How this calculator works
A shelf is a beam resting on two supports. The load on it bends it into a shallow curve, and the sag in the middle grows with the fourth power of the span: a shelf twice as long sags sixteen times as much. It shrinks as the board gets thicker, with the cube of the thickness, and as the board gets stiffer. Wood-based boards also creep: left under load for months, they sag about twice as much as they do at first.
Worked example: a 3/4 in plywood shelf, 12 in deep, with books on it, can span 30.4 in within the sag limit. At 36 in it sags 0.30 in after a few years, which is 1 in 121 of the span, so the verdict is: will sag visibly. A 1 × 2 in strip glued under the front edge lifts the span to 56.2 in, and a 1 in board to 40.6 in.
The sag limit of 1/200 of the span is deliberately strict, because a shelf that sags is visible against the straight lines of a bookcase. Published charts use limits from 1/240 to 1/180, which is why they disagree.
Assumptions and sources
The assumptions behind your numbers (waste, sizes, rates) are listed in the notes directly under your results, and they update when you change an input.
The formula and a worked example are shown above, so you can check any result by hand. Read how we calculate and check our numbers. Results are estimates for planning: supplier products vary, so check the size printed on the label.
Longest shelf span for books by board and thickness
Books at 25 lb/ft², total sag including creep within 1/200 of the span, no stiffening strip.
| Board | 1/2 in | 3/4 in | 1 in |
|---|---|---|---|
| Particleboard | 15 in | 22 in | 30 in |
| MDF | 17 in | 26 in | 34 in |
| Plywood | 20 in | 30 in | 41 in |
| Solid pine | 24 in | 36 in | 47 in |
Tips before you buy
- Doubling the thickness makes a shelf eight times as stiff. Going from 18 mm to 25 mm board is a much bigger gain than adding a bay.
- A strip of solid wood glued under the front edge (a "lip") is the traditional cure: it adds depth where it counts and hides the edge of the board.
- Turn a shelf with a slight bow upwards when you put it in, and the sag takes it level. Most boards are not perfectly flat.
- Cut the shelf a hair short of the opening (about 2 mm or 1/16 in) so it drops in, and pin it so it cannot lift out.
- For a heavy load, such as a record collection or tools, use a thicker board, a stiffening strip and shorter spans, even if the calculator says a longer shelf is fine.
Tools & materials for this project
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Frequently asked questions
How far can a shelf span without sagging?
With books on it, a 3/4 in plywood shelf about 30 in, MDF about 26 in and particleboard about 22 in. Solid pine is stiffer. The calculator gives the span for your board, thickness and load.
How do I stop a bookshelf sagging?
Shorten the span with a middle support or a divider, use a thicker or stiffer board, or glue a solid wood strip under the front edge. The strip is the cheapest fix: a 1 × 2 in strip adds 85% to the span for the defaults.
Is plywood stronger than MDF for shelves?
Plywood is stiffer and sags less than MDF or chipboard of the same thickness, and holds screws better. MDF is flatter, cheaper and takes paint more evenly.
How much weight can a shelf hold?
That depends on the span, the board and the supports at the ends, not just the board. At the default, the shelf is within the sag limit for 25 lb per square foot, which is about 25 lb per foot of a 12 in deep shelf.
Does shelf depth change how much it sags?
Not by much for a given load per square foot: a deeper shelf is stiffer in proportion to the extra weight it carries. What matters is the thickness and the span.
What load should I use for books?
About 25 lb per square foot suits a mix of paperbacks and hardbacks. Use the heavy setting for art books, records or tools.
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Related calculators & guides
Estimates only. Results assume standard materials and simple shapes. Supplier products vary, and the final call on quantity, structure and safety is yours. Check your local code and your supplier's guidance before ordering.