FreeShelf Sag Calculator
Enter the material, the span and what goes on the shelf: the calculator shows how much it bends today, how much more it sags after months under the load, and the longest span that still looks flat. In inches or millimetres.
Your shelf
The shelf rests on pins or cleats at both ends. Plywood is assumed to have its face grain along the span.
Visible sagThe shelf will bow where everyone can see it. Try one of the fixes below.
- Sag when loaded
- 0.088 in
- Sag long term
- 0.16 in
- Longest flat span
- 22"
What would fix it
- Glue a 19 × 38 mm (3/4 × 1 1/2 in) hardwood strip under the front edge0.050 in
- Add a support in the middle (two half spans)0.010 in
- Make it 25 mm (1 in) thick0.072 in
- Use birch plywood0.100 in
Long-term sag with each change on its own.
- Pick the material and type the span, depth and thickness.
- Choose what goes on the shelf, or type its total weight.
- Read the sag and the longest flat span; if it bends too much, compare the fixes.
How far can a shelf span?
The longest span that stays flat for an 18 mm (3/4 in) shelf, 250 mm (10 in) deep, resting on pins, after months under the load:
| Material | Paperback books | Hardcover books | Heavy: records, cans, tools |
|---|---|---|---|
| Melamine / particle board | 410 mm (16 in) | 330 mm (13 in) | 290 mm (12 in) |
| MDF | 430 mm (17 in) | 350 mm (14 in) | 310 mm (12 in) |
| OSB | 540 mm (21 in) | 440 mm (17 in) | 390 mm (15 in) |
| Plywood, pine or fir | 650 mm (26 in) | 530 mm (21 in) | 470 mm (18 in) |
| Birch plywood | 760 mm (30 in) | 620 mm (24 in) | 550 mm (22 in) |
| Solid pine | 790 mm (31 in) | 640 mm (25 in) | 560 mm (22 in) |
| Solid oak | 870 mm (34 in) | 710 mm (28 in) | 630 mm (25 in) |
| Solid hard maple | 880 mm (35 in) | 720 mm (28 in) | 640 mm (25 in) |
A 19 × 38 mm (3/4 × 1 1/2 in) hardwood strip glued under the front edge roughly doubles these spans for MDF and melamine.
How the calculator works
A shelf resting on pins at both ends bends like a simple beam under an even load. Its sag is 5 × w × L⁴ / (384 × E × I), so it grows with the fourth power of the span: a shelf twice as long sags sixteen times more. Thickness works the other way, cubed: a 25 mm shelf is about 2.7 times stiffer than an 18 mm one.
Wood-based boards keep bending under a load that stays for months. This is creep, and it is large in particle board and MDF: the calculator multiplies their first sag by 3.25, plywood by 1.8 and solid wood by 1.6, the creep factors Eurocode 5 gives for furniture indoors.
A sag under 1/600 of the span (0.02 in per foot, 1.7 mm per metre) is the usual limit for a shelf that looks flat. Beyond 1/360 of the span most people see it.
Four ways to stop a shelf sagging
Shorten the span: a divider or a middle support halves it and cuts the sag sixteen times. Glue a hardwood strip on edge under the front: a 3/4 × 1 1/2 in (19 × 38 mm) strip makes an MDF or melamine shelf several times stiffer and hides the board edge. Use a stiffer board: birch plywood or solid wood instead of MDF or particle board. Or screw the back edge to a cleat or to the cabinet back, so the shelf is held along its length.
A Sagulator alternative
If you were looking for the Sagulator, the long-standing shelf deflection calculator: this one answers the same question, adds the long-term creep of each material, gives the longest span that stays flat and compares the fixes side by side. It runs in your browser, in inches or millimetres.
The values behind the numbers
Stiffness along the span (modulus of elasticity): melamine and particle board 2,500 MPa, MDF 3,000, OSB 4,500, pine or fir plywood 5,500, birch plywood 9,000, pine 8,500, oak 12,000 and hard maple 12,500. Loads: paperbacks about 15 kg/m (10 lb/ft), hardcover books about 30 kg/m (20 lb/ft). Real boards vary by maker and moisture by 20% or more, so keep a margin on long shelves.
Start from a furniture plan instead
All plans →Do not want to work out every part? Pick a design, type its size and get the cut list.
Frequently asked questions
How far can a 3/4 in plywood shelf span?
Under hardcover books, a 10 in deep pine or fir plywood shelf stays flat up to about 22 in and starts to show a sag after about 26 in. Glue a 3/4 × 1 1/2 in hardwood strip under the front and it stays flat to about 33 in.
How far can an MDF or melamine shelf span?
Less than people expect, because both creep: an 18 mm (3/4 in) shelf 10 in deep loaded with hardcover books stays flat only to about 14–15 in. With paperbacks it reaches about 16 in, and a hardwood front strip doubles it to about 28 in.
What matters more, thickness or material?
Both. Stiffness grows with the cube of the thickness, so 25 mm is 2.7 times stiffer than 18 mm. Switching from MDF to birch plywood helps even more in the long run, because plywood creeps far less.
Do shelves glued into dadoes sag less?
Yes, roughly half as much, because the joints stop the ends from rotating. The calculator assumes shelf pins, the common and safer case.
Learn more
How to Build a BookshelfHow to build a bookshelf from one sheet of plywood or MDF: pick the size, cut the parts, drill for shelf pins, join the case, fit the back and stop shelves sagging.MDF vs PlywoodMDF vs plywood for cabinets, shelves and doors: strength, sag, screw holding, paint finish, moisture, weight and cost compared, with the right use for each.Standard Bookshelf DimensionsStandard bookshelf depth is 10–12 in (25–30 cm). See standard heights and widths, the shelf spacing for each book size and the longest span before a shelf sags.