A 3D bin packing calculator solves the classical problem of fitting items into the fewest fixed-capacity containers while keeping every item whole and never exceeding capacity. The Bin Packing Calculator on this page addresses that problem with a one-dimensional scalar model: each item carries a single positive size and every bin has one equal capacity, so the tool fits weight, memory, length, and workload batches that reduce to one dimension rather than three. The algorithm is First Fit Decreasing (FFD), a deterministic heuristic that sorts items from largest to smallest, places each one into the first already-open bin where it fits, and opens a new bin only when no current bin has room. The page reports the number of bins opened, the full assignment list with used and remaining capacity per bin, overall utilization, and the size-based lower bound ceil(total item size divided by bin capacity). It does not model three-dimensional box geometry, orientation, balance, fragility, stacking strength, hazardous separation, or vehicle axle limits, so it is planning assistance rather than a physical loading solution.
Most readers who search for a 3D bin packing calculator expect a tool that arranges physical boxes inside a truck or shipping container, which is a separate discipline with safety rules and a different solver family. The Google OR-Tools documentation for the bin packing problem defines the formal version the page follows: each item is assigned to exactly one bin, no bin exceeds capacity, and the objective is the minimum bin count for a fixed bin size. The Bin Packing Calculator uses that scalar definition rather than an integer-programming solver, which keeps the trace inspectable and reproducible.
What the Calculator Returns
The page accepts one capacity and up to 1,000 items, sorts them in decreasing order, and places each item into the first open bin with enough remaining capacity. The result block exposes four diagnostic numbers plus the full assignment list:
- The number of bins opened.
- Every item-to-bin assignment with used and remaining capacity per bin.
- Overall utilization, defined as total item size divided by the total capacity of opened bins.
- The size lower bound, computed as ceil(total item size divided by bin capacity).
Every value comes from the items you entered and the FFD trace the page ran. Because processing stays in your browser, no upload is required, saved examples are reproducible, and the order of equal-sized items is preserved by the stable sort.
Where a Scalar Model Fits the Job
Many real packing decisions collapse to a single resource once you fix the unit. The following table lists scenarios where the Bin Packing Calculator gives a usable draft and the matching unit convention.
| Scenario | Scalar size per item | Bin capacity |
|---|---|---|
| Truck or pallet weight batching | Weight of each load in kg or lb | Max legal or safe weight per bin |
| Cloud or container memory allocation | Memory request in MB or GB | Memory per instance |
| Workload partitioning | Compute units or run time per job | Per-server or per-batch capacity |
| Cable, pipe, or bar cut planning | Required length per piece | Stock length per roll |
| Operations-research teaching | Any positive integer or decimal | Same unit as the items |
For one-dimensional cut lists with explicit kerf and waste, the Cut List Optimizer extends the same deterministic FFD idea to stock lengths. For three-dimensional box geometry, neither tool is appropriate, and a container-loading solver with orientation and safety rules is the right next step.
Run the Bin Packing Calculator
- Open the Bin Packing Calculator in your browser; nothing is uploaded because processing stays on your device.
- Enter the common capacity shared by every bin in the unit you will use throughout, such as 10 kg, 512 MB, or 60 minutes.
- List one item per line, either as a bare size like 8 or as label, size such as jobA, 7. The label and size are separated by a single comma, the size is positive, and it cannot exceed one bin.
- Run the calculation. The tool sorts items largest first, places each into the earliest open bin where it fits, and opens a new bin when none has room.
- Inspect the number of bins, the assignment list, the used and remaining capacity per bin, the overall utilization, and the size lower bound.
- If the plan is useful, copy it for a worksheet, a loading draft, or an operations-research exercise. If utilization is low, reorder the inputs and rerun, because FFD is sensitive to the input order even though it is internally deterministic.
Worked Example: Capacity 10 with Seven Items
To make the FFD trace concrete, run the tool with capacity 10 and the following seven items in any order: 8, 7, 5, 4, 3, 3, 2. After the decreasing sort the list is 8, 7, 5, 4, 3, 3, 2, and the placements go as follows.
| Step | Item placed | Bin 1 contents | Bin 2 contents | Bin 3 contents | Bin 4 contents |
|---|---|---|---|---|---|
| 1 | 8 | 8 | — | — | — |
| 2 | 7 | 8 (no room for 7) | 7 | — | — |
| 3 | 5 | 8 + 5 = 13 > 10 (open) | 7 (no room) | 5 | — |
| 4 | 4 | 8 (no room) | 7 (no room) | 5 + 4 = 9 | — |
| 5 | 3 | 8 (no room) | 7 + 3 = 10 | 9 (no room) | — |
| 6 | 3 | 8 (no room) | 10 (full) | 9 (no room) | 3 |
| 7 | 2 | 8 + 2 = 10 | full | 9 | 3 |
The final plan is Bin 1 = {8, 2} with used 10 and remaining 0, Bin 2 = {7, 3} with used 10 and remaining 0, Bin 3 = {5, 4} with used 9 and remaining 1, and Bin 4 = {3} with used 3 and remaining 7. Total item size is 8 + 7 + 5 + 4 + 3 + 3 + 2 = 32, the lower bound is ceil(32 / 10) = ceil(3.2) = 4, and overall utilization is 32 / (4 × 10) = 32 / 40 = 0.80 or 80%. FFD matched the lower bound here, but matching it does not by itself prove optimality, as the next section explains.
How to Read the Lower Bound and Utilization
The lower bound is a floor, not a guarantee. It is computed as ceil(total item size divided by capacity), so no valid solution can use fewer bins than that value. When the displayed bin count equals the lower bound, the plan uses the smallest number of bins any arrangement could possibly use given only the totals; it does not say every feasible combination of items will fit in that count. Individual items may still force an extra bin even when the totals look favorable, which is why bin packing is computationally difficult and heuristics such as FFD are the practical default.
Utilization measures how much of the opened capacity you actually filled, defined as total item size divided by the total capacity of all opened bins. A high utilization means little unused space inside the bins you opened, while a low utilization means the heuristic opened bins it could not fill. Both numbers are diagnostic: they tell you when the plan looks healthy and when you should reorder inputs, try a different heuristic, or shift the problem to a related model such as a knapsack problem for value-prioritized selection or a cutting-stock model for stock-length layouts.
Limits You Should Not Cross
The scalar model is deliberately simple, and the limits below are part of the contract rather than work-in-progress features.
- No three-dimensional geometry, so box dimensions, orientation, rotation, and stacking are not modeled.
- No balance, center of gravity, fragility, hazardous separation, or vehicle axle distribution.
- Items are indivisible: every item is assigned whole to exactly one bin, and the tool never splits an item across bins or combines bin capacities.
- Items must be greater than zero and no larger than one bin; negative or oversized inputs return a clear error.
- The list accepts at most 1,000 items, capacity is bounded, and labels cannot include commas because the import format uses a single comma between label and size.
For any of those concerns, a different model applies. Container loading in the physical sense is a separate discipline with safety rules, and scheduling or batching with priorities becomes a different operations-research problem rather than a tuning of this one.
Verifying the Plan for Real Decisions
Use the Bin Packing Calculator as transparent planning assistance: draft batch groupings, study how reordering inputs changes the bin count, and rehearse operations-research exercises. Before any safety-critical decision such as loading a vehicle, allocating real cloud capacity, or scheduling production runs, run the same items through a validated domain solver and confirm the final assignment. The page labels both the heuristic and the lower bound without turning either into a false certificate, so you always know what kind of answer you are reading.