Luhn Checksum Calculator

The Luhn algorithm (also called mod 10 or modulus 10) is a simple checksum formula invented by IBM scientist Hans Peter Luhn in 1954 and patented in 1960 (US Patent 2,950,048). The patent expired and the algorithm entered the public domain in 1977, which is why it shows up in so many open standards. From the rightmost digit moving left, every second digit is doubled (and 9 subtracted if the result exceeds 9), then all the digits are summed. The number is valid if the total is divisible by 10.

Luhn catches every single-digit typo and most adjacent-digit transpositions, which together account for the vast majority of human keying errors. It does not catch the specific transposition of 09 to 90 or 90 to 09 (both pairs sum to the same Luhn contribution), nor twin-digit substitutions like 22 swapped with 55. It also will not detect insertions or deletions that change the digit count. Luhn is a cheap, lightweight checksum, not a cryptographic hash.

Most magnetic-stripe credit and debit card numbers carry a Luhn check digit (Visa, Mastercard, Amex, Discover, Diners, JCB). It also appears in IMEI device identifiers, the Canadian Social Insurance Number (SIN), the US National Provider Identifier (NPI) for healthcare, some national identifiers (Greek SSN, Israeli ID), survey IDs, and many internal account-number schemes. Anywhere a system needs a quick format check on a hand-keyed identifier, Luhn is the default.

No. Luhn is only a checksum. For example, 4111 1111 1111 1111 passes the calculation, but that result does not establish an issued or authorized account. Issuer, expiration, authorization, and fraud checks are separate.

A string of identical digits where the doubling pattern works out to a multiple of 10 will pass Luhn trivially, even though no issuer would ever assign such a number. The flag on all-same-digit inputs is there so you do not mistakenly conclude that a placeholder, test value, or empty form field is a valid identifier. The check digit is doing its job mathematically; the warning is doing its job semantically.