The Luhn algorithm, also called Modulus 10 or the mod 10 check, tests whether a payment card number passes a checksum. Starting from the second digit from the right, double every other digit; subtract 9 from any doubled result above 9; then add those adjusted digits to the untouched digits. A total divisible by 10 passes. That result shows checksum plausibility only—it does not establish that the number was issued, is active, belongs to you, or can be authorized.
How to calculate the Luhn checksum
The check digit is the rightmost digit. Leave it untouched, then work from right to left, doubling the digit immediately to its left and every other digit after that. For a doubled value above 9, subtract 9; add the resulting values and the digits you did not double. The number passes if the sum has a remainder of zero when divided by 10. PCI Security Standards Council describes the method in FAQ 1137.
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- Start at the right edge of the full number, including its check digit.
- Keep the rightmost digit as it is. Moving left, double the next digit, then alternate between unchanged and doubled digits.
- For each doubled result greater than 9, subtract 9. For example, 7 doubled is 14, and 14 minus 9 is 5.
- Add all the transformed and unchanged digits.
- If the sum is divisible by 10, the number passes the Luhn checksum.
What a passing result means
A pass means only that the digits meet the checksum rule. It can help catch some entry errors, but it does not confirm that an account number was issued or remains active. The PCI Security Standards Council explicitly distinguishes a number that is possible under the formula from one that is actually issued and active.
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CyberSource describes the check as a validation that can be applied to a user-entered account number before sending it for authorization. Authorization is a separate step: the checksum does not establish account status, ownership, available funds, or whether a transaction will be approved. See CyberSource’s account-number verification guidance.
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How to use the check in an implementation
Process digits in the correct direction
Apply the alternating pattern from right to left, keeping the rightmost check digit untouched. Starting the pattern at the opposite end, or doubling the check digit, changes the calculation and can produce an incorrect result.
Handle formatting separately
If an input field accepts spaces or separators, normalize those characters before applying digit-by-digit processing, and reject input that does not meet the field’s digit-format requirements. Do not let punctuation alter which digits are doubled. The checksum itself does not define a complete input-format policy.
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Apply length and product rules separately
CyberSource documents account numbers of up to 19 digits, including the check digit. That maximum is not a universal rule for every payment product or issuer. Enforce the applicable format and length requirements for the product or payment provider independently of the checksum.
Use authorization for the actual payment decision
Treat a successful checksum as an input-quality signal, not as approval to accept a payment. A payment flow still needs the relevant processor or issuer authorization process.
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How Luhn fits into payment-data protection
Luhn is not a security control and does not protect payment account data. PCI DSS is a broader baseline of technical and operational requirements intended to protect that data. PCI Security Standards Council says the standard is for entities that store, process, or transmit payment account data, or can affect the security of cardholder-data environments. See the PCI DSS overview.
MOD 10 terminology also appears in payment-tokenization documentation, including J.P. Morgan Payments’ tokenization documentation; that context does not change what a checksum pass establishes.
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