3D bin packing
Paste your box list and get a stacked, three-dimensional load plan in seconds — every box turned through all six orientations, your stacking and weight rules respected, nothing to install.
Your first load needs no account. After that, ten calculations a month, free, no card.
Three-dimensional bin packing is the problem of placing a set of rectangular items inside one or more containers so that nothing overlaps, nothing protrudes through a wall, and as few containers as possible are used. It sounds like arithmetic and it is not. Volume is necessary but nowhere near sufficient: a load whose boxes total 28 m³ will not go into a 33 m³ container unless the shapes happen to agree, and whether they agree depends on the order the boxes go in and on how each one is turned.
The problem is NP-hard, which has a precise and slightly deflating meaning: nobody knows a method that finds the provably best arrangement for a real load in reasonable time, and most people who study it expect nobody will. What is achievable is very good arrangements found quickly. For a container of freight, the gap between a good arrangement and the theoretical optimum is usually a point or two of utilisation; the gap between a good arrangement and stacking by eye is routinely ten or fifteen.
That second gap is where the money is. A 40 ft container costs the same to ship whether it leaves 78 per cent full or 91 per cent full, so every point of utilisation is a point off the freight bill for exactly the same cargo. The same holds one scale down, where an order shipped in a box one size too large pays dimensional weight on air.
A rectangular box can sit axis-aligned in a container six ways. A packer that only tries one is leaving space on the floor.
| Orientation | Footprint | Height |
|---|---|---|
L × W × H |
L × W | H |
L × H × W |
L × H | W |
W × L × H |
W × L | H |
W × H × L |
W × H | L |
H × L × W |
H × L | W |
H × W × L |
H × W | L |
Six per box compounds quickly: thirty boxes present 6³⁰ orientation combinations before you have even chosen an order to load them in, which is why a good arrangement is searched for rather than enumerated. In practice not every box gets all six. A pallet marked “this way up” has two, a drum has one, and the planner treats that as a hard constraint rather than a hint it is free to ignore when space runs short.
A load that needs four containers stacked the obvious way, and three stacked well.
Pack 60 crates 120×80×90, 180 cartons 60×40×40 and 40 flat panels 100×100×30 into 20 ft containers. Keep the panels off the floor.
| Item | Size (L × W × H) | Quantity | Total volume |
|---|---|---|---|
| Crates of machine parts | 120 × 80 × 90 cm |
60 | 51.8 m³ |
| Cartons of tinned goods | 60 × 40 × 40 cm |
180 | 17.3 m³ |
| Flat panels, must not sit on the floor | 100 × 100 × 30 cm |
40 | 12.0 m³ |
That is 81.1 m³ of cargo against a 20 ft container's 33.2 m³ interior, so no arrangement whatsoever fits it into fewer than three containers — the arithmetic floor is 2.44. Loaded in the order it was typed with every crate upright, it takes four, because the crates stand 90 cm tall in a 239 cm interior and the third tier will not go in: 28 cm of headroom is wasted the length of the container. Turned onto their 120 × 90 faces the crates stand 80 cm, three tiers reach 240 cm — near enough that the cartons absorb the remainder instead of opening a fourth container.
Utilisation is the number everyone quotes, and it is rarely the number that decides whether a plan is usable. These four decide it.
A plan that fills the container and crushes the bottom tier has not solved anything. Every item can carry a maximum stack height or a weight ceiling for whatever rests on it, and the solver treats both as hard limits rather than preferences — it will open another container before it will put six tiers on something rated for two.
A load can fit perfectly and still be dangerous. Concentrate the heavy items at one end and the container is over its axle limit on the road even though it is legal by total weight. The centre of gravity is tracked as the plan builds, so you see the imbalance on screen rather than at the weighbridge.
A multi-drop load has to be unloaded in reverse. The densest possible arrangement is worthless if the third customer's pallets are behind the first customer's, so items carry a priority that constrains where in the sequence they can be placed — a deliberate trade of a little space for a load the driver can actually work.
Some constraints never make it into a spreadsheet: the forklift at that depot, the door that opens the wrong way, the customer who wants their pallet visible. Any box in a finished plan can be dragged where you want it, and everything else re-solves around the position you pinned.
Choosing the box is half the problem, and it is the half usually decided by habit. Give the planner several container types at once — a 20 ft against two 40 ft high cubes, or three candidate carton sizes — and it reports what each option actually costs you in space rather than assuming the one you always order.
