How the shelf sag calculator works
A shelf resting on two brackets behaves like a simply supported beam, and engineers have a textbook answer for how far such a beam bends. The result depends on four things: the load, the span cubed, the stiffness of the material (its modulus of elasticity, E) and the stiffness of the board's shape (its second moment of area, I).
Sag = 5 × W × L³ ÷ (384 × E × I), with I = depth × thickness³ ÷ 12W is the total weight in newtons, L the clear span between supports. When the weight is concentrated in the middle, such as a heavy speaker or a stack of plates, the factor 5/384 becomes 1/48 and the sag is 1.6 times larger for the same weight. The calculator compares the result with a limit of 0.02 inch per foot of span (about 0.5 mm per 25 cm, or span ÷ 600), the point at which most people start to see a bow. Floors and beams in buildings are usually held to span ÷ 360, but a shelf is judged by eye against the straight line of the wall or cabinet, so a tighter limit makes sense.
Worked example
An 18 mm pine board, 25 cm deep, spans 80 cm and carries 20 kg of books. I = 0.25 × 0.018³ ÷ 12 = 1.215 × 10⁻⁷ m⁴, and the load is 20 × 9.81 = 196.2 N. Sag = 5 × 196.2 × 0.8³ ÷ (384 × 9 × 10⁹ × 1.215 × 10⁻⁷) = 0.0012 m, or 1.20 mm. The limit for 80 cm is 800 ÷ 600 = 1.33 mm, so the shelf passes and could take about 22.3 kg before the bow shows. Swap the pine for MDF of the same size and the sag rises to 3.1 mm, well past the limit.
Stiffness of common shelf materials
| Material | E (GPa) | E (million psi) | Sag in the example |
|---|---|---|---|
| Oak, maple, other dense hardwood | 12 | 1.74 | 0.90 mm |
| Pine, spruce, other softwood | 9 | 1.31 | 1.20 mm |
| Plywood (grain of face veneers along the span) | 8 | 1.16 | 1.35 mm |
| MDF | 3.5 | 0.51 | 3.08 mm |
| Particleboard / chipboard | 2.5 | 0.36 | 4.31 mm |
These are typical figures for dry, clear material; individual boards vary by 20% or more, and knots near the middle of a span weaken solid wood.
Ways to stop a shelf sagging
- Shorten the span. Because the span is cubed, moving brackets from 90 cm to 60 cm apart cuts the sag by more than two thirds for the same load.
- Go thicker rather than deeper. Doubling depth halves the sag; doubling thickness divides it by eight.
- Glue a lip on the front edge. A 20 × 40 mm (¾ × 1½ in) hardwood strip on edge makes the whole shelf act like a much deeper beam.
- Fix the back edge. A cleat screwed to the wall under the rear edge supports the shelf along a third side and removes most of the bow.
- Allow for creep. MDF and chipboard keep bending slowly under a permanent load; after months the sag can be well above the figure here, so keep them comfortably inside the limit.
This tool covers the bending of the board only. The brackets, wall plugs and the wall itself have their own limits: heavy loads belong on fixings into studs or solid masonry, and anything above head height or near children should be checked against the fixing manufacturer's ratings.
Frequently asked questions
How far can a 3/4 inch shelf span without sagging?
For books spread along it, a 3/4 in pine shelf 10 in deep stays under the visible limit at about 32–36 in between supports, depending on how heavy the books are; 3/4 in MDF should be kept to roughly 24–26 in.
How much weight can an 18 mm MDF shelf hold?
At 80 cm span and 25 cm depth, 18 mm MDF reaches the visible-sag limit at about 9 kg. It will not break at that weight, but it will bow, so shorten the span or add a front lip for books.
Is plywood or MDF better for shelves?
Plywood is more than twice as stiff as MDF and creeps less, so it sags much less over time. MDF gives a smoother paint finish but needs shorter spans or a stiffening edge strip.
What is an acceptable amount of shelf sag?
Woodworkers usually aim for no more than 0.02 in per foot of span, about 0.5 mm per 25 cm. On an 80 cm shelf that is 1.3 mm, which is hard to see.
Does a thicker shelf sag less?
Yes, sharply. Sag falls with the cube of thickness, so going from 18 mm to 25 mm reduces it by about 2.7 times with the same load and span.
Last reviewed: 2026-09-27 · How we calculate