Luhn Algorithm Calculator
Validate numbers and calculate check digits using the Luhn algorithm
Enter the number to validate. Spaces and dashes will be automatically removed.
How to Use This Calculator
Enter the Number
Enter the credit card number or ID number you want to validate. You can include spaces or dashes for readability - they will be automatically removed.
Validate or Calculate
Click "Validate Number" to check if the number is valid. Click "Calculate Check Digit" to find the correct check digit for an incomplete number.
Review Results
The calculator will show whether the number is valid, the checksum value, and detailed calculation steps showing how each digit was processed.
Formula
Sum all digits (doubling every second from right) mod 10 = 0
If sum mod 10 = 0, the number is valid
Algorithm Steps:
- Starting from the rightmost digit (excluding check digit), double every second digit
- If doubling results in a two-digit number, sum the digits (e.g., 18 → 1 + 8 = 9)
- Sum all the digits (doubled and original)
- Add the check digit
- If the total mod 10 = 0, the number is valid
Check Digit Calculation:
check_digit = (10 - (sum mod 10)) mod 10
Example:
Number: 4532 0151 1283 0366
From right: 6, 3, 8, 0, 2, 1, 1, 5, 0, 1, 2, 3, 5, 3, 4
Double every second: 6, 6, 8, 0, 4, 1, 2, 5, 0, 1, 4, 3, 10, 3, 8
Sum digits: 6+6+8+0+4+1+2+5+0+1+4+3+1+0+3+8 = 52
52 mod 10 = 2, so this example would be invalid (should be 0)
About Luhn Algorithm Calculator
The Luhn algorithm, also known as the "modulus 10" algorithm, is a simple checksum formula used to validate various identification numbers, most notably credit card numbers. It was invented by Hans Peter Luhn, an IBM scientist, in 1954 and is now widely used in the financial industry.
What is the Luhn Algorithm?
The Luhn algorithm is a checksum algorithm that detects simple errors in identification numbers. It works by applying a mathematical formula to the digits of a number and verifying that the result is divisible by 10. While it can't detect all errors, it catches common mistakes like single-digit errors and most transpositions.
Applications
- Credit Cards: Validates credit card numbers (Visa, Mastercard, American Express, etc.)
- Debit Cards: Validates bank card numbers
- IMEI Numbers: Validates International Mobile Equipment Identity numbers
- National ID Numbers: Used in some countries for ID card validation
- Canadian Social Insurance Numbers: Used for validation (though not for security)
- SIM Card Numbers: Validates SIM card identification numbers
How It Works
The algorithm processes digits from right to left, doubling every second digit (starting from the second digit from the right). If doubling produces a two-digit number, the digits are added together. All digits are then summed, and if the total is divisible by 10, the number is valid.
Limitations
- Not Cryptographic: The Luhn algorithm is a checksum, not encryption. It only detects errors, not fraud.
- Limited Error Detection: It catches about 90% of common errors but can't detect all possible mistakes.
- Reversible: Given most of a number, the check digit can be calculated, so it doesn't provide security.
Why It's Used
The Luhn algorithm is simple to implement, fast to compute, and effective at catching the most common types of errors (typos, single-digit mistakes, and most transpositions). This makes it ideal for real-time validation in point-of-sale systems and online forms where users type card numbers.
Frequently Asked Questions
Does a valid Luhn checksum mean a credit card is real?
No. The Luhn algorithm only checks if the number follows the correct format. A valid checksum doesn't verify that the card exists, has funds, or is authorized for use. Additional validation (card type, expiration date, CVV, etc.) and authorization are required.
Can the Luhn algorithm detect all errors?
No. The Luhn algorithm can detect about 90% of common errors, including single-digit errors and most transpositions (swapping adjacent digits). However, it cannot detect certain errors like swapping non-adjacent digits (e.g., 1234 → 4231) or certain systematic errors.
What credit cards use the Luhn algorithm?
Most major credit card networks use the Luhn algorithm, including Visa, Mastercard, American Express, Discover, Diners Club, and JCB. However, the algorithm is just one part of card validation - card types have different length requirements and starting digit patterns.
Is the Luhn algorithm secure?
No, the Luhn algorithm is not a security feature. It's purely for error detection. Anyone can calculate the check digit if they know the other digits. Real card security relies on the CVV code, expiration date, and authorization systems, not the Luhn checksum.
How do I calculate the check digit for a new number?
Enter all digits except the last one, then click "Calculate Check Digit". The calculator will determine what the last digit should be to make the number pass the Luhn validation. This is useful when generating test card numbers or designing new numbering systems.