The densest arrangement is not always the one you want. Interlocking every layer wins a few points of utilisation and can produce a load nobody can unload without dismantling half of it, so density is something you ask for deliberately rather than something applied by default.
Simulated annealing — and it is worth knowing why, because it explains what the tool will and will not promise you.
3DPACK.ING searches for arrangements using simulated annealing. It starts from a workable arrangement and repeatedly makes one small random change — swap two boxes in the loading order, rotate one, move a stack — then keeps or discards it. Early in the search it will accept changes that make the load slightly worse; as the search proceeds it grows steadily less willing to. The name is borrowed from metallurgy, where cooling a metal slowly lets its crystal structure settle somewhere lower-energy than quenching it ever would.
Accepting a worse arrangement sounds perverse, and the alternative is worse. A search that only ever improves walks into the first local optimum it meets and stops — typically a tidy-looking load with one awkward void it cannot undo, because undoing it means going backwards first. Tolerating a temporary loss is precisely what lets the search climb out of that void and find the arrangement on the far side of it.
There is no claim of optimality here, and there should not be. The solver returns the best arrangement it found in the time it was given, and running it twice on the same load can return two different plans of near-identical quality. What it does guarantee is feasibility: every plan it returns physically holds. Nothing intersects, nothing floats, nothing exceeds the payload, and nothing sits on a box you said could not bear it.
Interior dimensions, not exterior — the numbers that decide what fits.
| Container | Interior (metric) | Interior (imperial) | Capacity | Max payload |
|---|---|---|---|---|
| 20 ft standard | 5.90 × 2.35 × 2.39 m |
19'4" × 7'8" × 7'10" |
33.2 m³ / 1,172 ft³ | 28,200 kg / 62,170 lb |
| 40 ft standard | 12.03 × 2.35 × 2.39 m |
39'5" × 7'8" × 7'10" |
67.7 m³ / 2,390 ft³ | 26,700 kg / 58,865 lb |
| 40 ft high cube | 12.03 × 2.35 × 2.69 m |
39'5" × 7'8" × 8'10" |
76.3 m³ / 2,694 ft³ | 26,460 kg / 58,335 lb |
| 45 ft high cube | 13.56 × 2.35 × 2.69 m |
44'6" × 7'8" × 8'10" |
86.1 m³ / 3,040 ft³ | 25,600 kg / 56,440 lb |
| 20 ft reefer | 5.44 × 2.29 × 2.27 m |
17'10" × 7'6" × 7'5" |
28.3 m³ / 999 ft³ | 27,400 kg / 60,410 lb |
Nominal figures. Real interiors vary by builder, by age and by whether the floor has been replaced, and payload is limited further by road weight rules at both ends of the journey. Confirm against the container you have actually been allocated before planning to the centimetre.
Yes. Your first load runs with no account at all, up to ten box types and five hundred pieces. With a free account you get ten calculations every month, no card. Paid packs cover higher volumes, and nothing rolls over into a subscription you did not ask for.
No. One calculation runs without an account, so you can see a real plan for your own boxes before deciding whether the tool is worth an email address.
Two-dimensional packing arranges shapes on a surface — nesting parts on a steel sheet, or laying pallets out on a trailer floor. Three-dimensional packing stacks them as well, and stacking is what introduces the constraints that make the problem hard: what can bear weight, what has to stay upright, and where the centre of gravity ends up once everything is in.
All six for every box, unless you say otherwise. Marking an item “keep upright” reduces it to two, and that restriction is treated as a hard constraint — the solver will use another container before it will lay that item on its side.
Yes, on a paid plan. A free calculation plans a single container; spreading one shipment across several, and reporting how many more items would fit, is part of Pro.
Both. Every item carries a weight, the plan respects the container's maximum payload, and the centre of gravity is tracked as the load builds — so an arrangement that fits but would tip is visible on screen rather than at the weighbridge.
Yes, on a paid plan. The same solver is reachable over a REST endpoint that accepts a plain-English description of the load; the API reference documents the request, the response and every failure it can return.
Comfortably more than one container's worth. The practical limit is search time rather than item count — a larger load simply gets more of it. Without an account a calculation is capped at ten box types and five hundred pieces; a free account lifts that cap but plans one container at a time.
Type what you are shipping in plain English, or paste a list. No install, no card, and no account for the first one.
Ten calculations a month stay free once you do sign up.