Woodworking calculator
Shelf Sag Calculator
A loaded shelf bows in the middle, and past a certain point that sag looks bad and eventually fails. This calculator treats the shelf as a beam, uses the published stiffness of your chosen wood or sheet good, and predicts the deflection for your span, board size, and load, then compares it against a sensible sag limit so you know whether the design holds.
How it works
Deflection of a uniformly loaded shelf follows the standard beam formula: sag equals a coefficient times the load times the span cubed, divided by the stiffness times the moment of inertia. The moment of inertia of a rectangular board is its depth times its thickness cubed, divided by 12, which is why thickness matters far more than depth: doubling thickness cuts sag to one eighth.
Stiffness is the modulus of elasticity of the material, a measured constant. This tool reads it from a small library of grounded species values, so denser stiffer woods like hard maple and oak sag less than pine, and particleboard or MDF sag far more than solid wood for the same dimensions. You can also choose how the load sits, spread evenly or concentrated in the center, and whether the ends simply rest on supports or are fixed, since fixed ends cut deflection to a fifth.
The result is compared against an allowable sag of about 0.02 inch per foot of span, the common point where sag becomes visually noticeable on a bookshelf. Fine furniture often aims tighter. A front edge stiffener, a lip glued under the front of the shelf, adds depth to the section and can dramatically reduce sag, which the calculator accounts for with the parallel-axis theorem.
Worked example
A Red Oak shelf, 36 in span, 10 in deep, 0.75 in thick, holding 50 lb spread evenly on simple supports sags about 0.049 in (L/734), which is within the 0.02 in/ft guideline.
Stiffness of common woods and panels
Shelf sag is driven by the modulus of elasticity of the material. These are the grounded values this calculator uses; stiffer woods and higher numbers sag less.
| Species / material | Type | MOE (psi) | Specific gravity | Janka (lbf) | Movement CT / CR |
|---|---|---|---|---|---|
| African Blackwood | hardwood | 2,603,000 | 1.27 | 3,670 | — |
| African Mahogany | hardwood | 1,410,000 | 0.54 | 850 | — |
| African Padauk | hardwood | 1,895,000 | 0.69 | 1,710 | — |
| Afrormosia | hardwood | 1,715,000 | 0.72 | 1,570 | — |
| Alaska Yellow Cedar | softwood | 1,420,000 | 0.50 | 580 | — |
| American Basswood | hardwood | 1,460,000 | 0.42 | 410 | — |
| American Beech | hardwood | 1,720,000 | 0.72 | 1,300 | 0.00431 / 0.00190 |
| American Elm | hardwood | 1,340,000 | 0.56 | 830 | — |
| American Holly | hardwood | 1,110,000 | 0.64 | 1,020 | — |
| American Hornbeam | hardwood | 1,693,000 | 0.79 | 1,780 | — |
| American Sycamore | hardwood | 1,420,000 | 0.55 | 770 | — |
| Anigre | hardwood | 1,588,000 | 0.55 | 990 | — |
| Bald Cypress | softwood | 1,440,000 | 0.51 | 510 | 0.00216 / 0.00130 |
| Balsam Fir | softwood | 1,387,000 | 0.40 | 400 | — |
| Bigleaf Maple | hardwood | 1,450,000 | 0.55 | 850 | — |
| Bigtooth Aspen | hardwood | 1,430,000 | 0.43 | 420 | — |
| Black Ash | hardwood | 1,600,000 | 0.55 | 850 | — |
| Black Cherry | hardwood | 1,490,000 | 0.56 | 950 | 0.00248 / 0.00126 |
| Black Locust | hardwood | 2,050,000 | 0.77 | 1,700 | — |
| Black Tupelo | hardwood | 1,188,000 | 0.55 | 800 | — |
| Black Walnut | hardwood | 1,680,000 | 0.61 | 1,010 | 0.00274 / 0.00190 |
| Black Willow | hardwood | 1,010,000 | 0.42 | 430 | — |
| Bloodwood | hardwood | 3,013,000 | 1.05 | 2,900 | — |
