Box Compression Strength: McKee, Stacking Loads and Humidity Derating

The container is opened in Long Beach and the bottom two rows have gone. Sidewalls bowed, top flaps dished, product intact but unsellable in its packaging. The carton spec says 32 ECT, and the box compression strength your supplier calculated — 2,460 newtons — was five times the 471 newtons actually sitting on that bottom box. The arithmetic was correct. The number was a laboratory prediction for a new, dry, perfectly stacked box under a load applied for about sixty seconds, and none of those four conditions described the inside of a container that spent 31 days at 88% relative humidity.

McKee's formula is easy. Deciding what fraction of its answer survives a real journey is the actual engineering, and it is where most carton specifications quietly fail.

McKee in one line, with the units that matter

The simplified McKee relationship, published in 1963, predicts the top-to-bottom compression strength of a regular slotted container from three inputs: the board's edge crush value, the board's caliper, and the box's perimeter.

In US units:

BCT (lbf) = 5.87 × ECT (lb/in) × √( h (in) × Z (in) )

In metric units, with a convenience that is worth knowing:

BCT (N) = 5.87 × ECT (kN/m) × √( h (mm) × Z (mm) )

The coefficient is the same number in both. Converting pounds-force per inch to kilonewtons per metre, inches to millimetres, and pounds-force to newtons happens to cancel out to within a rounding error, so you can work entirely in kN/m, mm and newtons without touching the constant. Z is the box perimeter, 2 × (length + width) of the erected carton; h is the caliper of the combined board.

A worked example you can copy

Take a regular slotted container with internal dimensions 400 × 300 × 300 mm, in single-wall C-flute board with a caliper of 4.0 mm and an edge crush value of 5.60 kN/m (the metric equivalent of 32 ECT).

• Perimeter Z = 2 × (400 + 300) = 1,400 mm
• h × Z = 4.0 × 1,400 = 5,600; √5,600 = 74.8
• BCT = 5.87 × 5.60 × 74.8 = 2,460 N

That is about 251 kgf, or 553 lbf. Run the same box in US units — 32 lb/in, 0.157 in caliper, 55.1 in perimeter — and you get 553 lbf, which is the same answer.

Two things fall out of the shape of the formula. Edge crush enters linearly, so a 10% better board is 10% more compression strength — which is why the edge crush figure, and the test method behind it, carries more weight in a carton spec than any other single number. Caliper enters as a square root, so doubling board thickness buys only about 41% more. That is why moving to a heavier single wall often competes well with moving to double wall, and why the flute and grammage decision made at the board stage sets the ceiling on everything downstream.

Where McKee stops being reliable

The simplified form was calibrated on single-wall regular slotted containers of ordinary proportions, with flutes running vertically, unprinted and undamaged. It becomes progressively less trustworthy as you leave that envelope: very tall or very narrow boxes, double and triple wall constructions, die-cut styles that are not RSCs, boxes with hand-holes or display windows, and boxes with heavy print coverage or a laminated face. For any of those, treat McKee as a screening estimate and get a physical test.

The derate chain: from a lab number to a container floor

A McKee output is a prediction of what a compression tester would read under TAPPI T804 or ISO 12048: a new box, conditioned to 23 °C and 50% relative humidity, crushed between platens at a constant speed of about 12.5 mm/min, failing in under a minute. Four things then take that number apart.

Humidity

Corrugated board is a hygroscopic structure held together by starch and fibre-to-fibre bonding, and both soften as they take up water. Board that sits at roughly 7–8% moisture content at 50% RH will equilibrate to something in the range of 12–16% at 85–90% RH, and its compression capacity falls sharply as it does. The commonly used derating pattern, relative to the 50% RH lab condition, runs approximately:

Treat those as planning figures rather than constants — the exact curve varies with board construction, adhesive and liner type. What is not in dispute is the direction and the magnitude: a tropical ocean leg costs you roughly half your laboratory number before anything else happens. A container crossing the equator routinely runs above 85% RH internally, with a day-night temperature swing that condenses moisture onto the underside of the roof and drips it back onto the top layer. Buyers planning full-container ocean shipments out of South China should be assuming this condition, not hoping against it.

Time under load (creep)

A compression tester loads a box to failure in seconds. A pallet stack loads it for weeks. Corrugated board creeps: under a constant sustained load, it deforms progressively and fails at a load well below its short-term strength. Widely used planning factors put retained strength at roughly 60% of short-term BCT after about ten days under load, and around 50% or below for storage measured in months. If your product sits in a distribution centre for a quarter after a month at sea, the two effects compound.

Pallet pattern, overhang and alignment

Most of a carton's compression capacity is carried by its four vertical corners — commonly cited as something like two-thirds of the total. Anything that stops the corners transferring load straight down costs you disproportionately:

• Overhang. A box whose corner hangs past the pallet deck by 25 mm can lose on the order of 20–30% of its capacity, because the corner has nothing under it.
• Interlocked or brick stacking. Cross-stacking for pallet stability puts box corners over box faces. It is common to lose 40–50% versus column stacking, where corners sit on corners.
• Misalignment. Two pallets stacked out of register do the same thing on a larger scale.
• Hand-holes and windows. A die-cut hole near a corner removes column material exactly where it was doing the most work.

Column-stack whenever the load is stable enough to allow it, and if stability forces interlocking, put the strength back in the board or in edge protection rather than pretending the penalty is not there.

And everything that happened before the stack. Flute crush from a heavy print impression, a scored line placed a few millimetres off, board that sat in a humid warehouse before erection, and vibration damage on the road leg all reduce capacity before the box ever carries a load. This is the argument for treating carton dimensional and score accuracy as a production quality control item rather than a cosmetic one.

