Shelf Span Calculator — Maximum Shelf Length Before Sagging
Calculate the maximum unsupported shelf span before sagging based on material, thickness, and load.
How We Calculate This
This calculator uses beam deflection theory to determine the maximum unsupported span for a shelf before it sags beyond your acceptable limit.
The formula
For a uniformly distributed load on a simply supported beam:
Deflection = (5 x w x L⁴) / (384 x E x I)
Where w = load per unit length (N/mm), L = span (mm), E = modulus of elasticity (MPa), and I = moment of inertia = (b x h³) / 12 for a rectangular cross section.
The calculator rearranges this formula to solve for L (maximum span) given an acceptable deflection, then applies a 10% safety factor for the recommended span. Because deflection scales with the fourth power of span, dropping to 90% of the maximum span reduces sag to about 66% of the limit.
The formula gives the initial elastic deflection. A loaded timber shelf creeps a further 50% or so over months and years (more for MDF and chipboard), so build to the Recommended Span to leave a margin for this long-term sag.
Frequently Asked Questions
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Last updated: February 2026
All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.