Sag
Enter the shelf size and thickness.
- Sag limit (length ÷ 200)–
- Bending stress (limit 750 psi)–
- Shelf's own weight–
- Thickness used–
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The calculator treats the shelf as a beam and uses the standard beam formulas, with acrylic's flexural modulus E = 450,000 psi (3.1 GPa). Stiffness comes from the moment of inertia, I = width × thickness³ ÷ 12, which is why thickness matters so much: double the thickness and the shelf is eight times stiffer.
- Two brackets, even load: sag = 5wL⁴ ÷ 384EI, where w is the load per inch of length (the same as 5WL³ ÷ 384EI for a total load W).
- Two brackets, one load in the middle: sag = PL³ ÷ 48EI.
- Wall-mounted, even load: sag = wL⁴ ÷ 8EI.
- Wall-mounted, one load at the front edge: sag = PL³ ÷ 3EI.
On two brackets, L is the span between them and the width is the shelf depth. For a shelf held along its back edge (in a slot or a channel on the wall), the shelf bends front to back, so L is the depth and the width is its length along the wall. The shelf's own weight is added as an even load.
Bending stress is the bending moment times half the thickness, divided by I. The bending moment is WL ÷ 8 for an even load on two supports, PL ÷ 4 for a load in the middle, WL ÷ 2 for an even load on a cantilever, and PL for a load at its front edge.
A shelf passes when both checks pass:
- Sag no more than the length ÷ 200. A 36 in. shelf may sag 0.18 in. Beyond that, most people see the bow.
- Stress no more than the long-term limit. Acrylic's short-term strength is about 10,000 psi, but under a constant load it creeps: it keeps slowly bending for months, and high constant stress can lead to crazing (fine cracks). Acrylite's technical data limits continuous loads to 1,500 psi for cast sheet and 750 psi for extruded sheet, so the calculator uses those, and treats sheet of unknown type as extruded.
Example: a 36 × 10 in. shelf of 1/4 in. (6 mm) acrylic on two brackets holding 20 lb of books sags about 2.9 in., far past the 0.18 in. limit. In 1/2 in. it sags about 0.42 in., still too much. In 3/4 in. it sags about 0.14 in. at 166 psi, which passes. Adding a third bracket in the middle would let a thinner shelf work.
These are estimates for a flat sheet with no edge lip or bonded rib. Real sheet varies in thickness, and loads stacked near the front of a wall-mounted shelf are the worst case. For a deeper look, read how much weight an acrylic shelf can hold and how strong acrylic is, or see ideas for acrylic shelves. You can also check the shelf's weight in the acrylic weight calculator.
Questions about acrylic shelves
How thick should an acrylic shelf be?
For a typical 30 to 36 in. bookshelf on two brackets, plan on 1/2 to 3/4 in., or add a middle support. Short display shelves under 24 in. with light loads are usually fine in 3/8 in. Run your exact size through the calculator above.
Why do acrylic shelves sag more over time?
Plastics creep: under a constant load they keep deforming slowly, especially when warm. Keeping the stress under the maker's long-term limit (1,500 psi for cast, 750 psi for extruded acrylic) and the shelf stiff keeps creep small.
Does acrylic sag more than glass?
Yes. Glass is about 20 times stiffer, so an acrylic shelf needs to be thicker or better supported to stay as flat. In exchange it is about half the weight and much harder to break. Acrylic vs glass