Shelves only sag after the glue is dry and the books are loaded. Check your shelf before you build — enter span, thickness, material and load to see exactly how much it will bend, and whether anyone will notice.
Your shelf
How the math works
A shelf is a beam. Under a uniform load the mid-span sag is 5wL⁴ / 384EI (free span) or wL⁴ / 384EI (fixed ends), where E is the material’s stiffness and I = depth × thickness³ ÷ 12:
Sag = 5 × load × span³ ÷ (384 × E × I), simplified for uniform load
Tips for sag-free shelves
- Thickness beats material. Doubling thickness cuts sag 8×; switching from pine to oak only halves it. For 30″+ spans, go 1″ thick or add a front edge strip.
- Fix the ends. Dadoes or screws into both ends cut sag to one-fifth of a free span — the support selector shows the difference.
- Plywood wins for books. ¾″ plywood on a 36″ span with 30 lbs sags just 0.037″ — barely noticeable, exactly the default calculation above.
- Building the shelf? Figure your lumber with the board foot calculator, and if it’s painted, estimate finish with the paint coverage calculator.
Frequently asked questions
How much sag is acceptable for a shelf?
The woodworking rule of thumb is 0.02″ of sag per foot of span — anything under that looks flat to the eye. The calculator flags your result against this standard.
Will a 36 inch plywood shelf sag?
With ¾″ plywood carrying 30 lbs, sag is about 0.037″ total (0.012″ per foot) — barely noticeable. Heavier loads or particle board push it into visible territory.
Does MDF sag more than plywood?
Yes — MDF’s stiffness (E ≈ 0.55M psi) is less than half of plywood’s (1.4M psi), so the same shelf sags roughly 2.5× more. Keep MDF spans under 24″ for books.
Do shelf pins or fixed ends matter?
A lot. A shelf dadoed or screwed at both ends behaves as a fixed beam and sags only one-fifth as much as the same shelf resting on pins.