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Shelf sag calculator
Pick the species, enter the shelf size and the weight it will carry, and see how far the middle will bend, whether that meets a common 0.02 inch per foot target and how thick the shelf would need to be.
How to use this calculator
The calculator treats the shelf as a simply supported beam with an evenly spread load, the textbook case for a shelf resting on pins or cleats at each end. Mid-span deflection is δ = 5wL⁴ / (384EI), where w is the load per unit length (total load divided by span), L is the span, E is the modulus of elasticity of the wood and I is the second moment of area of the shelf cross-section, b × h³ ÷ 12 for a board of depth b and thickness h.
E comes from the USDA Forest Products Laboratory Wood Handbook (FPL-GTR-282), Chapter 5, which lists the modulus of elasticity of small clear specimens at 12% moisture content: for example 1.24 million psi for eastern white pine, 1.68 million psi for black walnut and 1.83 million psi for sugar maple. Those values come from bending tests on short specimens, and real boards with knots or slope of grain can be less stiff.
Because thickness is cubed, it matters far more than species. Going from 3/4 inch to 1 inch thick makes a shelf about 2.4 times stiffer, while switching from pine to maple makes it about 1.5 times stiffer. Shortening the span helps most of all: sag grows with the span to the fourth power for the same load per foot.
The 0.02 inch per foot target is a widely used woodworking rule of thumb for sag you won't notice, not a building-code limit. Wood under a constant load also creeps, so a shelf loaded for years will end up sagging more than this short-term figure. If the verdict is close, add thickness, an edge strip, or a support in the middle.
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Questions about this calculator
How thick should a bookshelf be?
It depends on the span, depth, species and the books. Enter your numbers above: the calculator shows the thickness needed to stay within 0.02 inch per foot. Shorter spans let you use thinner shelves.
Does a front edge strip reduce sag?
Yes. A solid strip glued to the front edge adds depth where it counts, because stiffness rises with the cube of the height of the section. This calculator models a plain rectangular board, so an edged shelf will do better than shown.
Can I use this for plywood or MDF?
Not directly. The stiffness values are for solid, clear wood. Plywood and MDF are less stiff than most solid hardwoods, so they will sag more for the same size.