How a quote is built, line by line

Five variables that appear on every quote line

A quote looks like a long document and it is built from five inputs. The first is the weight of the parcel on a scale. The second is the three dimensions of the carton as it will actually be handed over. The third is the divisor the line applies to those dimensions. The fourth is the size of the rounding step applied to the result. The fifth is the rate, whether that is a per-kilo figure or a tiered one.

Each of the five has a place where it should be visible. The scale weight appears on the warehouse slip. The dimensions appear on the same slip or on a photograph of the sealed carton against a measure. The divisor should be stated by the line, and the rounding step should be stated alongside it. The rate is the line of the quote people read first and understand last.

When a quote cannot be rebuilt from those five, it is not checkable, and this desk treats an unrebuildable quote as an open question rather than an answer. The rebuild takes a minute with a calculator and settles most disputes about a figure before they start.

Chargeable weight written as a single formula

The formula is one line. Multiply the length, the width and the height in centimetres to get a cubic figure, divide that figure by the divisor to get a cubic weight, take whichever is greater between the cubic weight and the scale weight, and then apply the rounding step to that result. The answer is the chargeable weight, and it is the number the rate multiplies.

Written out for a carton of 42 by 32 by 24 centimetres, the cubic figure is 32,256 cubic centimetres. Divide by 5,000 and it reads 6.4512 kilos; divide by 6,000 and it reads 5.376; by 7,000 it is 4.608; by 8,000 it is 4.032. If the parcel weighs 5.2 kilos on the scale, the greater number is the cubic weight at divisors of 5,000 and 6,000, and the scale weight at divisors of 7,000 and 8,000.

That flip is the whole trick of reading a quote. The divisor does not scale the answer smoothly; it changes which of the two numbers is in charge, and it does so at a different point for every carton shape. A tall, light carton flips early. A dense, small carton never flips at all and is billed on the scale whatever the divisor says.

First substitution: a 42 by 32 by 24 carton of garments

Put numbers into the formula for a carton of folded garments. The cubic figure is 32,256 cubic centimetres and the scale reads 5.2 kilos. At a divisor of 6,000 the cubic weight is 5.376 kilos, which beats the scale by 0.176 of a kilo and becomes the number the rate multiplies. At 7,000 the cubic weight falls to 4.608 and the scale takes over.

The rounding step then decides what the reader is actually billed for. Quotes are written on a half-kilo step, so a raw figure of 5.376 lands on 5.5 under either a rounding-up step or a nearest-step rule, while a raw figure of 5.2 lands on 5.5 under a rounding-up rule and 5.0 under a nearest-step rule. The same parcel, the same scale, two different billed figures depending on a rule that is often not printed on the quote at all.

This is exactly the point recorded in the divisor check, where the half-kilo step changed the chargeable figure on 31 of 88 sampled parcels. Nearly two parcels in five came out with a different number because of the step rather than because of anything about the goods, which is why the desk keeps the step as a switchable input rather than a fixed assumption.

Second substitution: a tall carton where five centimetres costs two kilos

Take a taller carton of 55 by 40 by 35 centimetres holding one bulky item. The cubic figure is 77,000 cubic centimetres, which divides to 12.833 kilos at a divisor of 6,000. The scale reads 6.8 kilos, so the cubic figure wins by a wide margin and the parcel is billed as though it weighed nearly twice what it does.

Now take five centimetres off the height. The carton becomes 55 by 40 by 30, the cubic figure falls to 66,000, and the divided figure lands on exactly 11 kilos. Five centimetres of cardboard has removed 1.833 kilos from the raw figure and two kilos from the rounded reading, on a parcel whose actual contents did not change by a gram.

Two lessons come out of that substitution. First, on a volume-billed parcel the largest saving available is usually dimensional rather than postal, and it happens before the parcel is sealed. Second, the saving is not linear: the same five centimetres taken off a carton that is already below its scale weight would have produced no change at all, which is why measuring comes before requesting.

Third substitution: the same carton across four divisors

Return to the 42 by 32 by 24 carton with a 5.2 kilo scale reading and push it through all four recorded divisors, then apply both directions of the half-kilo step. At 5,000 the answer is 6.4512 and rounds to 6.5 either way. At 6,000 it is 5.376 and rounds to 5.5 either way. At 7,000 the scale weight of 5.2 takes over and rounds to 5.5 or to 5.0. At 8,000 the same thing happens, and the answer is again 5.5 or 5.0.

So one carton has three defensible billed figures: 5.0, 5.5 and 6.5. Nothing about the parcel changed between them. The divisor moved which number was in charge, and the step moved the result by half a kilo on top of that.

This is why the desk asks which divisor a quote used before discussing anything else about it. Two people comparing figures of 5.0 and 6.5 for the same parcel are not disagreeing about the parcel; they are comparing two different arithmetic setups, and the conversation cannot settle until both are on the table.

Error sources that make the last line unpredictable

Four error sources account for most of the drift between an estimate and an invoice. The unstated divisor is the first and largest, worth up to two kilos on the carton above. The rounding direction is the second, worth half a kilo per parcel and much more across a consolidated build. The third is the difference between the carton a reader measures at home and the carton the warehouse builds, which is usually larger because void fill and an outer box are added.

The fourth is the one that surprises people: a build that gains parcels between the estimate and the handover. Adding a fourth parcel to a three-parcel build can push the cubic figure past the scale weight and flip the parcel into volumetric billing, at which point every rate comparison made earlier is void.

All four are handled the same way. Ask for the carton dimensions and the scale weight to be recorded at the moment of sealing, keep the divisor and the step on the same note, and rebuild the figure before paying rather than after. A quote that cannot survive that rebuild was never a quote; it was a guess with a number attached.

The rebuild also tells a reader when a quote is not worth arguing about. If the figure matches the arithmetic at the stated divisor and the stated step, the quote is correct by its own rules, and the only question left is whether the parcel needs to be that size. That is a decision about packing rather than about the line, and it is settled before the parcel is sealed.

Divisor table for checking a quote at a glance

The slip below does the division in advance for two common cartons, so a reader can see which divisor a quote was built on by working backwards from the figure. If a quote for the 42 by 32 by 24 carton comes back at 5.5, the divisor was 6,000 or 7,000 with a rounding-up step. If it comes back at 6.5, the divisor was 5,000.

Working backwards like that is faster than asking, and it produces a better question. Instead of asking why a figure is high, a reader can state which divisor and which step the figure implies and ask whether that is right. That is a question a line can answer in one line, and it is the difference between a dispute and a correction.

The data point behind this note

Basis: four recorded divisors of 5,000, 6,000, 7,000 and 8,000 applied to sampled parcels with the half-kilo step held as a switchable input; the step changed the chargeable figure on 31 of the 88 parcels sampled (KB-2026-02).

◇KB-2026-02· 2026-09-30 Batch ledger · Challenge a figure

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