Shelf Sag Calculator

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Estimate only, not a structural design tool. It checks stiffness (sag) of a solid rectangular board on two simple supports, never strength: it does not check breaking, shear, brackets, fasteners or wall anchors. Do not use it to size shelves that carry people, heavy equipment, or anything where failure could injure someone; ask a qualified engineer.

How it works

Moment of inertia I = depth × thickness³ / 12. Uniform load: sag = 5·W·L³ / (384·E·I). Centre point load: sag = W·L³ / (48·E·I), where W is the total load in lb and L the span in inches (USDA Wood Handbook, FPL-GTR-282, Table 9-1: kb = 5/384 and 1/48). Shear deflection is ignored. The visible flag trips when sag exceeds span/300, a common comfort rule of thumb, not a code limit for shelves.

Middle support assumption: the board is treated as two separate simply supported spans of L/2, each carrying half the load, so sag is the uniform result divided by 16 and the L/ratio uses the half span. A real continuous board deflects somewhat less, so this is conservative. The middle-support option is ignored for a centre point load.

Wood presets: modulus of elasticity at 12% moisture content from Wood Handbook FPL-GTR-282 (2021), Table 5-3b (inch-pound), in 10⁶ psi: eastern white pine 1.24, western redcedar 1.11, Sitka spruce 1.57, loblolly pine 1.79, Coast Douglas-fir 1.95, yellow-poplar 1.58, black cherry 1.49, black walnut 1.68, red maple 1.64, sugar maple 1.83, northern red oak 1.82, white oak 1.78. These are clear-wood averages; real lumber, especially with knots, varies, and the handbook notes E was measured with some shear deflection included. Plywood, MDF, particleboard and other panels have no preset: enter E from the manufacturer's data sheet for your product and its grain direction. Wood also creeps, so sag under a long-term load grows over the years.