This shelf sag calculator predicts how much a loaded shelf will bow in the middle, based on its span, the material, its thickness, and the weight on it. It helps you choose a span and thickness that stay below a noticeable — or structurally risky — amount of deflection.
What drives deflection
A shelf behaves like a beam. Deflection rises steeply with span — roughly with the cube or fourth power of the unsupported length depending on how the load is spread — so doubling the span sags far more than twice as much. It falls with the cube of thickness, so adding depth (in the loaded direction) is the most effective fix. Material stiffness matters too: solid hardwood resists sag far better than particleboard or MDF, with plywood in between.
The calculator combines these using the material's modulus of elasticity and the shelf's geometry to estimate the midspan sag for your load, letting you compare options before you build.
Keeping shelves flat
A common guideline is to keep deflection under about 1/180 of the span for appearance, and tighter for heavy or precise loads. If a shelf sags too much you can shorten the span by adding a support, increase the thickness, add a stiffening front edge or apron, or switch to a stiffer material — and the calculator lets you test each change quickly.
Comparing a 900 mm pine shelf with a 600 mm one under the same book load.
- Deflection grows sharply with span (roughly to the third or fourth power).
- Cutting the span from 900 mm to 600 mm is a factor of 0.67 in length.
- That reduces sag by roughly 0.67³ ≈ 0.3 — to about a third.
Shortening the span to 600 mm cuts the sag to roughly a third — the most effective single change.
