Shelf Sag Calculator (Deflection by Span, Thickness and Material)

How thick does a shelf need to be? This shelf sag calculator answers the question the way engineers do: it treats the shelf as a beam and computes its deflection from the span, cross-section, load and the published stiffness (modulus of elasticity) of the wood or panel. It adds the shelf’s own weight, handles free or fixed ends, uniform or centred loads, and a solid edging strip on the front. The 0.02 in per foot target is the same rule the well-known Sagulator uses.

Shelf sag calculator

How it works

Second moment of area I = depth × thickness³ ÷ 12 (plus the edging strip, combined about the joint centroid)
Uniform load, ends free: sag = 5 × W × L³ ÷ (384 × E × I)
Uniform load, ends fixed: sag = W × L³ ÷ (384 × E × I)
Centre load: P × L³ ÷ (48 × E × I) free, or ÷ 192 fixed, plus the self-weight term
Target: 0.02 in per foot of span, or 1.7 mm per metre. Wood creeps, so expect about 50% more over the years

E is taken at 12% moisture content from the Wood Handbook tables for solid wood; MDF uses a Grade 130 manufacturer data sheet; plywood and particleboard use typical values you should check against your panel.

Worked example

A 36 in red oak bookshelf, 11-1/4 in deep and 3/4 in thick, resting on pins and carrying 60 lb of books spread along it:

Units: Inches and feet
Shelf material: Red oak
Span between supports: 36 in
Shelf depth (front to back): 11.25 in
Shelf thickness: 0.75 in
Load on the shelf: 60 lb
How the load sits: Spread evenly along the shelf
Shelf ends: Resting on pins or cleats (free to rotate)
Front edging height (0 for none): 0 in
Front edging thickness: 0.75 in

The calculator gives:

Predicted sag at mid-span: 0.059 in (0.02 in per ft)
Verdict: Acceptable: at or under 0.02 in per foot (1.7 mm per m)
Sag after long-term creep (about 1.5 x): 0.089 in
Load including the shelf’s own weight: 67.7 lb (shelf itself 7.7 lb)
Stiffness used: Red oak: E = 1,761,000 psi (12,141.7 MPa), I = 0.396 in⁴

About 0.059 in of sag, or 0.020 in per foot: right at the limit of what reads as flat. Glue a 3/4 × 1-1/2 in strip to the front edge and the sag drops to about 0.032 in, because the strip nearly doubles the section’s stiffness. The same shelf in 3/4 in MDF would sag about six times as much and should be kept to 24 in spans or edged.

Notes and limits

Loads: books are 20 to 40 lb per running foot; a foot of paperbacks about 10 lb. Enter the whole load on the shelf, not per foot.
Fixed ends means glued and screwed into dadoes or a case that really restrains rotation. Shelf pins, cleats and most metal standards are free ends.
The result is elastic deflection. Wood shelves creep, so a shelf right at the limit today looks bowed in a few years.
Species values are averages at 12% moisture. Plywood, particleboard and MDF vary by grade and maker; use the modulus on the product data sheet if you have one.
Depth (front to back) adds stiffness in proportion; thickness adds it with the cube, so 1 in stock is 2.4 times as stiff as 3/4 in.

Frequently asked questions

How long can a shelf be without sagging?

It depends on thickness, material and load. A 3/4 in hardwood shelf with a moderate book load is fine to about 36 in; 3/4 in MDF or particleboard to about 24 in. Put your own numbers in the calculator.

How much shelf sag is acceptable?

A common target is 0.02 in per foot of span, which most people cannot see. Twice that is visible; more than that looks broken.

How do I stop a shelf from sagging?

Shorten the span, make it thicker, glue a solid strip along the front edge (standing on edge), or fix a back rail under it. Adding a centre support cuts sag to about a tenth.

Is plywood stiffer than MDF for shelves?

Yes, by a wide margin. Typical hardwood plywood is roughly five times as stiff as MDF of the same thickness; solid hardwood is stiffer still.

Does the shelf’s own weight matter?

A little for wood, more for MDF and particleboard, which are heavy and flexible. The calculator adds it automatically from the material density.

Sources

Last reviewed: 26 September 2026. The calculation is covered by automated tests with known answers taken from the sources above. Found an error? Please let us know.