About

The Luhn algorithm (also called the Modulus 10 or Mod 10 algorithm) is a checksum formula published by Hans Peter Luhn in 1954 via U.S. Patent 2,950,048. It detects single-digit transcription errors and most transpositions of adjacent digits in numeric identifiers. It is not a cryptographic hash. It does not protect against deliberate fraud. Its sole purpose is catching accidental corruption during manual entry. The algorithm operates in O(n) time where n is the digit count. Every major credit card network (Visa, Mastercard, American Express, Discover, JCB, UnionPay) requires the final digit of the Primary Account Number (PAN) to satisfy the Luhn check. IMEI numbers on mobile devices (15 digits, ITU-T E.212) also use it. Canadian Social Insurance Numbers, some national ID schemes, and ISBNs partially rely on similar modular arithmetic. A failed Luhn check means the number was corrupted during entry or is structurally invalid. A passing check does not guarantee the account exists or is active.

This tool performs the complete Luhn computation, shows the digit-by-digit breakdown so you can audit each step, detects the card network from IIN/BIN prefixes per ISO/IEC 7812, and can generate the correct check digit for an incomplete number. Limitation: prefix-based card detection covers published BIN ranges and may not identify every issuer sub-brand or co-branded cards.

Formulas

The Luhn algorithm processes a number string of n digits d₁, d₂, …, d_n (where d_n is the check digit, the rightmost). Starting from the rightmost digit and moving left, double every second digit:

d_i^′ =

{

2 ⋅ d_i − 9 if 2 ⋅ d_i > 92 ⋅ d_i otherwise

The total checksum is computed as:

S = n∑i=1 d_i^′

The number is valid if and only if:

S mod 10 ≡ 0

To generate a check digit d_n for a partial number d₁ … d_n−1, compute the Luhn sum S^′ of the partial digits (treating the missing position as 0), then:

d_n = (10 − (S^′ mod 10)) mod 10

Where d_i = individual digit at position i, n = total number of digits, S = Luhn checksum, d_i^′ = transformed digit after doubling rule.

Reference Data

Card Network	IIN/BIN Prefix(es)	Length(s)	Check Algorithm	Example Prefix
Visa	4	13, 16, 19	Luhn	4XXX
Mastercard	51 - 55, 2221 - 2720	16	Luhn	5500
American Express	34, 37	15	Luhn	3782
Discover	6011, 644 - 649, 65	16 - 19	Luhn	6011
JCB	3528 - 3589	16 - 19	Luhn	3530
Diners Club Carte Blanche	300 - 305	14	Luhn	3000
Diners Club International	36	14	Luhn	3600
Diners Club USA/Canada	54	16	Luhn	5400
UnionPay	62	16 - 19	Luhn	6200
Maestro	5018, 5020, 5038, 6304	12 - 19	Luhn	5018
Mir	2200 - 2204	16 - 19	Luhn	2200
Verve	506099 - 506198, 650002 - 650027	16, 18, 19	Luhn	5061
RuPay	60, 65, 81, 82, 508	16	Luhn	6521
IMEI (Mobile Device)	TAC (8 digits) + serial	15	Luhn	3568...
Canadian SIN	1 - 9 (province code)	9	Luhn	046...

Frequently Asked Questions

No. The Luhn algorithm only verifies structural integrity - it catches accidental typos and single-digit errors. A number can pass the Luhn check and still be completely fictitious. To confirm an account is real and active, an authorization request to the issuing bank via the card network is required. The Luhn check is the first gate, not the only gate.

The Luhn algorithm detects all single-digit substitution errors (changing any one digit) and most transpositions of two adjacent digits. It fails to detect the transposition of 09 to 90 (or vice versa), because both produce the same Luhn contribution. It also cannot detect some twin errors (e.g., 22 ↔ 55, 33 ↔ 66, 44 ↔ 77) in certain positions. For higher-security applications, the Verhoeff algorithm or Damm algorithm provide strictly stronger error detection.

Yes. The IMEI (International Mobile Equipment Identity) is a 15-digit number where the last digit is a Luhn check digit, per 3GPP TS 23.003. Canadian Social Insurance Numbers (9 digits) also use the Luhn formula. Enter any numeric string and the tool will compute the checksum. Card network detection only activates when the prefix and length match known IIN/BIN ranges - for non-card numbers, it will report the identifier type as unknown while still validating the Luhn checksum.

Enter the first n − 1 digits of your number. The tool appends a placeholder 0 as the last digit, runs the Luhn sum on the full string, then computes (10 − (S mod 10)) mod 10 to find the unique check digit that makes the complete number valid. This is identical to how issuing banks compute the check digit for new card numbers.

Luhn validity and card network identification are independent checks. The checksum formula works on any digit string regardless of length or prefix. Card network detection relies on matching the IIN/BIN prefix (first 1-8 digits) and total length against published ranges from ISO/IEC 7812 and individual network specifications. Private-label cards, regional networks, or very new BIN ranges may not be in the detection database. The number is still arithmetically valid per Luhn.

Yes. The tool strips all non-digit characters (spaces, dashes, dots) before processing. The input 4539 1488 0343 6467 is treated identically to 4539148803436467. This matches real-world usage where card numbers are printed in groups of four. However, the algorithm itself operates strictly on the raw digit sequence.