Luhn Algorithm Check: Validate Any Number Step by Step

What a Luhn check does

A Luhn check (also called the mod 10 check) is a checksum test that catches typing mistakes in long numbers. You double every second digit starting from the right, sum all the digits, and divide the total by 10. If the remainder is 0, the number passes. If not, at least one digit is wrong or out of place.

The test says nothing about whether a card is real, active, or funded. It only confirms that the digits are internally consistent, so treat a pass as proof of formatting, not of validity.

Run the check step by step

1. Strip spaces, dashes, and other separators so only digits remain.
2. Start at the rightmost digit and move left, doubling every second digit (the second, fourth, sixth from the right).
3. If a doubled value is greater than 9, subtract 9 from it.
4. Add every resulting digit to a running total.
5. Divide the total by 10 and look at the remainder.
6. Accept the number when the remainder is 0, and reject it otherwise.

Worked example

Test the sequence 79927398713. Reading from the right, the digits in doubled positions are 1, 8, 3, 2, 9 and the digits in single positions are 3, 7, 9, 7, 7. The doubled values become 2, 16, 6, 4, 18, and after subtracting 9 where needed you get 2, 7, 6, 4, 9. The full sum is 3 + 2 + 7 + 7 + 9 + 6 + 7 + 4 + 9 + 9 + 7 = 70. Since 70 divides by 10 with no remainder, the number passes.

Find the missing check digit

1. Remove the final digit, which is the check digit.
2. Run the doubling and summing steps on the remaining digits.
3. Double the result and subtract it from 10, then take the result mod 10.
4. Place that digit at the end and re-run the full check to confirm a zero remainder.

Errors the algorithm misses

Luhn catches every single-digit error and most swaps of two adjacent digits. It does not catch a swap of 09 with 90, and it cannot detect two errors that cancel each other in the sum. A passing number can still be mistyped in ways the checksum hides, so verify the number against its source when accuracy matters.

Where the check is used

The same mod 10 formula appears in payment card numbers, IMEI codes on phones, the National Provider Identifier used in US healthcare billing, and many loyalty and account numbers. The formula is public, documented in ISO/IEC 7812-1, and simple enough to implement in a few lines of code or on paper.