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: October 2026
Expected Sag
0.07 inches
Formula below · 3 sources (research.fs.usda.gov, awc.org, hardwoodinfo.com) · Updated Oct 2026
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About this calculator
A board supported only at its ends sags in proportion to the load and the fourth power of the span, and in inverse proportion to its stiffness: a 48-inch, 1.5 × 8-inch black cherry board under 40 lb per foot sags about 0.07 inch here, well inside the common L/360 limit of 0.13 inch. The calculator uses the standard formula for a simply supported beam under a uniform load, δ = 5wL⁴ ÷ (384EI).
The inputs
w is the load per inch of span (the load setting in lb per foot divided by 12), L is the unsupported span in inches, E is the wood's modulus of elasticity in psi, and I = width × thickness³ ÷ 12 is the board's second moment of area. The species settings use the USDA Wood Handbook's average values for clear wood at 12% moisture, from 1.11 million psi for western red cedar to 1.95 million psi for coast Douglas fir; the oak or hard maple setting uses white oak's 1.78 million psi, the lowest of the three. Real boards with knots or slope of grain can be less stiff than these averages, so leave some margin below L/360.
What changes sag most
Span matters most: doubling it multiplies sag by 16. Thickness comes next: doubling it cuts sag to one eighth, while doubling the width only halves it. That is why adding a front apron or an edge strip set on edge stiffens a shelf far more than using a wider board. Stiffer species help in direct proportion to their modulus.
Long-term loads
Wood creeps under a sustained load, so a permanently loaded shelf keeps sagging slowly after the first day. The National Design Specification for Wood Construction multiplies the long-term part of deflection by a creep factor of 1.5 for seasoned (dry) lumber and 2.0 for unseasoned lumber. Aim for well under L/360 for shelves that carry books year-round. The table below lists the calculator's Wood Handbook stiffness values and the sag they give for the default board.
| Species | Modulus of elasticity at 12% moisture (million psi) | Sag (in) | Within L/360 (0.133 in)? |
|---|---|---|---|
| Douglas-fir (coast) | 1.95 | 0.053 | Yes |
| White oak (oak or hard maple setting) | 1.78 | 0.058 | Yes |
| Black walnut | 1.68 | 0.061 | Yes |
| Black cherry | 1.49 | 0.069 | Yes |
| Eastern white pine | 1.24 | 0.083 | Yes |
| Western redcedar | 1.11 | 0.092 | Yes |
How to use
Enter the unsupported span between supports, the board thickness and width in inches, and choose the wood and the load. The default, a 48-inch span of 1.5 × 8-inch cherry under a standard table load of 40 lb per foot, gives about 0.07 inch (0.069 before rounding), under the L/360 limit of 48 ÷ 360 = 0.13 inch. For a 12-inch-wide eastern white pine shelf of the same span and thickness, the result is about 0.06 inch (0.055).
Frequently asked questions
How thick should a wood shelf be to avoid sagging?
It depends on span and load more than species. Run your span and load through the calculator and choose the thickness that keeps sag under L/360 (span ÷ 360). Because sag falls with the cube of thickness, going from 3/4 inch to 1 inch cuts sag by more than half; shortening the span or adding a mid support helps even more.
What is the L/360 rule?
It limits deflection to the span divided by 360, about 0.1 inch on a 36-inch shelf. It comes from floor and beam design, where it keeps deflection from being noticeable, and woodworkers borrow it as a stiffness target for shelves and tabletops.
Why does thickness matter more than width?
Stiffness depends on width × thickness³. Doubling the width doubles stiffness and halves sag; doubling the thickness multiplies stiffness by eight and cuts sag to one eighth. Gluing two boards face to face is therefore much stiffer than gluing them edge to edge.
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