Shelf Sag Calculator: Span, Load and Thickness

Choose the material, the thickness and span, and the load.

Last reviewed 29 Oct 2026

Your measurements

Enter the shelf and the load. Everything updates as you type.

The shelf

Material

Modulus of elasticity (stiffness) values are typical and rounded; real boards vary by 20% or more. Enter your own if you know it. For plywood, the face grain should run along the span.

Shelf thickness

The real thickness, not the nominal. A 3/4 in board or sheet is often a little under.

Shelf depth (front to back)

Span between supports

The clear distance from one support to the next, not the length of the board.

The load and the supports

Total load on the shelf

The whole weight on the shelf between the supports, not the weight per foot.

How the load sits

How the ends are held

Resting on brackets, pins or cleats: the ends can turn. This is the safe choice for most shelves.

Visible sag limit

A rule of thumb for what the eye notices, not a code. Span ÷ 360 is a common choice. Use 480 for a shelf that must look flat.

Sag0.0557 in

Sag at the middle of the shelf

0.0557in

= 1.416 mm

Eastern white pine, 0.75 in thick, 36 in span, 40 lb spread evenly: the sag is within the span ÷ 360 limit of 0.1 in.

Against the limit: Within the limit; span ÷ 645.8; limit span ÷ 360
Thinnest that meets the limit: 0.6172in; = 15.68 mm; round up to a thickness you can buy
Longest span at the limit: 48.22in; = 1224.79 mm; same thickness, depth and load
Modulus used: 1.24million psi; 8.55 GPa

Before you rely on this (2)

The modulus is a typical, rounded value. Real boards vary by 20% or more. Enter your own if you know it.
The shelf's own weight, shear, and the brackets, pins and fixings are not included, and wood sags more over months under a steady load. This is a guide, not an engineering check for heavy loads.

How this was calculated

Stiffness, sag and the limit, with your numbers.

Step 1: Stiffness of the shelf section
I = depth × thickness³ ÷ 12
= 10 × 0.75³ ÷ 12 = 10 × 0.421875 ÷ 12
= I = 0.3515625 in⁴
I is how much the cross-section resists bending. Thickness is cubed, so a little extra thickness helps a lot, and depth only counts once.
Step 2: Stiffness of the material
E = modulus of elasticity
= Eastern white pine: 1.24 million psi
= E = 1,240,000 psi (8.55 GPa)
A typical, rounded value. Real boards vary by 20% or more, and plywood and MDF vary by maker. 1 million psi is 6.894757 GPa.
Step 3: Sag at the middle
sag = 5 × W × L³ ÷ (384 × E × I)
= 5 × 40 × 36³ ÷ (384 × 1,240,000 × 0.3515625)
= 0.0557 in (1.416 mm)
W is the total load in pounds and L is the span in inches. The sag grows with the cube of the span, so doubling the span with the same total load makes the shelf sag eight times as much.
Step 4: Compare with the limit
limit = span ÷ 360
= 36 ÷ 360
= 0.1 in (2.54 mm): within the limit
The sag is span ÷ 645.8. Span ÷ 360 is a common rule of thumb for what the eye notices on a shelf; it is not a code limit.
Step 5: Thinnest shelf that meets the limit
h_min = h × (sag ÷ limit)^(1/3)
= 0.75 × (0.0557 ÷ 0.1)^(1/3)
= 0.6172 in
The sag scales with 1 ÷ thickness³, so the thickness that brings the sag to the limit is the cube root of the ratio times the thickness you have. The span, depth, load and material stay the same.

In short

Sag = 5 × W × L³ ÷ (384 × E × I) for a load spread evenly on a shelf resting on supports. A 0.75 in Eastern white pine shelf, 10 in deep, over 36 in with 40 lb sags 0.0557 in (1.416 mm), within the span ÷ 360 limit of 0.1 in.

The calculator gives the sag at the middle, checks it against a visible-sag limit and finds the thinnest shelf that stays within it.

Typical shelf boards at 3/4 in: sag and longest span

A 0.75 in thick, 10 in deep shelf resting on supports, with 40 lb spread evenly. The sag is for a 36 in span; the longest span keeps the sag within span ÷ 360.