| Bocote | hardwood | 1,767,000 | 0.85 | 2,010 | — |
| Bubinga | hardwood | 2,670,000 | 0.80 | 2,410 | — |
| Bur Oak | hardwood | 1,040,000 | 0.72 | 1,360 | — |
| Butternut | hardwood | 1,180,000 | 0.43 | 490 | — |
| Canarywood | hardwood | 2,164,000 | 0.83 | 1,520 | — |
| Chestnut Oak | hardwood | 1,590,000 | 0.75 | 1,130 | — |
| Cocobolo | hardwood | 2,712,000 | 1.10 | 2,960 | — |
| Cumaru | hardwood | 3,237,000 | 1.09 | 3,330 | — |
| Douglas-Fir | softwood | 1,765,000 | 0.51 | 620 | 0.00267 / 0.00165 |
| East Indian Rosewood | hardwood | 1,783,000 | 0.80 | 2,350 | — |
| Eastern Cottonwood | hardwood | 1,370,000 | 0.45 | 430 | — |
| Eastern Hemlock | softwood | 1,200,000 | 0.45 | 500 | — |
| Eastern Redcedar | softwood | 880,000 | 0.53 | 900 | 0.00162 / 0.00106 |
| Eastern White Pine | softwood | 1,240,000 | 0.40 | 380 | 0.00212 / 0.00071 |
| Engelmann Spruce | softwood | 1,369,000 | 0.39 | 390 | — |
| European Beech | hardwood | 2,075,000 | 0.71 | 1,450 | — |
| European Hornbeam | hardwood | 1,755,000 | 0.74 | 1,630 | — |
| Gaboon Ebony | hardwood | 2,449,000 | 0.96 | 3,080 | — |
| Garapa | hardwood | 2,257,000 | 0.82 | 1,650 | — |
| Goncalo Alves | hardwood | 2,401,000 | 0.85 | 2,170 | — |
| Hackberry | hardwood | 1,190,000 | 0.60 | 880 | — |
| Hard Maple | hardwood | 1,830,000 | 0.71 | 1,450 | 0.00353 / 0.00165 |
| Honduran Mahogany | hardwood | 1,458,000 | 0.59 | 900 | — |
| Honey Locust | hardwood | 1,630,000 | 0.75 | 1,580 | — |
| Imbuia | hardwood | 1,394,000 | 0.66 | 970 | — |
| Incense Cedar | softwood | 1,040,000 | 0.38 | 470 | — |
| Ipe | hardwood | 3,089,000 | 1.05 | 3,490 | — |
| Iroko | hardwood | 1,580,000 | 0.66 | 1,190 | — |
| Jack Pine | softwood | 1,350,000 | 0.50 | 570 | — |
| Jatoba | hardwood | 2,745,000 | 0.91 | 2,690 | — |
| Koa | hardwood | 1,503,000 | 0.61 | 1,170 | — |
| Leopardwood | hardwood | 2,887,000 | 0.89 | 2,150 | — |
| Lignum Vitae | hardwood | 2,481,000 | 1.26 | 4,390 | — |
| Live Oak | hardwood | 1,960,000 | 1.00 | 2,680 | — |
| Loblolly Pine | softwood | 1,790,000 | 0.57 | 690 | 0.00263 / 0.00176 |
| Lodgepole Pine | softwood | 1,340,000 | 0.47 | 480 | 0.00234 / 0.00148 |
| Longleaf Pine | softwood | 1,980,000 | 0.65 | 870 | — |
| Lyptus | hardwood | 2,049,000 | 0.85 | 1,420 | — |
| Makore | hardwood | 1,552,000 | 0.69 | 1,200 | — |
| Massaranduba | hardwood | 3,344,000 | 1.08 | 3,130 | — |
| Monkeypod | hardwood | 1,149,000 | 0.60 | 900 | — |
| Noble Fir | softwood | 1,619,000 | 0.42 | 410 | — |
| Northern Catalpa | hardwood | 1,210,000 | 0.46 | 550 | — |
| Olivewood | hardwood | 1,797,000 | 0.98 | 2,710 | — |
| Oregon Ash | hardwood | 1,360,000 | 0.61 | 1,160 | — |
| Osage Orange | hardwood | 1,689,000 | 0.86 | 2,620 | — |
| Paper Birch | hardwood | 1,590,000 | 0.61 | 910 | — |
| Pau Ferro | hardwood | 1,574,000 | 0.87 | 1,960 | — |
| Pecan | hardwood | 1,730,000 | 0.74 | 1,820 | — |
| Persimmon | hardwood | 2,010,000 | 0.83 | 2,300 | — |
| Pin Oak | hardwood | 1,713,000 | 0.71 | 1,500 | — |
| Pink Ivory | hardwood | 2,193,000 | 1.04 | 3,230 | — |
| Ponderosa Pine | softwood | 1,290,000 | 0.45 | 460 | — |
| Port Orford Cedar | softwood | 1,646,000 | 0.47 | 590 | — |
| Purpleheart | hardwood | 2,937,000 | 0.90 | 2,520 | — |
| Quaking Aspen | hardwood | 1,180,000 | 0.42 | 350 | — |
| Red Alder | hardwood | 1,380,000 | 0.45 | 590 | 0.00256 / 0.00151 |
| Red Elm | hardwood | 1,490,000 | 0.60 | 860 | — |
| Red Maple | hardwood | 1,640,000 | 0.61 | 950 | 0.00289 / 0.00137 |
| Red Oak | hardwood | 1,761,000 | 0.70 | 1,220 | 0.00369 / 0.00158 |
