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A shelf doesn’t have to break to fail — a visible sag looks bad and gets worse over time. Enter the material, span, depth, thickness and load to see how far the middle will sag and how much weight it can take before the sag becomes noticeable.
How it works
For a load spread evenly along a shelf supported at both ends, the sag in the middle is δ = 5wL⁴ ÷ (384EI), where w is the load per inch, L the span, E the stiffness of the material and I depends on the shelf’s depth and thickness (depth × thickness³ ÷ 12). Woodworkers commonly treat 0.02 in of sag per foot of span as the point where sag becomes visible.
What changes sag the most
- Span: sag grows with the fourth power of the span — halving the span cuts sag by 16×.
- Thickness: sag falls with the cube of thickness — going from ¾ in to 1 in cuts sag by more than half.
- A front edge strip glued on edge adds a lot of stiffness for very little material.
- Material: MDF and particleboard are only about a quarter as stiff as hardwood.
FAQ
How far apart should shelf brackets be?
For ¾ in plywood carrying books or tools, about 24–32 in apart is a common safe spacing. Run the calculator with your actual load.
Will a shelf keep sagging over time?
Yes — wood creeps under constant load, so a shelf at the limit today will sag more in a year. Design with some margin.
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