How to Calculate A Valid Credit Card Number

Credit card numbers must pass the Luhn algorithm check to be valid. This guide explains how to calculate a valid credit card number using the algorithm, including a working calculator, formula, examples, and FAQ.

What is the Luhn Algorithm?

The Luhn algorithm, also known as the "modulus 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, particularly credit card numbers. It was created by IBM scientist Hans Peter Luhn in 1954.

The algorithm works by processing each digit of the number from right to left, doubling every second digit, and then summing all the digits. If the total modulo 10 equals 0, the number is valid.

How to Calculate a Valid Credit Card Number

To calculate a valid credit card number using the Luhn algorithm, follow these steps:

Start with a partial credit card number (excluding the check digit).
Double the value of every second digit from the right.
If doubling a digit results in a number greater than 9, add the digits of the product.
Sum all the digits.
Calculate the sum modulo 10.
If the result is 0, the number is valid. Otherwise, it's invalid.

Luhn Algorithm Formula

Let N be the number of digits in the card number (excluding the check digit).

For each digit position i (from right to left, starting at 1):

If i is odd, double the digit value.
If doubling results in a number greater than 9, add the digits of the product.
Sum all the processed digits.
If (sum % 10) == 0, the number is valid.

For example, to validate the number 4532015112830366:

Start with 453201511283036 (remove the last digit).
Double every second digit from the right: 4 10 3 4 0 2 5 2 1 2 8 6 0 6.
Sum the digits: 4 + 1 + 0 + 3 + 4 + 0 + 2 + 5 + 2 + 1 + 2 + 8 + 6 + 0 + 6 = 42.
42 % 10 = 2, so the check digit should be 8 (10 - 2 = 8).
The complete valid number is 4532015112830366.

Examples

Here are some examples of valid and invalid credit card numbers:

Credit Card Number	Valid/Invalid	Check Digit
4532015112830366	Valid	6
5500005555555559	Valid	9
378282246310005	Valid	5
1234567890123456	Invalid	6

Common Mistakes

When calculating valid credit card numbers, common mistakes include:

Forgetting to start from the rightmost digit.
Doubling the wrong digits (should be every second digit from the right).
Not adding the digits of products greater than 9.
Incorrectly calculating the final check digit.
Using the wrong modulo operation.

Remember: The Luhn algorithm only checks the format of the number, not whether it's actually assigned to a card. A valid number might not correspond to an active card.

FAQ

What is the purpose of the Luhn algorithm?: The Luhn algorithm is used to validate identification numbers, particularly credit card numbers, by checking their format without requiring a database lookup.
Can the Luhn algorithm generate valid credit card numbers?: No, the Luhn algorithm only validates existing numbers. It cannot generate new valid credit card numbers.
Are all valid credit card numbers accepted by banks?: No, a valid number according to the Luhn algorithm might not correspond to an active card. Banks also check other factors like issuer identification numbers.
Can the Luhn algorithm be bypassed?: Yes, the Luhn algorithm is a simple checksum and can be bypassed with more sophisticated validation methods used by banks.
Is the Luhn algorithm used for other identification numbers?: Yes, the Luhn algorithm is used for validating various identification numbers, including IMEI numbers, National Provider Identifier numbers, and more.