| Red Pine | softwood | 1,630,000 | 0.55 | 560 | — |
| Red Spruce | softwood | 1,560,000 | 0.43 | 490 | — |
| Redwood | softwood | 1,220,000 | 0.42 | 450 | 0.00229 / 0.00101 |
| Santos Mahogany | hardwood | 2,380,000 | 0.91 | 2,400 | — |
| Sapele | hardwood | 1,790,000 | 0.67 | 1,360 | — |
| Sassafras | hardwood | 1,120,000 | 0.50 | 630 | — |
| Shagbark Hickory | hardwood | 2,160,000 | 0.80 | 1,880 | 0.00411 / 0.00259 |
| Shortleaf Pine | softwood | 1,750,000 | 0.57 | 690 | — |
| Silver Maple | hardwood | 1,140,000 | 0.53 | 700 | 0.00252 / 0.00102 |
| Sitka Spruce | softwood | 1,600,000 | 0.42 | 510 | 0.00263 / 0.00148 |
| Spanish Cedar | hardwood | 1,323,000 | 0.47 | 600 | — |
| Sugar Pine | softwood | 1,190,000 | 0.40 | 380 | 0.00194 / 0.00099 |
| Swamp White Oak | hardwood | 2,029,000 | 0.77 | 1,600 | — |
| Sweet Chestnut | hardwood | 1,248,000 | 0.59 | 680 | — |
| Sweetgum | hardwood | 1,640,000 | 0.55 | 850 | — |
| Tamarack | softwood | 1,640,000 | 0.59 | 590 | — |
| Teak | hardwood | 1,781,000 | 0.66 | 1,070 | — |
| Wenge | hardwood | 2,548,000 | 0.87 | 1,930 | — |
| Western Larch | softwood | 1,870,000 | 0.58 | 830 | — |
| Western Redcedar | softwood | 1,110,000 | 0.37 | 350 | — |
| White Ash | hardwood | 1,740,000 | 0.67 | 1,320 | 0.00274 / 0.00169 |
| White Fir | softwood | 1,485,000 | 0.42 | 480 | — |
| White Oak | hardwood | 1,762,000 | 0.75 | 1,350 | 0.00365 / 0.00180 |
| White Spruce | softwood | 1,315,000 | 0.43 | 480 | 0.00274 / 0.00130 |
| Willow Oak | hardwood | 1,804,000 | 0.77 | 1,460 | — |
| Yellow Birch | hardwood | 2,010,000 | 0.69 | 1,260 | 0.00338 / 0.00256 |
| Yellow Poplar | hardwood | 1,580,000 | 0.46 | 540 | 0.00289 / 0.00158 |
| Yellowheart | hardwood | 2,413,000 | 0.83 | 1,790 | — |
| Zebrawood | hardwood | 2,374,000 | 0.74 | 1,830 | — |
| Ziricote | hardwood | 1,585,000 | 0.81 | 1,970 | — |
| Birch Plywood | sheet-good | 1,450,000 | 0.68 | — | — |
| MDF | sheet-good | 350,000 | 0.75 | — | — |
| Melamine | sheet-good | 250,000 | 0.70 | — | — |
| Particleboard | sheet-good | 320,000 | 0.70 | — | — |
Frequently asked questions
How much shelf sag is acceptable?
A common rule of thumb is no more than about 0.02 inch of sag per foot of span for a bookshelf. Fine furniture and display shelves usually aim for half that, around 0.01 inch per foot.
What matters most for shelf sag?
Thickness matters most because deflection depends on thickness cubed, so doubling thickness cuts sag to one eighth. Span is next, since sag grows with the cube of the span, then the material stiffness.
Why does the wood species change the result?
Each species has a measured modulus of elasticity, its stiffness. Stiffer woods like oak and hard maple resist bending better than pine, and engineered panels like particleboard and MDF are far less stiff.
Does a front edge stiffener really help?
Yes, a lot. A lip glued under the front edge greatly increases the moment of inertia of the section, and since sag is inversely proportional to that value, even a modest stiffener can cut deflection sharply.
Are these results exact?
They are good engineering estimates using average published stiffness values. Real boards vary with grain, knots, moisture, and grade, so treat the output as guidance and build in margin for important loads.
Related calculators
Sources
These calculators are for planning and estimation. Engineering results (shelf sag, wood movement) use published average material properties; real boards vary by grade, grain, moisture and defects. Verify load-bearing designs with a professional.