Ti and Hi: the two numbers that describe a pallet
Every packed pallet in a distribution network is described by two integers. Ti is the number of cases in one layer — the tier count. Hi is the number of layers stacked on the pallet. Multiply them and you have cases per pallet, the unit of measure that drives purchase order quantities, slotting decisions, truck loading and the freight bill.
The names come from tier and height, and they matter because almost every other logistics number is derived from them. A retailer's minimum order quantity is usually a whole pallet or a whole layer. A warehouse assigns a pick slot based on how many layers fit under the beam. A truckload plan works in pallet positions, and a 53 ft dry van holds 26 positions on the floor, so cases per pallet decides how many cases move per load.
Improving Ti by one case is worth more than it sounds. On a six-layer pallet, one extra case per layer is six extra cases per pallet, and across 26 positions that is 156 cases per trailer that did not need a second truck. The search this calculator runs is exactly the search a packaging engineer does by hand on graph paper, and it takes the same three patterns seriously.
How the layer patterns are found, and where the limits come from
Start with the deck. A case laid with its length along the pallet length fits floor(Lp/Lc) across and floor(Wp/Wc) deep, and the product is the block pattern. Turn every case ninety degrees and you get the rotated block. Both are trivial to compute and both waste whatever strip of deck is left over.
The third family recovers that strip. Fill part of the pallet with cases in one orientation and the remaining band with cases turned ninety degrees. On a 48 × 40 pallet with a 20 × 13 case, block gives 2 × 3 = 6 and rotated gives 3 × 2 = 6, but taking one 20 in slice of the pallet length holds 3 cases stacked across the 40 in width, and the remaining 28 in of length holds 2 × 2 = 4 more turned ninety degrees, for 7. That is the split pattern, and it is where the extra case usually comes from. The calculator evaluates every possible band count in both directions and keeps the best.
Height is the simpler limit: subtract the pallet deck from the maximum load height and divide by the case height, taking the floor. Weight is a second, independent limit. Subtract the pallet tare from the maximum gross weight to get the payload allowance, divide by case weight to get the case count the weight permits, and divide that by Ti to get whole layers. The number of layers you can actually build is the smaller of the two, because a part layer is not a layer.
Cube utilization then measures how well the answer uses the space you are paying to ship. The denominator is the full pallet footprint multiplied by the stacking height above the deck, so it charges you for the air you cannot fill as well as the air between the cases.
Worked example: a 12 × 10 × 8 in case on a GMA pallet
Your case is 12 in long, 10 in wide and 8 in tall, weighing 20 lb. It ships on a 48 × 40 GMA pallet with a 5.5 in deck, the customer allows a 53.5 in maximum load height, and the rack beam is rated for a 2,500 lb pallet. The empty pallet weighs 40 lb.
- Block pattern. 48 ÷ 12 = 4 across, 40 ÷ 10 = 4 deep, so 4 × 4 = 16 cases per layer.
- Rotated block. 48 ÷ 10 = 4 (remainder 8 in), 40 ÷ 12 = 3 (remainder 4 in), so 4 × 3 = 12 cases. Worse.
- Split patterns. Every band split you can try returns 16 or fewer here, because the block pattern already leaves zero waste. Ti = 16.
- Layers by height. 53.5 − 5.5 = 48 in of stacking height. 48 ÷ 8 = 6 layers exactly.
- Layers by weight. Payload = 2,500 − 40 = 2,460 lb. 2,460 ÷ 20 = 123 cases, and 123 ÷ 16 = 7.7, so 7 whole layers. Height binds first, so Hi = 6.
- Cases per pallet. 16 × 6 = 96 cases.
- Gross weight. 96 × 20 + 40 = 1,960 lb, comfortably inside 2,500 lb.
- Cube utilization. Case volume is 12 × 10 × 8 = 960 in³, so 96 cases occupy 92,160 in³. The envelope is 48 × 40 × 48 = 92,160 in³. Utilization is 92,160 ÷ 92,160 = 100%.
A perfect fit like this is what happens when the case is a clean divisor of the pallet in every axis — a 12 × 10 footprint tiles a 48 × 40 deck exactly, and 8 in divides 48 in exactly. Real cases rarely do. Change the case height to 9 in and the height limit gives floor(48 ÷ 9) = 5 layers, cases fall to 80, and cube utilization drops to 80 × 1,080 ÷ 92,160 = 93.75%. The 3 in of headroom you cannot use is the entire loss.
Reading the result and deciding what to change
Look first at which constraint binds. If height binds, the fix is a shorter case or a taller allowed load — you have weight capacity going unused, and the pallet is shipping headroom. If weight binds, the fix is a lighter case or a stronger rack, and you are shipping air above the top layer. When height and weight bind at the same layer count, the configuration is balanced and there is nothing cheap left to take.
