Luhn Algorithm Checker

Validate credit card numbers and detect errors using the industry-standard Luhn algorithm

Understanding the Luhn Algorithm

The Luhn algorithm, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate identification numbers, particularly credit card numbers. Developed by IBM researcher Hans Peter Luhn in 1954, it has become the industry standard for detecting simple errors in credit card numbers.

How the Algorithm Works

Starting from the rightmost digit, double every second digit
If doubling results in a two-digit number, add the digits together
Sum all the digits (original and modified)
If the total sum is divisible by 10, the number is valid

Credit Card Number Structure

Number Components

IIN: First 6-8 digits (Issuer ID)
Account Number: Middle digits
Check Digit: Last digit (Luhn checksum)
Length: Usually 13-19 digits

Major Card Types

Visa: Starts with 4, 13-19 digits
Mastercard: Starts with 5, 16 digits
Amex: Starts with 34/37, 15 digits
Discover: Starts with 6, 16 digits

Error Detection

Errors It Catches (~95%)

Single digit errors: Any single digit changed
Adjacent transposition: Two adjacent digits swapped
Twin errors: aa → bb where a ≠ b
Common arithmetic mistakes

Errors It Misses (~5%)

Some transpositions: 09 ↔ 90, 18 ↔ 81
Multiple errors: Two or more errors that cancel
Complex substitutions: Certain patterns
Systematic errors: All digits shifted

Applications

Payment Processing

Credit card validation
POS system checks
E-commerce validation
Payment gateway pre-processing

Other Uses

IMEI numbers (mobile devices)
Healthcare provider IDs
Government identification
Product codes

Example Calculation

Validating 4532015112830366

Step 1: 4 5 3 2 0 1 5 1 1 2 8 3 0 3 6 6

Step 2: 4 [10] 3 [4] 0 [2] 5 [2] 1 [4] 8 [6] 0 [6] 6 [12]

Step 3: 4 1 3 4 0 2 5 2 1 4 8 6 0 6 6 3

Step 4: Sum = 55

Result: 55 mod 10 = 5 ≠ 0, so INVALID

Security Note

The Luhn algorithm is NOT a security feature. It only validates format, not authenticity. Generated "valid" numbers are for testing only and should never be used for actual transactions.