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.
Last updated: September 2026
Formula below · 2 sources (fpl.fs.usda.gov, Wikipedia) · Updated Sep 2026
Compare with similar
About this calculator
This calculator applies the standard beam deflection formula for a simply supported board under a uniformly distributed load: δ = (5 × w × L⁴) / (384 × E × I). Here δ is the mid-span deflection in inches, w is the load per inch of span (the load setting is in pounds per foot, so it is divided by 12), L is the unsupported span in inches, E is the modulus of elasticity of the wood in psi, and I = (width × thickness³) / 12 is the second moment of area of the board in in⁴. The E values used (600,000 to 1,200,000 psi) are deliberately on the low side of published averages, so the sag estimate errs high. A stiffer wood (higher E) deflects less, and doubling the thickness reduces sag by a factor of eight because thickness is cubed. A deflection of L/360 or less is a common target for shelving and furniture. Wood also creeps under long-term load, so a shelf loaded permanently can sag up to about 1.5–2 times this initial figure over time.
How to use
Say you have a pine shelf (E = 800,000 psi in this calculator) that is 48 inches long, 12 inches wide and 1.5 inches thick, carrying the Standard table load of 40 lb per foot (3.33 lb per inch). I = (12 × 1.5³) / 12 = 3.375 in⁴. δ = (5 × 3.33 × 48⁴) / (384 × 800,000 × 3.375) = (5 × 3.333 × 5,308,416) / 1,036,800,000 ≈ 0.085 inches. The L/360 limit is 48 / 360 ≈ 0.133 inches, so this shelf passes. The default 8-inch-wide cherry board gives about 0.10 inches.
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).