Luhn Formula Calculator

Luhn Algorithm:

\[ \text{1. Double every second digit from right} \] \[ \text{2. Subtract 9 if result > 9} \] \[ \text{3. Sum all digits} \] \[ \text{4. Valid if total mod 10 = 0} \]

Validation Result:

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1. 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, especially credit card numbers. It was created by IBM scientist Hans Peter Luhn.

2. How Does the Calculator Work?

The calculator uses the Luhn formula:

\[ \text{1. Double every second digit from right} \] \[ \text{2. Subtract 9 if result > 9} \] \[ \text{3. Sum all digits} \] \[ \text{4. Valid if total mod 10 = 0} \]

Example: For number 49927398716:

Double appropriate digits: 4(18)9(4)7(6)9(16)7(2)6
Adjust >9 numbers: 4(9)9(4)7(6)9(7)7(2)6
Sum all digits: 4+9+9+4+7+6+9+7+7+2+6 = 70
70 mod 10 = 0 → Valid

3. Importance of Luhn Validation

Details: The Luhn algorithm is crucial for detecting single-digit errors and most adjacent digit transpositions in identification numbers. It's widely used in credit cards, IMEI numbers, and various ID systems.

4. Using the Calculator

Tips: Enter the number you want to validate. The calculator will automatically remove any non-digit characters before processing.

5. Frequently Asked Questions (FAQ)

Q1: What numbers use the Luhn algorithm?
A: Credit cards, IMEI numbers, National Provider Identifier numbers (US), Canadian Social Insurance Numbers, and more.

Q2: Can Luhn detect all errors?
A: No, it catches about 90% of single-digit errors and most adjacent transpositions, but not all possible errors.

Q3: How is the check digit calculated?
A: The check digit makes the entire number pass the Luhn test. Calculate what digit would make the sum ≡ 0 mod 10.

Q4: Does Luhn provide security?
A: No, it's only for error detection, not cryptographic security or number authenticity.

Q5: Why subtract 9 from numbers >9?
A: This is equivalent to adding the digits of the number (since n-9 = digit sum for n=10-18).