Then look at footprint utilization. Anything below about 90% means the deck itself is not being covered, which is usually a case-size problem rather than a stacking problem. Packaging engineers work backwards from this: choose case footprints that tile 48 × 40 cleanly — 12 × 10, 16 × 10, 24 × 20, 16 × 13.33 — and Ti follows without a search.
Cube utilization combines both effects and is the number worth tracking over time. Above 85% is good for a real product; between 65% and 85% is normal and usually reflects an awkward case height; below 65% means you are paying to move a large volume of air, and it will show up directly in your freight density and class, because density is weight divided by exactly the envelope this calculator measures.
Do not chase the last case at the expense of stack strength. Overhang past the deck edge removes support from the corner posts of the bottom cartons, and corners carry most of a box's compression strength. A pattern that gains one case by overhanging half an inch on every side can lose far more than one case worth of value when the bottom layer crushes in a warm trailer.
Cases per layer on a 48 × 40 in pallet for common case footprints
| Case footprint (in) | Cases per layer | Deck area used | Pattern that wins |
|---|---|---|---|
| 12 × 10 | 16 | 100.0% | Block, 4 × 4 |
| 16 × 10 | 12 | 100.0% | Block, 3 × 4 |
| 20 × 12 | 8 | 100.0% | Rotated block, 4 × 2 |
| 24 × 16 | 5 | 100.0% | Split across the width |
| 20 × 13 | 7 | 94.8% | Split along the length |
| 15 × 12 | 10 | 93.8% | Split across the width |
| 13 × 9 | 15 | 91.4% | Rotated block, 5 × 3 |
| 18 × 12 | 8 | 90.0% | Rotated block, 4 × 2 |
| 14 × 11 | 11 | 88.2% | Split across the width |
| 22 × 15 | 5 | 85.9% | Split across the width |
Deck area used is cases per layer × case footprint ÷ 1,920 in². Values are produced by running the same pattern search this calculator uses, with a zero overhang allowance.
Assumptions and limits you should know about
- Every case is identical and stacks squarely. Mixed-SKU pallets and slip-sheeted loads need a different tool.
- Interlocking is not modelled. Rotating alternate layers ties a stack together but rarely changes the case count, and where it does it usually costs a case rather than gains one.
- Compression strength is not checked. The number of layers a box can survive depends on board grade, humidity, storage time and stack alignment. Ask your corrugated supplier for the box compression test value and apply their safety factor.
- Bulge is ignored. Bags, sacks and soft goods spread when stacked, so measure a filled case rather than a flat blank.
- The pallet is assumed rigid. A stringer pallet deflects under load and a deflecting deck can make a tight pattern rub.
- The result is per pallet, not per trailer. Trailer capacity also depends on pallet positions, door height and whether you can double-stack.
Which pallet footprint you are actually on
North American grocery and consumer goods run almost entirely on the GMA pallet, 48 in long by 40 in wide, which is why case footprints in that market cluster around divisors of 48 and 40. Europe runs the 1200 × 800 mm Euro pallet, which is 47.24 × 31.50 in — close enough to a GMA in length that a case designed for one will look nearly right on the other and then waste a full band of width. If you export, run the calculation on both footprints before you commit a case size, and switch the input units to millimetres so you are working in the numbers your supplier quotes.
Where the pallet pattern sits in the wider cost picture
The pattern you choose propagates outward. Cases per pallet sets the order multiple, which feeds the order quantity you would otherwise pick from an economic order quantity model — rounding an EOQ to whole pallets is almost always cheaper than shipping a broken pallet. It also sets the cube of the shipping unit, and therefore the density that decides the freight class and the rate you pay per hundredweight.
On the outbound side, gross weight per pallet multiplied by pallet positions is what fills a trailer, and it is the input to the axle loading check in the federal bridge formula calculator. Heavy dense pallets fill a trailer's weight before its cube; light bulky ones do the opposite, and the crossover is around 12 to 13 lb per cubic foot for a standard 53 ft van — roughly 45,000 lb of legal payload spread over about 3,489 cubic feet of trailer cube.
Inside the building, Ti and Hi decide how a slot is designed. A full-pallet reserve slot needs the load height plus clearance under the beam; a case-pick slot is usually sized to one layer. And the weight of a single layer decides whether an operator can layer-pick it by hand or needs a layer-picking attachment, which brings the forklift's own limits into play — see the forklift capacity calculator once an attachment is fitted, because the attachment derates the truck before the load is even lifted.
If you are re-designing a case rather than loading an existing one, work in the other direction: pick the case footprint from the pallet, pick the case height from the load height divided by a whole number, and let the product design follow. That sequence produces the 100% fits; the reverse sequence produces the 70% ones.