Running the numbers on a real stack

Back to the 400 × 300 × 300 mm carton, packed at 12 kg gross, floor-stacked five high in a container for a 31-day door-to-door journey through the tropics.

Demand. The bottom box carries the four above it: 4 × 12 kg = 48 kg = 471 N.

Capacity, derated:

Effective capacity 590 N against a 471 N demand: a margin of 1.25.

Now look at the same box the way most specifications look at it. Lab BCT 2,460 N ÷ demand 471 N = a safety factor of 5.2. Plenty of packaging guidance suggests a factor of 3 to 5 against lab BCT for long ocean and warehouse journeys, so this carton clears the headline screen while sitting on a real margin of 25%. Add one row to the stack, or one week of dwell, or one pallet with 25 mm of overhang, and it is gone.

Both numbers describe the same box. The derate chain is the one that tells you where the margin went — and it is the version to put in front of a supplier when you are asking for a heavier board and want a reason that is not "make it stronger".

Three levers, in cost order

1. Fix the stack before the board. Column-stack instead of interlocking, eliminate overhang by resizing the carton to the pallet footprint, and cap dwell time. These cost drawing time, not unit price.
2. Add edge protection. L-profile paper corner protectors and edge boards put material back exactly where the load travels, and they also stop pallet strapping crushing the top edges. Corner protectors are usually a small fraction of the carton price and are specified by length, wing width and wall thickness.
3. Then change the board. Heavier liners, a heavier medium, a taller flute, or double wall — and note from the McKee shape that edge crush pays back linearly while caliper pays back as a square root.

What to test instead of, or alongside, a McKee number

A calculated BCT is a design tool. If stacking is your actual failure mode, buy a test:

• ISO 12048 / TAPPI T804 / ASTM D642 — the constant-rate compression test. This is what a BCT figure means. It is fast, cheap and short-duration.
• ISO 2234 — the dead-load stacking test. A known mass sits on the box for a specified time in a specified climate. Run it at 90% RH for 24 to 72 hours and it captures creep and humidity together, which a sixty-second BCT cannot. For an ocean route this is the far more predictive test, and far fewer buyers ask for it.
• ISTA and ASTM D4169 transit protocols include compression elements alongside drop and vibration, and are usually what a retail customer means when it asks for a transit test report.
• Cobb value (ISO 535) on the liners, plus a water-resistant adhesive, if the route is tropical. Ask what adhesive the corrugator runs and whether a water-resistant option is available.

Specify the climate in the test request. A compression test result with no stated conditioning is a 50% RH number by default, which is the condition you were trying to design away from.

Verifying the claims a supplier makes about compression

Suppliers competing for heavy-export work often reference structural know-how, in-house testing, or a patent on a compression-resistant carton design. Any of those may be real and useful; none of them is evidence until you have read the document. The checks are the same in every case:

• For a patent: get the publication or grant number, look it up in the national register yourself, read the granted claims rather than the title, and then ask whether the feature described in those claims is actually present in your die-line. A patent on a carton structure says nothing about a box that does not use that structure.
• For in-house testing: ask what instrument, which standard, what conditioning chamber, and whether a report can be issued against your production lot rather than against a board sample.
• For third-party reports: check who commissioned the report, what article it was run on, and the date.

Jindong Packaging is a case in point for how to run that process rather than an example of a verified answer. Its published CMH listing covers heavy-duty corrugated cartons for machinery, hardware and industrial exports, L-profile paper corner protectors and edge boards in custom length, width and thickness, and board produced in-house on automatic corrugated lines at a 12,000 m² plant in Xinqiao, Bao'an, Shenzhen, operating since 2007. It does not state a BCT figure, a stacking-height rating, a maximum gross mass, or the scope of any structural patent. Those are things to request and read, and the same is true of every carton supplier you shortlist — including the ones that volunteer a number first.

Common questions

Can I just ask my supplier for the BCT of my carton?

You can, and you should — but ask three follow-ups: was it measured or calculated, under what conditioning, and on a production carton or a board sample. A calculated McKee figure quoted as a test result is the most common ambiguity in this whole subject.

How high can I stack a 32 ECT carton in a container?

There is no answer without the box dimensions, the gross weight, the dwell time and the route humidity. Run the McKee estimate, apply a derate chain like the one above, and compare with the load the bottom box will actually carry. If the derated margin comes out under about 1.5, change something.

Does double wall solve a humidity problem?

It raises the starting number, so the same percentage loss leaves more behind. It does not change the percentage. If the route is tropical, pair the board change with a water-resistant adhesive, a Cobb target on the liners, corner protection, and a stacking pattern that puts corners over corners.

What to ask your carton supplier next

Take these six into the quotation, and keep the answers with the drawing:

1. What is the caliper (mm) and the edge crush value (kN/m or lb/in) of the board you are quoting, and by which test method?
2. Give me the McKee BCT estimate for my box dimensions, showing the perimeter and caliper used.
3. Can you run a physical compression test to ISO 12048 or TAPPI T804 on a production carton, and issue a report naming the conditioning?
4. Can you run a dead-load stacking test to ISO 2234 at high humidity, and if not in-house, through which laboratory?
5. What adhesive does the corrugator run, and is a water-resistant option available for a tropical route?
6. Quote L-profile corner protectors sized to my pallet pattern, with length, wing width and wall thickness stated.

Jindong Packaging is a reasonable place to send that list — a Shenzhen carton maker whose listed scope covers heavy-duty and export cartons plus custom corner protectors and edge boards, building to drawing or sample from 1,000 pieces, with sampling quoted at about seven days and bulk production at about fifteen working days. Questions 3 and 4 are the useful ones: a supplier that answers them precisely, or says plainly which lab it uses, is telling you something a brochure cannot. Pair the answers with a realistic view of how export packaging behaves on the water and the derate chain stops being theory.