This site is supported by donations to The OEIS Foundation.

# UPC

Please do not rely on any information it contains.

A Universal Product Code (UPC) is a number, almost always barcoded, that allows for the unique identification of a specific product, packaged in a specific portion, in a manner intelligible for any manufacturer, distributor or retailer in the world.

The most commonly used UPC format in the United States is the 12-digit UPC, which consists of a general category digit, five digits that identify the manufacturer, followed by five digits that identify the product, and then a check digit. For example, the UPC for a house numeral 7 from National (a division of Stanley) is 0 38613 23869 5. (The human-readable number is typically spaced in this way, but inventory software

• 0 - Available for general use
• 1 - Reserved
• 2 - Some food items of variable weight
• 3 - Pharmaceuticals (but not over-the-counter medications)
• 4 - Store use only
• 5 - Coupons
• 6 - Available for general use
• 7 - Available for general use
• 8 - Reserved
• 9 - Reserved

To calculate the check digit, the digits in the one's place, hundred's place, ten hundred's place, etc., are multiplied by 3. Then this is added to the digits in the ten's place, thousand's place, etc. This sum is multiplied by –1, and the remainder of that modulo 10 is the check digit:

${\displaystyle c(n)=-\left(\left(\sum _{i=1}^{\lfloor {\frac {\mathcal {L}}{2}}\rfloor }d(2i-1)\right)+3\left(\sum _{j=0}^{\lfloor {\frac {\mathcal {L}}{2}}\rfloor }d(2j)\right)\right)\mod 10}$, where ${\displaystyle {\mathcal {L}}}$ is how many digits ${\displaystyle n}$ has, ${\displaystyle d({\mathcal {L}}-1)}$ is the most significant digit of ${\displaystyle n}$, ..., and ${\displaystyle d(0)}$ is the ones place digit.

Theoretically, a UPC check digit can be used with 1- or 2-digit numbers as well as numbers with more than 17 digits. There is probably no practical need for the former, while the latter would probably require a more robust error-detecting (if not error-correcting) mechanism.

However, the UPC check digit is a more robust mechanism than a simple digital root would be, as it guards against dyslexia when a seemingly scannable UPC code does not scan and the human operator has to type in the code (whether a cash register or a mobile scanner).

See A237042 and A231963.

Some manufacturers that have or might have UPCs ending in the numbers shown above include H. J. Heinz (013000) and the Hershey Company (068000).

UPCs carry no information on price. At receiving, stocking and sale, DESCRIBE LOOKUP PROCESS

STUFF ABOUT ZERO SUPPRESSION GOES HERE

## The relationship between manufacturer part numbers, UPCs, SKUs and serial numbers

In some cases, a particular item may be identified by as many as four different numbers, of which only the UPC might be intelligible to all manufacturers, distributors and retailers. A useful oversimplification might be to think of these numbers as being on a spectrum from most specific to least specific, with serial numbers being the most specific to a particular instance of an item, to stock-keeping units (SKUs) being the least specific.

SKUs allow distributors and retailers to lump together items from different manufacturers which may in some regards be exactly the same. Suppose for example, that, for some reason, a hardware store sells 1-pint cans of lacquer thinner from three different manufacturers at the same price. There are three different UPCs involved, but sometimes the staff need only know how many cans of 1-pint lacquer thinner there are without regard for which cans come from which manufacturer. They can have one SKU associated with the three different UPCs.

Of course there can also be SKUs associated only with a particular manufacturer, and, in the case of distributors with many franchised stores, we may witness a remarkable unity among SKUs, manufacturer part numbers and UPCs. For example, older ACE Hardware products sold at ACE Hardware stores have 5-digit SKUs at those stores. That 5-digit number then appears in the UPC, with 82901 before it and the check digit after it. Some newer ACE products have 7-digit SKUs, so the relationship between UPCs and SKUs is not as straightforward.

The case of National products in interesting in that the manufacturer part numbers consist of the letter N followed by a 6-digit number, the first five digits of which go into the UPC. (The SKU at an ACE Hardware store might consist of the letters N and A followed by that 6-digit number). The check digit for the UPC does not usually coincide with the sixth digit that gets left out.

The following table of five products randomly selected from a hardware store illustrates these relations.

 SKU Description Manufacturer part number UPC 34521 Terminal, insulated FML INS16-14250TB 0 82901 34521 3 NA238790 4" brass #7 N238790 V??? 0 38613 23879 4 NA238691 4" black #7 NA238691 V871 0 38613 23869 5 NA118430 Screw eyes 19/16" N118430 0 38613 11843 0 55500 Soft brass wire 123124 RM96129 0 38902 39220 6

These items don't need serial numbers. But items like cars and computers do.