Free · runs in your browser · nothing uploaded
Shelf sag calculator
Span, thickness, wood and load in — how far the shelf bends now and after years under the same books out, judged against the threshold where sag becomes visible. If it fails, you get the fix, not just the number.
Your shelf
A metre of paperbacks is roughly 25 kg; hardcovers run 35–40 kg per metre. The shelf's own weight is added automatically.
The sag
To make it stiff
The verdict appears here — sag now, sag after years of load, and what to change if it fails.
Shelf sag check from https://sketchmethis.com/shelf-sag — free, no signup.
What the numbers mean
A shelf on two supports is a beam. Under an evenly spread load it deflects by δ = 5WL³ / 384EI — the span cubed over the stiffness, where the stiffness I = bh³/12 depends on the cube of the thickness. Those two cubes are the whole story of sagging shelves: doubling the span makes the sag eight times worse, doubling the thickness makes it eight times better, and nothing else you can do comes close.
The often-quoted limit for "looks straight" is about 1.7 mm of sag per metre of span — beyond roughly 2.6 mm/m almost everyone sees it. The verdict here judges against those thresholds.
Why the second number is bigger
Wood creeps: under a constant load it keeps bending slowly for years, ending up at roughly twice the initial deflection (the engineering literature gives 1.5–2× for seasoned wood indoors; this tool shows the 2× end, which is the honest one for a bookshelf that stays loaded). A shelf that looks fine on day one and bows in year three is not a mystery — it is this line.
Stiffness by material
The elastic modulus used per material, along the grain at indoor moisture. Individual boards vary by ±20% — knots, grain slope and density all matter — so treat the verdict as a good estimate, not a certificate:
| Material | E (GPa) | Density (kg/m³) |
|---|---|---|
| Birch | 13.9 | 640 |
| Beech | 13.0 | 710 |
| Douglas fir | 13.0 | 530 |
| Maple (hard) | 12.6 | 705 |
| Oak | 12.3 | 700 |
| Ash | 12.0 | 670 |
| Walnut | 11.6 | 610 |
| Cherry | 10.3 | 560 |
| Pine / spruce | 10.0 | 450–500 |
| Plywood (birch) | 8.3 | 680 |
| Plywood (softwood) | 7.0 | 500 |
| MDF | 3.2 | 750 |
| Chipboard | 2.8 | 650 |
Note where MDF and chipboard sit: a quarter of the stiffness of solid wood. An 18 mm chipboard shelf at 800 mm span sags where an 18 mm beech shelf would not — which is why flat-pack bookcases bow and the same-sized solid ones don't.
What the ends do
A shelf resting on pins is free to rotate at its ends; one glued into dados or screwed through the sides is partially restrained, which can cut deflection by up to a factor of five in the ideal case. Real joints land somewhere between the two options this tool offers — if the verdict only passes with "fixed" ends, treat it as marginal.
Questions
Will the shelf break?
Almost certainly not — this is a stiffness check, not a strength check. Wood fails at loads far beyond what makes a shelf look terrible. For shelves, sag is the limit that matters, which is why it is the one this tool computes.
Does shelf depth matter?
Only linearly — twice as deep is twice as stiff, but it also carries twice the books. Thickness is cubed; depth is not. Spend your material on thickness.
What about a front lip / edging strip?
A solid-wood strip glued on edge under the front of a shelf acts like a small joist and helps considerably — a 30 × 18 mm lip can make an MDF shelf behave like solid wood. This tool doesn't model composite sections; treat a lipped shelf as roughly one material class better.
Where do the formulas come from?
Standard Euler–Bernoulli beam theory — the same equations in every engineering handbook — with elastic moduli from the published wood-properties literature and a 2× long-term creep factor for sustained indoor loads. All of it runs in your browser; nothing is uploaded.
This checks one board. The real problem is the whole piece.
Sag is one of a dozen sums hiding in even a simple bookcase — widths that ignore dados, shelves that forget the back panel, cut lists that forget the kerf. Sketch Me This is a tool being built to do all of it: sketch or describe the piece, get dimensioned drawings and the full cut list with the joinery already subtracted.