Shelf sag and span
How far the shelf bends under what you put on it, drawn against the straight line it should have been. Change the span, the thickness or the material and watch the number move — and if it fails, see the span and thickness that would pass.
Solid wood figures are species averages, not the board in your hand
Between supports
= 11.25"
= 0.75"
Rule of thumb — edit it
Zero for an ordinary shelf
Front edge stiffener
A strip glued to the front edge, standing proud below the shelf. Set the height to zero if there is not one.
= 0.75"
Sag in the middle
0.077"
Which is
span ÷ 469
Limit (span ÷ 360)
0.100"
Carrying
75 lb
Before you cut
- Sag within span ÷ 360 — passes0.077" of sag against an allowance of 0.100" — that is span ÷ 469.
- Under 1/32" of sag per foot of span — passes0.026" per foot. Past about 0.031" the curve is visible against a straight line above or below it — which is how anyone notices a sagging shelf.
Span ÷ 360 is the deflection limit the IRC puts on a floor under live load, borrowed here because it is a published number rather than a feeling. The thirty-second of an inch per foot is the woodworking rule of thumb for when sag becomes visible. Neither is a strength calculation: a shelf that sags past both of these is ugly long before it is unsafe.
Where the stiffness comes from
- Material stiffnessNominal for the panel — mills vary
- 1.50 million psi
- SectionBare shelf — thickness cubed, depth only to the first power
- 0.396 in⁴
- Spread load25 lb per running foot
- 0.077" of the sag
- Longest span that passesEverything else unchanged
- 39 5/16"
What this does not know
It works out deflection, not strength, and a shelf has to fail this check by a long way before it is anywhere near breaking. It assumes the load is spread evenly and the supports are solid; a shelf on two pins in a plywood side is only as good as the pins.
It also assumes the shelf is dry and stays dry. Wood creeps: a shelf under a constant load settles further over years than this number says, roughly half as much again, and particleboard in a damp room is worse than that. Design for a little less than the limit if the load is going to sit there for a decade.
About shelves that sag
- How far can a 3/4" shelf span?
- It depends almost entirely on the material. Loaded with hardbacks at 25 lb per running foot and held to a sag of span ÷ 360, 3/4" particleboard manages about 24", hardwood plywood about 38", and solid hard maple about 40". The same shelf with a 3/4" by 2" strip glued to its front edge reaches close to 60". Depth barely enters into it.
- Why does thickness help so much more than depth?
- Because stiffness depends on the cube of the depth of the section in the direction it bends. A shelf bends downward, so its thickness is cubed and its front-to-back depth only counts once: going from 3/4" to 1" stock cuts the sag by more than half, while making the shelf twice as deep only halves it — and costs twice the material to do it.
- Does a strip on the front edge really stop a shelf sagging?
- Yes, and it is the cheapest fix there is. A 3/4" by 2" strip glued to the front edge of a 3/4" plywood shelf more than triples its stiffness, because the strip puts material where the section is deepest. It has to be glued along its whole length and it has to stand proud below the shelf — an edge band flush with the surface is decoration and does nothing.
- How much do books weigh?
- About 20 lb per running foot for paperbacks, 25 for ordinary hardbacks and 35 for large-format art and reference books packed tight. Vinyl records are the heaviest thing most shelves carry, near 55 lb a foot. These are rules of thumb and your shelf is not average, which is why the figure is editable here.
- Will the shelf sag further over time?
- Yes. Wood and wood panels creep: under a constant load they keep deflecting for years, ending up roughly half as much again as the initial figure, and more in a damp room or in particleboard. A shelf that is exactly at the limit on the day you build it will be past it in a decade, so leave some margin on anything that will be loaded and left.