Working the calculation by hand
Convert each letter to a number: A is 10, and the scale skips 11, 22 and 33, so B is 12 and Z is 38. Digits keep their own value. Multiply the ten characters by 1, 2, 4, 8 and so on, doubling up to 512, then add the results. Divide by 11 and keep the remainder. That remainder is the check digit, except that a remainder of 10 is written as 0.
Slips it catches and slips it misses
Because digits differ by less than 11, a single wrong digit in the serial number is nearly always caught, and so is a swap of two neighboring digits. Letters are weaker. A and K differ by exactly 11, so swapping one for the other in the owner code leaves the check digit unchanged. Nor does a valid digit prove the container exists. A number can pass the test and still belong to a different box.
What to do when the digit fails
Go back to the source rather than guessing a fix. Look at a photo of the doors, the equipment interchange receipt or the carrier's documents, and compare character by character. Common culprits are O and 0, I and 1, and B and 8. If the number painted on the box itself fails, report it to the owner, since a container re-marked with a new code needs a recalculated digit.
Example
For MSCU1234566, the weighted sum of the first ten characters is 5,528, which leaves a remainder of 6 when divided by 11, so the check digit is 6.
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Official sources
Questions
What does Check Digit mean?
A check digit is the 11th character of a container number, calculated from the first ten under ISO 6346. If one character is typed or scanned wrongly, the recalculated digit usually no longer matches, so the error shows up before a search or filing fails.
Why is the check digit often shown in a box?
Framing it on the container helps separate it from the six-digit serial number, so people do not read it as part of the serial. Documents and systems usually show it without the frame.
Do booking and B/L numbers have check digits?
Not under any shared standard. Each carrier sets its own booking and bill formats, so a mistyped reference usually shows up only as a failed lookup.