WoodCalcs.uk
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
For fine furniture and bookcases, 2-3mm of sag is generally considered acceptable and barely visible. Workshop shelves may tolerate 5mm. For display shelves, aim for less than 1mm deflection.
Yes, dramatically. A 6mm hardwood lip glued and pinned to the front edge of an 18mm shelf can reduce sag by 40-50% because it effectively increases the thickness of the cross section where bending stress is highest.
Ash and maple have the highest stiffness (12,000-12,600 MPa). Oak is also excellent at 11,000 MPa. Birch plywood at 10,500 MPa is a great sheet material option. Avoid MDF and chipboard for spans over 600mm with heavy loads.
Paperback books weigh about 20-25 kg per metre of shelf. Hardbacks average 30-40 kg/m. Large reference books or records can be 50+ kg/m. A good default for general bookshelves is 30 kg/m.
Yes. The deflection shown here is the initial elastic sag the moment the load goes on. Wood creeps under constant load, so a permanently loaded shelf can sag roughly 50% more than the initial figure over the years (the Sagulator and Hoadley’s Understanding Wood use the same ~50% rule of thumb; EN 1995-1-1 gives a creep factor kdef = 0.6 for solid timber in dry indoor conditions, i.e. total ≈ initial × 1.6). For a permanent bookcase, design so the initial deflection is comfortably under your sag limit — aim for about two-thirds of it — to leave headroom for long-term creep.
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Last updated: March 2026
All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.