Shelf sag calculator

The shelf is a simply supported beam (resting on pins or in dados at each end, free to rotate).

Mid-span sag — spread load: δ = 5wL⁴ / 384EI; point load at the centre: δ = PL³ / 48EI, with span L, load w per unit length or P total, modulus of elasticity E, and second moment of area I = bt³/12 for depth b and thickness t.
Stiffeners — a strip glued to the front (or front and back) edge, flush with the top, adds to I through the parallel-axis theorem; a strip of a different material counts as a transformed width scaled by its stiffness ratio. Height matters most: stiffness grows with the cube of depth.
Materials — E for solid woods is the Wood Handbook value at 12% moisture content; sheet goods are typical published figures and vary by maker and grade.
Limit — 0.02" per foot of span (span ÷ 600) is the usual threshold where sag becomes visible. Wood creeps under a sustained load, so a shelf loaded for months sags roughly 1.5–2× the initial figure; the tool shows that estimate too.

A book load of 20–25 lb per foot (30–40 kg/m) is typical for a 10" (250 mm) deep shelf of hardbacks. Shelves fixed rigidly at both ends sag less than this model predicts — up to five times less in theory.

Share link copies a URL that opens this tool exactly as you have it set up. It carries the shelf, load and stiffener settings. Opening a link replaces your own saved settings for the tool; a Restore my settings button brings them back. To write a link by hand, use material, load, stiff, units — for example /tools/sagulator/?material=Pine.

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