Shelf sag calculator
A shelf that looks fine on the day it is fitted can bow under books a month later. Work out the sag before you cut, and choose the span, thickness or material that keeps the shelf straight.
What changes the sag
Span
The biggest lever: sag grows with the fourth power of the span. Half the span, one sixteenth of the sag.
Thickness
Sag falls with the cube of thickness: 25 mm board sags a little over a third as much as 18 mm.
Material
Plywood and solid wood are several times stiffer than MDF and chipboard.
Load
Books are heavy: a metre of shelf can easily carry 25 kg or more.
How it is calculated
The shelf is treated as a beam resting on a support at each end with the load spread evenly, the standard textbook case: sag = 5 W L³ / (384 E I), with I = b t³ / 12 for a shelf of depth b and thickness t. The shelf’s own weight is added to the load.
| Material | Stiffness used (E) | Where the figure comes from |
|---|---|---|
| MDF | 2,200 N/mm² | Minimum for 12–19 mm general-purpose MDF, EN 622-5 |
| MFC / chipboard | 1,600 N/mm² | Minimum for 13–20 mm P2 board, EN 312 |
| Birch plywood | 6,000 N/mm² | Conservative figure along the face grain |
| Softwood plywood | 4,000 N/mm² | Conservative figure along the face grain |
| Pine | 8,000 N/mm² | Mean for C16 timber, EN 338 |
| Oak | 11,000 N/mm² | Mean for D30 hardwood, EN 338 |
An estimate, not a structural checkReal boards vary, fixings and edge strips stiffen a shelf, and MDF and chipboard keep creeping under a constant load for years. Treat the result as a guide and leave a margin, especially for heavy loads.
Reading the result
The span/600 line is a common woodworking rule of thumb (about 1.7 mm per metre of span). The calculator also gives the longest span that stays within it for your board and load.
Stiffer shelves without a thicker board
Add a support
A centre bracket or divider halves the span and cuts the sag to a sixteenth.
Add a front strip
A hardwood lip glued on edge stiffens the shelf much more than its size suggests.
Run the grain along
On plywood the face grain along the shelf length gives the stiffest shelf.
Questions
How far can an 18 mm MDF shelf span?
For 250 mm deep shelves loaded with books at 25 kg per metre, the calculator gives about 500 mm for span/600. Longer shelves need a support, thicker board or a stiffer material.
Is plywood better than MDF for shelves?
For stiffness, yes: birch plywood is roughly three times as stiff as MDF, and it creeps less under long-term load.
Does the shelf depth matter?
Yes. A deeper shelf is stiffer, but it also holds more, so the load per metre usually rises with it.
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