A number that checks the others
The last digit of a GTIN-13 product identifier is calculated from the twelve digits before it. This check digit helps spot errors when the number is read or entered.
GS1 explains the check digit’s job. First meet the product identifier carried by a retail barcode; then try the arithmetic that checks its structure.
Alternate one and three
For this thirteen-digit format, take the first twelve digits from left to right. Multiply the first by 1, the second by 3, and keep alternating 1 and 3. Add the results.
The check digit is the smallest amount needed to reach an equal or higher multiple of ten. If the total already ends in zero, the check digit is 0. GS1’s manual guide shows the weights for each identifier format; do not reuse the left-to-right starting weight for a different-length format without checking it.
Try twelve made-up digits
Use the made-up sequence 123456789012. The odd positions add to 26. The even positions add to 22; multiply that by 3 to get 66.
Now 26+66=92. The next multiple of ten is 100, so the check digit is 8. The resulting thirteen digits are 1234567890128. This is an arithmetic example, not a claim that the number has been assigned to a real product.
A check is not an identity
Change the last digit of our example from 8 to 9. The weighted total with that last digit is 101 rather than 100, so the check no longer matches.
A matching calculation alone does not identify the product or establish that a number has been assigned. It checks a numerical relationship. For another approach to reading information, explore the grid inside a QR code, or follow Read the codes around you.