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The Luhn algorithm—also called the Mod 10 check—tests whether a payment-card number passes a checksum. Starting with the digit immediately left of the final digit, double every other digit moving left; subtract 9 from any doubled value greater than 9; then add those adjusted values to the untouched digits. A total divisible by 10 passes. That result shows only checksum plausibility, not whether the account was issued, is active, or can authorize a payment.
How the Luhn or Mod 10 check works
The rightmost digit is the check digit. Leave it unchanged and begin the alternating doubling pattern with the digit immediately to its left. Continue moving right to left: double the next digit, leave the one after it unchanged, and repeat. When a doubled value is greater than 9, subtract 9. Add the resulting values, including the unchanged digits and check digit. If the sum is divisible by 10, the number passes the Luhn checksum.
PCI Security Standards Council FAQ 1137 describes Luhn, or Modulus 10, as the algorithm most often used to validate Primary Account Numbers (PAN). Read the PCI SSC explanation.
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Worked example
Consider the sample digit string 79927398713. This is an arithmetic illustration of the checksum, not a claim that the string is an issued or usable payment card.
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- Keep the final digit, 3, unchanged. Moving left, double alternating digits: 1→2, 7→7, 8→16, 9→9, 3→6, 7→7, 2→4, 9→9, 9→18, 7→7.
- Reduce doubled values over 9 by subtracting 9: 16 becomes 7 and 18 becomes 9.
- Add the transformed values and untouched digits: 7 + 9 + 4 + 7 + 6 + 7 + 9 + 7 + 2 + 1 + 3 = 62.
- Divide the total by 10. Since 62 leaves a remainder of 2, this example does not pass the checksum.
What a passing result does—and does not—mean
A pass means the digits satisfy the checksum formula. It can help catch some mistyped or malformed input before a payment request is sent, but it does not establish that the number was issued, that an account is active, that the person entering it owns the account, that funds are available, or that a transaction will be authorized. PCI SSC explicitly distinguishes a number that is possible under the formula from one that has actually been issued and is active.
Using the check in an application
Separate checksum from formatting and length rules
Process the actual digits consistently. If the input field permits spaces or hyphens for readability, remove only the formatting characters your application explicitly allows before applying the checksum; reject unexpected characters rather than silently treating them as digits. Apply the relevant product, issuer, or payment-provider length and format rules separately. CyberSource documents account numbers up to 19 digits including the check digit, but that does not mean every payment product uses every length in that range.
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CyberSource describes checking a user-entered account number before sending it for authorization. The check is an input-quality step, not a replacement for the processor or issuer’s authorization flow. See its check-digit guidance.
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Present the result accurately
Use wording such as “passes the Luhn checksum” or “checksum format looks plausible.” Avoid labels such as “valid card” or “active card,” which imply facts the calculation cannot verify. A passing checksum can be one early validation step, while authorization determines whether a transaction can proceed.
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Checksum validation is not payment-data security
Luhn is not a security control and does not protect stored or transmitted card data. PCI DSS is a baseline of technical and operational requirements intended to protect payment account data. PCI SSC identifies its intended audience as entities that store, process, or transmit cardholder data, or can affect the security of cardholder-data environments. Consult the PCI DSS overview for the standard’s scope.
Luhn terminology also appears in payment tokenization documentation, including J.P. Morgan Payments’ tokenization materials; that context does not change what a checksum pass proves.
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