
Particleboard25 5/16"33 3/4"50 5/8"
Baltic birch plywood40 3/16"53 9/16"80 5/16"
Hardwood plywood39 5/16"52 7/16"78 5/8"
OSB31 7/8"42 1/2"63 3/4"
Softwood plywood (CDX)37 1/2"50"74 15/16"
MDO plywood38 7/16"51 1/4"76 13/16"
Hardboard (Masonite)30 1/2"40 5/8"61"
Walnut (solid)40 13/16"54 7/16"81 5/8"
White oak (solid)41 5/8"55 1/2"83 1/4"
Red oak (solid)41 15/16"55 7/8"83 7/8"
Hard maple (solid)42"56"84"
Soft maple (solid)40 1/2"54"81"
Cherry (solid)39 1/4"52 5/16"78 7/16"
Poplar (solid)40"53 5/16"80"
Ash (solid)41 5/16"55 1/16"82 5/8"
Hickory (solid)44 3/8"59 3/16"88 13/16"
Mahogany (solid)39 5/16"52 7/16"78 5/8"
Sapele (solid)41 3/8"55 3/16"82 3/4"
White pine (solid)36 7/8"49 3/16"73 13/16"
Douglas fir (solid)42 7/8"57 3/16"85 13/16"
Cedar (solid)35 9/16"47 7/16"71 1/8"

Worth knowing

  • Load matters as much as span. These assume books at 25 lb per running foot; a shelf of LPs is over twice that, and it changes the answer more than swapping the material would.
  • Fixing both ends properly — housed into dadoes rather than sitting on pins — deflects about a fifth as much as the simply supported case above. A 3/4" shelf that is marginal on pins is comfortable in dadoes.
  • A stiffening lip does more than thickness does, for less material: doubling the thickness to 1 1/2" helps, but a strip of wood glued to the front edge puts material where the bending stress is highest and is the standard fix for a shelf that is too long.
  • Panel moduli are nominal and vary by mill more than wood varies by tree. The ANSI minimum for particleboard is well under what a good sheet makes, so treat the panel rows as a guide and the solid wood rows as firmer.