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
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Last updated: March 2026
All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.