Shelf Span Calculator

About this calculator

An unsupported shelf behaves like a simply-supported beam under a uniform load, and its deflection (sag) at the center is given by δ = 5wL⁴ / (384EI), where w is the load per unit length, L is the span, E is the material's modulus of elasticity (stiffness), and I is the shelf's moment of inertia (a function of thickness and depth). Solving for the span that keeps δ under an acceptable limit gives the maximum safe shelf span before sag becomes visible.

Furniture and cabinet makers, along with DIYers building bookshelves or garage shelving, use this calculation to decide how far apart to space shelf supports or brackets for a given material and expected load, since shelves built from softer materials like particleboard sag over a far shorter span than solid hardwood or plywood of the same thickness.