Table Sag Calculator
Estimates the mid-span deflection of a table top or shelf under a given load using beam-bending theory. Use it to verify that your chosen wood thickness won't visibly sag under typical weight.
About this calculator
This calculator applies the standard Euler–Bernoulli beam deflection formula for a uniformly distributed load: δ = (5 × w × L⁴) / (384 × E × I). Here, δ is the maximum mid-span deflection, w is the load per unit length, L is the unsupported span, E is the modulus of elasticity of the wood species, and I is the second moment of area of the cross-section, calculated as I = (width × thickness³) / 12. A stiffer wood species (higher E) deflects less, as does a thicker board — crucially, doubling the thickness reduces sag by a factor of eight because thickness appears cubed. Engineers typically consider a deflection of L/360 or less acceptable for furniture and shelving. This formula assumes the board acts as a simply supported beam with ends resting freely on supports.
How to use
Say you have a pine shelf (E ≈ 1,500,000 psi) that is 48 inches long, 12 inches wide, and 1.5 inches thick, carrying a uniform load of 5 lb/in. I = (12 × 1.5³) / 12 = (12 × 3.375) / 12 = 3.375 in⁴ δ = (5 × 5 × 48⁴) / (384 × 1,500,000 × 3.375) = (25 × 5,308,416) / (1,944,000,000) ≈ 132,710,400 / 1,944,000,000 ≈ 0.068 inches The acceptable limit is 48/360 ≈ 0.133 inches, so this shelf passes comfortably.
Frequently asked questions
How thick should a wood shelf be to prevent sagging under heavy books?
For a typical 36-inch bookshelf span loaded with books (roughly 25–30 lb/linear foot), a 3/4-inch plywood shelf will deflect noticeably, while a 1-inch solid hardwood or 1.5-inch thick shelf keeps deflection within the L/360 rule of thumb. Stiffer species like oak or maple perform significantly better than pine or MDF at the same thickness. Adding a hardwood nosing or a back rail to the front and back edges creates a torsion box that dramatically stiffens the shelf. When in doubt, run the numbers with this calculator before committing to a design.
What is the L/360 deflection rule and why does it matter for furniture?
The L/360 rule states that maximum mid-span deflection should not exceed the span length divided by 360; for a 36-inch shelf that is 0.1 inches. Beyond this threshold, deflection becomes visually noticeable and can feel structurally unsafe to users. The rule originated in structural engineering for floor beams but is widely adopted by furniture designers as a practical comfort standard. Exceeding L/360 doesn't necessarily mean immediate failure, but it signals that the design is undersized for long-term use without creep or permanent set.
Why does doubling the thickness of a board reduce sag so much more than doubling the width?
Because the second moment of area I = (width × thickness³) / 12 raises thickness to the third power but width only to the first. Doubling the width halves the deflection, but doubling the thickness reduces deflection by a factor of eight (2³). This is why woodworkers and engineers prioritize board thickness over width when fighting sag. In practice, it means that laminating two thin boards face-to-face (doubling thickness) is far more effective than laminating them side-by-side (doubling width).