What is the Luhn algorithm?

The Luhn algorithm, also called mod 10, is a checksum formula that validates identification numbers such as credit cards and IMEIs. It doubles every second digit from the right, sums the digits, and a valid number has a total divisible by 10.

How is the Luhn check digit calculated?

Treat the payload as if a 0 check digit were appended, run the Luhn sum, then the check digit equals (10 - (sum mod 10)) mod 10. This is the single digit that makes the whole number pass.

Which numbers use Luhn?

Credit and debit card numbers (the final digit), IMEI device identifiers, some social insurance numbers and many other identifiers use Luhn as a built-in typo-detection check.

Does a valid Luhn result mean the card is real?

No. Luhn only confirms the digits are internally consistent, catching most typos and transpositions. It does not confirm the card was ever issued, is active, or has funds. Never treat it as authorization.

What errors does Luhn catch?

Luhn detects all single-digit errors and almost all adjacent transposition errors (swapping two neighbouring digits), except the specific swap of 0 and 9, which it misses.

What is the Luhn Algorithm Checker?

Validates any number with the Luhn (mod 10) algorithm and computes the correct check digit. Works for credit cards, IMEI numbers and many national IDs, showing the weighted sum and why a number passes or fails. It runs free in your browser on Gera Tools, with nothing uploaded.

Luhn Algorithm Checker

Name: Luhn Algorithm Checker
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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The Luhn algorithm (mod 10) is the check-digit formula behind credit card numbers, IMEI device identifiers and many national IDs. It exists to catch accidental typos and digit swaps before a number is processed. This checker validates any number and computes the correct check digit, entirely in your browser.

How it works

To validate a number that already includes its check digit:

Starting from the rightmost digit, double every second digit.
If a doubled value exceeds 9, subtract 9 (equivalently, add its two digits).
Sum all the resulting digits. The number is valid if the total is divisible by 10.

To compute the check digit for a payload that has no check digit yet, run the same weighting as if a 0 were appended, then the check digit is (10 - (sum mod 10)) mod 10.

Step-by-step trace: working through the algorithm manually

Take the number 4 5 3 9 1 4 8 8 0 3 4 3 6 4 6 7. Process from right to left, doubling every second digit (positions 2, 4, 6, … from the right):

Position from right:   1  2   3  4   5  6   7  8   9  10  11  12  13  14  15  16
Digit:                 7  6   4  6   3  4   3  0   8   8   4   1   9   3   5   4
Double every 2nd:      7  12  4  12  3  8   3  0   8   16  4   2   9   6   5   8
Subtract 9 if >9:      7  3   4  3   3  8   3  0   8   7   4   2   9   6   5   8

Sum = 7+3+4+3+3+8+3+0+8+7+4+2+9+6+5+8 = 80, which is divisible by 10. Valid.

What Luhn catches and what it misses

Luhn is specifically designed to catch single-digit transcription errors — typing a 5 where a 6 should be — and most adjacent transpositions — swapping 46 to 64. It detects all single-digit errors without exception. For transpositions, it catches every case except swapping 0 and 9, which produce the same weighted value after the subtraction step.

What Luhn does not catch:

Multiple simultaneous errors that happen to cancel out
The specific 0↔9 transposition
Completely invented numbers that happen to pass (there are many valid Luhn numbers for any partial payload)

Where Luhn is used in practice

Number type	Digits	Notes
Visa credit card	16	Starts with 4
Mastercard	16	Starts with 51–55 or 2221–2720
American Express	15	Starts with 34 or 37
IMEI (mobile device)	15	Last digit is Luhn check digit
Canadian SIN	9	Social Insurance Number
ICCID (SIM card)	18–19	May or may not use Luhn depending on issuer

Notes

Luhn detects all single-digit errors and nearly all adjacent transpositions, with the lone exception of swapping a 0 and a 9. A passing result means the digits are internally consistent, not that the card or device was ever issued or is currently active — it is a format check only. Payment processors run additional checks against live card databases. Nothing you type is sent anywhere; the algorithm runs locally in your browser.