Luhn Algorithm Explained

What it is

The Luhn algorithm (mod 10) is the checksum formula used to validate payment card numbers. It detects single-digit errors and most transpositions. It is not a security check - it only confirms the number is structurally valid.

• Developed by Hans Peter Luhn
• Used by all major card brands
• Catches single-digit errors
• Catches most transpositions
• Not a security or fraud check

How it works

Starting from the rightmost digit, double every second digit. If a doubled digit exceeds 9, subtract 9. Sum all digits. If the total is divisible by 10, the number passes.

History of Luhn

The Luhn algorithm was created by Hans Peter Luhn, an IBM scientist, in 1954. It was designed as a simple checksum to catch transcription errors in account numbers. It has since become the standard for payment card validation worldwide.

• Created by Hans Peter Luhn at IBM in 1954
• Originally for account number validation
• Adopted by all major card networks
• Simple to implement, effective at catching errors
• Now an ISO/IEC standard

Implementation examples

The algorithm is simple to implement in any language. The key steps are: reverse the number, double every other digit, subtract 9 from results over 9, sum all digits, check divisibility by 10. The free Luhn checker and mod-10 calculator on this site show the calculation step by step.

• Reverse the number string
• Double every second digit
• Subtract 9 from digits over 9
• Sum all resulting digits
• Check if sum mod 10 equals 0

Edge cases

Luhn does not catch all errors. It misses some transpositions (swapping two digits that are 5 apart). It also cannot detect missing or extra digits in certain positions. For production use, combine Luhn with other validation (BIN lookup, issuer verification).

• Misses transpositions of digits 5 apart
• Cannot detect all missing/extra digits
• Combine with BIN lookup for production
• Combine with issuer verification for full validation
• Not a fraud prevention tool

Other checksums

Luhn is not the only checksum algorithm. IMEI numbers use a Luhn variant. ISBN-13 uses a mod 10 checksum with different weights. IBAN uses mod 97. Each is designed for its specific use case.

Limitations

Luhn does not verify that a card exists, is active or has balance. It only confirms the number is structurally valid. Use the free Luhn checker on this site to test a number.

• Does not verify card existence
• Does not check active status
• Does not verify balance
• Only structural validity
• Combine with issuer checks for full validation