Theoretical or Actual Weight: What You Are Actually Paying For

Two documents arrive for the same shipment. The packing list says 20,000 kg. Your weighbridge says 20,180 kg. The invoice was raised on the first number. Nobody has made a mistake, and the 180 kg difference is where a quiet argument starts.

Aluminum is sold on three different weights, and most purchase orders name none of them.

The three weights

Theoretical weight — calculated from nominal dimensions and a density figure. 2.0 mm × 1220 mm × 2440 mm × 2.68 g/cm³ gives one number per sheet, multiplied by the count.

Actual weight — what the material weighs on a calibrated scale.

Invoiced weight — whichever of the above the contract says you pay for.

In flat-rolled aluminum the industry default is usually theoretical weight, because coil and sheet cannot be weighed piece by piece across a production run without stopping the line. That default is reasonable. It becomes a problem when nobody writes it down, because theoretical and actual drift apart in one consistent direction.

Where the difference comes from

Four sources, and they all push the same way.

Thickness sits in the upper half of the tolerance band. This is the big one. A mill rolling 2.0 mm sheet to a standard tolerance is allowed to deliver anywhere in a band around nominal. Rolling slightly heavy costs the mill metal; rolling to nominal or below costs nothing and is legal. When the order is priced on theoretical weight at nominal thickness, there is no incentive at all to run light — and when the order is priced on actual weight, there is a strong one.

The density figure used is a round number. Most theoretical weight calculations use 2.70 g/cm³ because it is the familiar figure for aluminum. Actual alloy density varies:

Using 2.70 for 5052 overstates the weight by about 0.75%. Using it for 5083 overstates by about 1.5%. In the other direction, using 2.70 for 7075 understates by roughly 4%.

Width and length run to the positive tolerance. Same logic, smaller effect.

Crown and gauge variation across the width. A rolled sheet is not perfectly uniform; the calculation assumes it is.

What the numbers look like

Take 100 sheets of 5052, 2.0 mm × 1220 × 2440 mm.

Volume per sheet: 2.0 × 1220 × 2440 = 5,953,600 mm³, or 5,953.6 cm³.

At 2.68 g/cm³ (5052 actual): 15.96 kg per sheet, 1,596 kg for the lot.

At 2.70 g/cm³ (the round figure): 16.07 kg per sheet, 1,607 kg for the lot. The lot is 11 kg heavier on paper than it is in fact — about 0.7%, and it is entirely an artefact of the density assumption.

Now run the thickness. If the mill rolls at 2.08 mm, still inside a normal standard tolerance, actual weight per sheet becomes about 16.59 kg — 4% above nominal. On a 20-tonne order that is 800 kg of metal nobody ordered, paid for at the price per kilogram.

At $3.00/kg, 800 kg is $2,400. That is the size of the question, and it is why the weight basis belongs on the purchase order rather than in a later email.

The four phrasings, and what each one buys

"Theoretical weight at nominal dimensions, density 2.70 g/cm³." Simple, standard, and favourable to the seller. You know exactly what you will pay before the material exists. Your risk is the positive tolerance band.

"Actual weight, weighed at the mill, weight ticket attached." You pay for metal received. The mill now has a reason to run close to nominal, and your invoice matches your inventory. Requires a calibrated scale and a document you trust — ask for the weighbridge ticket, not just a figure.

"Theoretical weight at nominal, and thickness measured on arrival; invoice adjusted to measured thickness." The most balanced of the three. It removes the density argument and ties payment to the dimension that actually drives weight. It needs an agreed sampling method and an agreed measurement point, or you have replaced one argument with another.

Silence. Then the mill's default applies, which is theoretical, and you find out which density and which tolerance band at the invoice stage.

The tolerance clause nobody reads

Separately from weight, almost every bulk aluminum contract carries a more-or-less clause: the seller may ship within a stated percentage of the ordered quantity, commonly ±5%, sometimes ±10% for coil.

That clause is not a weight basis and does not fix weight. It is permission to deliver a different quantity. If you have a ±5% clause and a theoretical weight basis running heavy, the two combine: you can receive 5% more metal than ordered, each kilogram of it weighing more than nominal, and both are contractually fine.

If your production plan cannot absorb 5%, say so. A ±2% clause is negotiable on a large order, and it is much easier to negotiate before the price than after.

Why coil is almost always theoretical

Sheet and plate can be counted and weighed. Coil usually cannot, for a plain reason: a coil weighs several tonnes, has to be lifted by crane or heavy forklift to reach a scale, and the mill's line does not stop for it. So the weight is calculated from width × gauge × length × density, and that calculated figure goes on the documents.

Two consequences specific to coil.

The length used in the calculation is not always the length you receive. Coil is shipped with the head and tail trimmed, and the figure quoted is often nominal. If your process depends on running meters — a blanking line, a roll former — ask for the actual length and the coil's inside and outside diameter, not just the weight.

Coil weight varies within a lot. A mill may ship coils in a weight range rather than at an exact figure, because coil weight is set by the rolling campaign. Two coils of the same width and gauge can differ by hundreds of kilograms. If your decoiler has a maximum coil weight, that number belongs in the specification, not in a later complaint.

The letter of credit wording

When payment runs through a letter of credit, the weight figure has a second life — it appears in the credit, the invoice must match it, and the bank will not exercise judgement.

UCP 600 addresses this directly. Under article 30(a), words such as "about", "approximately" or "circa" are read as permitting a tolerance of up to 10% more or less than the amount, quantity or unit price they qualify. So about 20,000 kg in a credit is a band, not a figure.

That tolerance sits on top of everything else. If the credit says "about 20,000 kg", and the goods are invoiced on theoretical weight, and the mill rolls to the top of the tolerance band, the invoice can still be compliant while the physical delivery differs from what your production plan expected. The bank is checking documents against documents; it has no view on whether the metal you received matches the metal you ordered.

Which is why a credit should state the weight basis and the tolerance explicitly rather than relying on "about". 20,000 kg ±2%, theoretical weight at nominal, density 2.68 g/cm3 leaves nothing for either the bank or the supplier to interpret.

How to check it in an hour

You do not need to weigh every sheet.

Weigh ten sheets from different positions in the bundle on a calibrated scale. Compare the average to the theoretical figure at nominal. A difference under 1% is consistent with density alone; a difference of 3–4% is thickness.

Measure thickness at five points per sheet — 25 mm in from each corner and one in the center — with a micrometer, not a caliper. Calipers read over the crown and flatter the material. Average the readings and compare to nominal.

Multiply. Measured average thickness ÷ nominal thickness tells you the gauge factor. Gauge factor × theoretical weight is what you should have received.

Reconcile once. If the difference is systematic and small, accept it and write the basis into the next order. If it is 3% or more, you are paying for metal you did not order, and the conversation is worth having before the next shipment rather than after this one.

Write it down once

Weight basis is one of those specification items that costs nothing to state and cannot be recovered afterwards.

One line on the purchase order:

Weight basis: theoretical at nominal dimensions, density 2.70 g/cm³.
Quantity tolerance: ±3%. Invoice to actual weight if deviation exceeds 1%.

That line does three jobs. It fixes the calculation, it caps the quantity drift, and it gives both sides a defined trigger for the conversation.

If you are comparing quotes from two suppliers and the per-tonne prices are close, check what weight each one is quoting on. A 2% difference in basis can be larger than the price gap you are negotiating over — which is, occasionally, exactly why the prices are close.

If you want the arithmetic for a specific size, the weight calculator returns kilograms per sheet from dimensions and alloy. Send us a quote you are comparing and we will tell you which weight basis is implied by the numbers, if it is not stated.