How to use the shelf sag calculator
- Measure the unsupported span, actual shelf depth, and thickness in inches.
- Enter the total load spread evenly across the shelf, including the shelf’s own weight if needed.
- Enter the appropriate elastic modulus. The default is illustrative and is not a rating for a wood species or panel.
The formula
Deflection = 5 × total load × span³ ÷ (384 × E × I), where I = depth × thickness³ ÷ 12
Worked example
A 36 in span, 12 in depth, ¾ in thickness, 50 lb distributed load, and E = 1,300,000 psi gives about 0.055 in of initial sag.
Before you measure and cut
The model assumes a rectangular, uniform shelf with simple supports at its ends. A center support, fixed ends, an edge stiffener, or a point load changes the model.
Thickness is cubed in section inertia. Small changes in thickness can therefore have a large effect on stiffness.
Frequently asked questions
Is this a safe-load calculator?
No. Deflection alone does not check bending strength, connection capacity, stability, or product suitability.
Will long-term sag be larger?
It can be. Creep, moisture changes, and duration of load are not included in this immediate elastic estimate.
Reference
USDA: Mechanical properties of wood. Material properties and setup conventions depend on the specific product.