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Deflection is rated after long-term creep, as a fraction of the span. Up to L/400 (0.03 in per foot, 2.5 mm per meter) is acceptable, because most people won't notice it. Up to L/300 is borderline, and beyond that the deflection is plainly visible.
Wood and wood panels keep bending under a steady load. The long-term figure uses Eurocode 5's creep factors for dry indoor use: deflection grows by 60% for solid wood, 80% for plywood, 150% for OSB, and 225% for particleboard and MDF. Plastics creep too: deflection grows by about 70% for polycarbonate, 120% for acrylic and 420% for HDPE, estimated from manufacturers' creep tests and, for HDPE, the DVS 2205 design code. Richlite and phenolic sheet are assumed to creep like plywood, since no creep data is published. Steel, aluminum and glass creep too, but so little at room temperature and shelf-level stresses that the calculator treats their long-term deflection as equal to the short-term.
Resting covers shelves on pins, cleats or brackets. Screwed or dadoed joints resist some rotation; the percentage says how much, compared with a perfectly rigid joint. 50% is a middle estimate, since real joints vary with fit, glue and the stiffness of the sides. Truly rigid ends are rare in furniture.
The shelf's own weight is added to the load. Shear deformation is included; it matters for deep, short beams but adds under 1% for most shelves. Solid-wood stiffness is raised 10% to remove the shear effect built into the test data, as the Wood Handbook recommends.
A glued strip works together with the shelf, so its placement matters: a strip hanging below the shelf adds more than one centered on it. Its height is measured vertically and its thickness front to back. A front strip stiffens the front edge most; the back edge deflects more unless it has a strip, cleat or back panel too.
The calculation assumes the strip is glued to the shelf along its full length, so the two bend as one piece. A strip that is only nailed or screwed on can slip against the shelf and adds less stiffness.
Solid-wood values are averages for clear, straight-grained wood. Sheet goods list either a measured average of ordinary boards from commercial mills, which is what stores sell, or a grade's minimum from the ANSI standard; minimums are conservative. Metals use handbook values, and plastics, phenolic and Richlite use the manufacturer's typical values. Phenolic sheet is stiffer in one direction; the weaker, crosswise value is used.
Soft board: individual boards vary in stiffness by about 22%. The soft-board figure shows a board in the least stiff 5%, which deflects about 1.6 times as much as an average board of the same species.
Plywood is much stiffer along its face grain, and OSB along its strength axis. Shelves cut lengthwise from a sheet usually have the grain along the span. Across-grain values for fir, pine and lauan plywood are estimated from a 5-ply layup.
Type decimals (10.5) or fractions (10 1/2, 10-1/2, 1/2). Lumber is sold by nominal size, so enter the actual dimensions: a 1×12 board measures 3/4 × 11 1/4 in. With sizes in feet, deflection is still shown in inches.
The North American Architectural Woodwork Standards design shelves for 50 lb per square foot for book, library and school shelving, and 40 lb per square foot for other shelving, with no more than 200 lb on one shelf. These values incorporate several factors of safety in excess of the actual load.
The default load is 40 lb per running foot, based on the maximum book density found on a typical household bookshelf.
Enter loads per foot with inch or foot sizes, and per meter with metric sizes.
For a beam set on edge, enter its height as Thickness and its width as Depth. For hardwood plywood with an MDF or particleboard core, choose the core material; the face veneers add some stiffness, so the result errs on the safe side.
Every carbon steel is equally stiff: the grade changes strength, not stiffness. Stainless 304 and 316 are slightly less stiff, and aluminum is about a third as stiff as steel. The calculation treats the shelf as a flat, solid plate. Sheet-metal shelves with bent-down edges, tubes and channels are far stiffer than a flat plate of the same thickness, so the calculation would overstate their deflection.
Compared with a 36 in white oak shelf, 11 1/4 × 3/4 in, resting on pins under a uniform load. Figures are long-term deflection from this calculator.
| Change | Long-term deflection |
|---|---|
| Glued 3/4 × 1 1/2 in strips, front and back | × 0.38 |
| 1 in thick instead of 3/4 in | × 0.44 |
| 30 in span instead of 36 in | × 0.48 |
| Glued 3/4 × 1 1/2 in strip, front only | × 0.54 |
| Screwed or dadoed ends (50% fixity) | × 0.60 |
| Baltic birch plywood instead of white oak | × 1.5 |
| Same load at one point in the middle | × 1.6 |
| MDF instead of white oak | × 8.4 |
| Particleboard instead of white oak | × 11 |
The longest span whose long-term deflection stays within L/400, for a shelf 11 1/4 in deep resting on pins and carrying 40 lb per foot. Plywood has its face grain along the span, and sheet goods are commercial averages. Figures are from this calculator, rounded down.
| Material | 3/4 in thick | 1 in thick |
|---|---|---|
| Red oak | 29 in | 39 in |
| White oak | 29 in | 39 in |
| Hard maple | 29 in | 39 in |
| Black walnut | 29 in | 38 in |
| Poplar | 28 in | 38 in |
| Black cherry | 28 in | 37 in |
| Eastern white pine | 26 in | 35 in |
| Baltic birch plywood | 25 in | 33 in |
| Douglas-fir plywood | 23 in | 30 in |
| MDF | 14 in | 18 in |
| Particleboard or melamine | 12 in | 16 in |