Material	Typical modulus (million psi)	Typical modulus (GPa)	Sag at 36 in (in)	Longest span at the limit (in)
Eastern white pine	1.24	8.55	0.0557	48.22
Birch plywood	1.2	8.27	0.0576	47.43
MDF	0.45	3.1	0.1536	29.05
Particleboard	0.35	2.41	0.1975	25.62

The modulus values are typical and rounded. Real boards vary by 20% or more, and plywood and MDF differ by maker and grade. The shelf's own weight is not included.

Worked example: 0.75 in pine shelf, 36 in span, 40 lb

A shelf 10 in deep with the load spread evenly, resting on two supports.

Step 1: Stiffness of the shelf section
I = depth × thickness³ ÷ 12
= 10 × 0.75³ ÷ 12 = 10 × 0.421875 ÷ 12
= I = 0.3515625 in⁴
I is how much the cross-section resists bending. Thickness is cubed, so a little extra thickness helps a lot, and depth only counts once.
Step 2: Stiffness of the material
E = modulus of elasticity
= Eastern white pine: 1.24 million psi
= E = 1,240,000 psi (8.55 GPa)
A typical, rounded value. Real boards vary by 20% or more, and plywood and MDF vary by maker. 1 million psi is 6.894757 GPa.
Step 3: Sag at the middle
sag = 5 × W × L³ ÷ (384 × E × I)
= 5 × 40 × 36³ ÷ (384 × 1,240,000 × 0.3515625)
= 0.0557 in (1.416 mm)
W is the total load in pounds and L is the span in inches. The sag grows with the cube of the span, so doubling the span with the same total load makes the shelf sag eight times as much.
Step 4: Compare with the limit
limit = span ÷ 360
= 36 ÷ 360
= 0.1 in (2.54 mm): within the limit
The sag is span ÷ 645.8. Span ÷ 360 is a common rule of thumb for what the eye notices on a shelf; it is not a code limit.
Step 5: Thinnest shelf that meets the limit
h_min = h × (sag ÷ limit)^(1/3)
= 0.75 × (0.0557 ÷ 0.1)^(1/3)
= 0.6172 in
The sag scales with 1 ÷ thickness³, so the thickness that brings the sag to the limit is the cube root of the ratio times the thickness you have. The span, depth, load and material stay the same.

Before you load the shelf

Use the real thickness. Sheet goods sold as 3/4 inch are often a little under, and the sag grows quickly as the thickness falls.
Pick "Fixed ends" only if the shelf is glued or tightly dadoed at both ends. A shelf on pins, cleats or brackets can turn at the ends, so use "Resting on supports".
For plywood, run the face grain along the span. Across the span the shelf is less stiff.
This checks the sag of the shelf board only. Brackets, pins and wall fixings need their own check, and local rules or the maker's data win for anything heavy.

Shelf sag: common questions

Limits, materials and what is left out.

How much can a shelf sag before it looks wrong?

A common rule of thumb is a sag of no more than the span divided by 360, which is 0.1 inch (2.5 mm) over 36 inches. Span ÷ 240 is more lenient and span ÷ 480 is stricter. It is a guide to what the eye notices, not a building code, and a dark shelf with a light wall behind it shows less than a long straight edge under a ceiling light.

Why does MDF sag so much more than solid wood or plywood?

Stiffness depends on the material's modulus of elasticity. The typical value used here for MDF is 0.45 million psi, against 1.24 for Eastern white pine and 1.2 for birch plywood, so the same MDF shelf sags about 2.8 times as much as pine. MDF and particleboard also keep creeping under a steady load, so a shelf that looks fine on day one can bow later.

How do I stop a shelf sagging?

Thickness helps the most, because the stiffness goes with the cube of the thickness: doubling it cuts the sag to one eighth. Halving the span with the same total load does the same, so a centre support or a closer bracket spacing works well. A solid wood strip glued under the front edge also stiffens the shelf. The calculator shows the thinnest board that meets your limit.

How accurate is this, and what does it leave out?

It treats the shelf as a simple beam. It does not include the shelf's own weight, shear, the give in brackets, pins or fixings, or the way wood sags further over months under a steady load. The modulus values are typical and rounded, and real boards vary by 20% or more, so use your own value if you know it. For heavy loads or anything that could hurt someone if it fails, ask an engineer and use the maker's load data for the supports.