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Luhn Mod N Algorithm Calculator

Reviewed by Calculator Editorial Team

The Luhn Mod N algorithm is a checksum formula used to validate identification numbers. It's commonly used in credit card numbers, IMEI numbers, and other identification systems. This calculator helps you verify or generate check digits using a custom modulus.

What is the Luhn Mod N Algorithm?

The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers. The "Mod N" variation allows you to specify a custom modulus instead of the standard modulus 10. This is particularly useful in systems that require different validation rules.

Key Features

  • Validates identification numbers with a checksum digit
  • Can be customized with different modulus values
  • Commonly used in credit card numbers, IMEI codes, and more
  • Simple to implement and verify

How It Works

The algorithm works by processing each digit in the number from right to left. For each digit in an odd position (1st, 3rd, etc.), the digit is added to the sum. For each digit in an even position (2nd, 4th, etc.), the digit is multiplied by 2, and if the result is more than 9, the digits of the result are added together. The final sum is then checked against the specified modulus.

Luhn Mod N Formula

For a given number with digits dn, dn-1, ..., d1, d0:

  1. Initialize sum = 0
  2. For each digit position i from n-1 down to 0:
    • If i is even: sum += di
    • If i is odd: sum += 2 × di (if result > 9, add digits of result)
  3. Check if sum ≡ 0 mod N

How to Use This Calculator

  1. Enter the number you want to validate or generate a check digit for in the "Number" field
  2. Specify the modulus value (N) you want to use in the "Modulus" field
  3. Click "Calculate" to perform the validation or generation
  4. Review the results showing whether the number is valid and the calculated check digit

Note

For generating a check digit, the calculator will append a digit to the end of your number that makes the entire number valid according to the Luhn Mod N algorithm.

Formula and Calculation

The Luhn Mod N algorithm uses the following steps to validate or generate a check digit:

Validation Steps

  1. Process each digit from right to left (excluding the check digit if present)
  2. For each digit in an odd position (1st, 3rd, etc.), add the digit to the sum
  3. For each digit in an even position (2nd, 4th, etc.), multiply the digit by 2 and add the digits of the result to the sum
  4. Calculate the remainder when the sum is divided by the specified modulus (N)
  5. If the remainder is 0, the number is valid

Check Digit Generation

  1. Process the digits as described above, but exclude the check digit position
  2. Calculate the sum as described
  3. Find the remainder when the sum is divided by the modulus (N)
  4. If the remainder is not 0, the check digit is (N - remainder)
  5. If the remainder is 0, the check digit is 0

Worked Examples

Example 1: Validation with Modulus 10

Let's validate the number 79927398713 using modulus 10:

  1. Process digits from right to left: 3, 1, 7, 8, 9, 3, 7, 2, 9, 9, 7
  2. Sum calculation:
    • 3 (odd position) → 3
    • 1 (even position) → 1 × 2 = 2
    • 7 (odd position) → 7
    • 8 (even position) → 8 × 2 = 16 → 1 + 6 = 7
    • 9 (odd position) → 9
    • 3 (even position) → 3 × 2 = 6
    • 7 (odd position) → 7
    • 2 (even position) → 2 × 2 = 4
    • 9 (odd position) → 9
    • 9 (even position) → 9 × 2 = 18 → 1 + 8 = 9
    • 7 (odd position) → 7
  3. Total sum = 3 + 2 + 7 + 7 + 9 + 6 + 7 + 4 + 9 + 9 + 7 = 64
  4. 64 mod 10 = 4 (not 0) → The number is invalid

Example 2: Check Digit Generation with Modulus 7

Let's generate a check digit for the number 123456 using modulus 7:

  1. Process digits from right to left: 6, 5, 4, 3, 2, 1
  2. Sum calculation:
    • 6 (odd position) → 6
    • 5 (even position) → 5 × 2 = 10 → 1 + 0 = 1
    • 4 (odd position) → 4
    • 3 (even position) → 3 × 2 = 6
    • 2 (odd position) → 2
    • 1 (even position) → 1 × 2 = 2
  3. Total sum = 6 + 1 + 4 + 6 + 2 + 2 = 21
  4. 21 mod 7 = 0 → Check digit is 0
  5. Final number: 1234560

Frequently Asked Questions

What is the difference between Luhn Mod 10 and Luhn Mod N?

The standard Luhn algorithm uses modulus 10, which is commonly used in credit card numbers. The Luhn Mod N algorithm allows you to specify any modulus value, making it more flexible for different identification systems.

How do I know which modulus to use?

The modulus value depends on the specific identification system you're working with. For example, credit card numbers typically use modulus 10, while some other systems might use different values. Check the documentation for your specific use case.

Can I use this calculator to generate check digits for credit card numbers?

Yes, you can use this calculator with modulus 10 to generate or validate check digits for credit card numbers. However, please note that this calculator is for educational purposes and should not be used for actual credit card processing.

What happens if I enter an invalid number?

If you enter an invalid number, the calculator will indicate that the number is invalid according to the Luhn Mod N algorithm. You can then adjust the number or modulus value as needed.