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Bookshelf Sag Calculator

Calculate maximum span before shelf sag for given wood species, thickness, and load.

Wood type determines stiffness (modulus of elasticity)

Cross-section height of the shelf

Front to back dimension

Unsupported distance between supports

Weight of items per metre of shelf (books ~30 kg/m)

How We Calculate This

Deflection is calculated using beam theory: delta = (5 x w x L\u2074) / (384 x E x I)

Where w is the load per unit length, L is the span, E is the modulus of elasticity for the wood species, and I is the moment of inertia of the shelf cross section (b x h\u00b3 / 12).

The maximum span is found by rearranging the formula to solve for L at the acceptable deflection limit.

Frequently Asked Questions

Last updated: March 2026

All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.