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Bookshelf Sag Calculator

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

How We Calculate This

Deflection is calculated using beam theory: delta = (5 x w x L⁴) / (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 h³ / 12).

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

The figure shown is the initial elastic deflection. Wood creeps under sustained load, so a permanently loaded shelf typically sags around 50% more than this over time (Hoadley, Understanding Wood; EN 1995-1-1 creep factor kdef ≈ 0.6 for dry indoor service). Allow headroom against your sag limit for long-term loading.

Frequently Asked Questions

Last updated: March 2026

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