Free Luhn algorithm calculator to validate credit card numbers, IMEI, and other IDs. Instantly check mod 10 checksums or generate valid test numbers online.
The Luhn algorithm (also known as the "modulus 10" or "mod 10" algorithm) is a simple checksum formula used to validate identification numbers including credit card numbers, Canadian Social Insurance Numbers, IMEI numbers, and National Provider Identifier numbers. Created by IBM scientist Hans Peter Luhn in 1954, this algorithm remains the industry standard for detecting accidental errors in number sequences.
This Luhn algorithm calculator allows you to instantly validate any number sequence using the Luhn check and generate valid numbers that pass verification—perfect for developers, payment processors, and anyone working with identification numbers.
Using this calculator is simple:
To Validate a Number: Enter the number you want to check (credit card, IMEI, etc.) and click "Validate." The calculator will instantly verify if the number passes the Luhn algorithm check.
To Generate a Valid Number: Select "Generate," specify the desired length, and the calculator will create a valid number that passes the Luhn algorithm verification.
View the Breakdown: Watch the step-by-step visualization showing exactly how the Luhn algorithm processes each digit to calculate the final checksum.
The Luhn algorithm validation process works as follows:
Here's a visual representation of the Luhn algorithm:
The Luhn algorithm can be expressed mathematically as follows:
Let be the -th digit, counting from the rightmost digit (excluding the check digit) and moving left. Then the check digit is chosen so that:
Where is the modulo operation.
The Luhn algorithm has various applications in different fields:
Let's validate the number 4532015112830366:
Testing 490154203237518 (note the last digit is wrong):
The correct check digit should be 1 to make the sum 60 (divisible by 10).
While the Luhn algorithm is widely used, there are other checksum algorithms for different purposes:
The Luhn algorithm was created by Hans Peter Luhn, an IBM computer scientist, in 1954. Luhn was a pioneer in the field of information science and is credited with several innovations, including the KWIC (Key Word In Context) indexing system.
The algorithm was originally designed to protect against accidental errors, not malicious attacks. It's important to note that while the Luhn algorithm can detect many common errors, it is not a secure form of encryption and should not be relied upon for data security purposes.
Despite its age, the Luhn algorithm remains widely used due to its simplicity and effectiveness in catching common transcription errors in payment systems and identification numbers.
Here are code examples to implement the Luhn algorithm in various programming languages:
1import random
2
3def luhn_validate(number):
4 digits = [int(d) for d in str(number)]
5 checksum = 0
6 for i in range(len(digits) - 1, -1, -1):
7 d = digits[i]
8 if (len(digits) - i) % 2 == 0:
9 d = d * 2
10 if d > 9:
11 d -= 9
12 checksum += d
13 return checksum % 10 == 0
14
15def generate_valid_number(length):
16 digits = [random.randint(0, 9) for _ in range(length - 1)]
17 checksum = sum(digits[::2]) + sum(sum(divmod(d * 2, 10)) for d in digits[-2::-2])
18 check_digit = (10 - (checksum % 10)) % 10
19 return int(''.join(map(str, digits + [check_digit])))
20
21## Example usage:
22print(luhn_validate(4532015112830366)) # True
23print(luhn_validate(4532015112830367)) # False
24print(generate_valid_number(16)) # Generates a valid 16-digit number
251function luhnValidate(number) {
2 const digits = number.toString().split('').map(Number);
3 let checksum = 0;
4 for (let i = digits.length - 1; i >= 0; i--) {
5 let d = digits[i];
6 if ((digits.length - i) % 2 === 0) {
7 d *= 2;
8 if (d > 9) d -= 9;
9 }
10 checksum += d;
11 }
12 return checksum % 10 === 0;
13}
14
15function generateValidNumber(length) {
16 const digits = Array.from({length: length - 1}, () => Math.floor(Math.random() * 10));
17 const checksum = digits.reduce((sum, digit, index) => {
18 if ((length - 1 - index) % 2 === 0) {
19 digit *= 2;
20 if (digit > 9) digit -= 9;
21 }
22 return sum + digit;
23 }, 0);
24 const checkDigit = (10 - (checksum % 10)) % 10;
25 return parseInt(digits.join('') + checkDigit);
26}
27
28// Example usage:
29console.log(luhnValidate(4532015112830366)); // true
30console.log(luhnValidate(4532015112830367)); // false
31console.log(generateValidNumber(16)); // Generates a valid 16-digit number
321import java.util.Random;
2
3public class LuhnValidator {
4 public static boolean luhnValidate(long number) {
5 String digits = String.valueOf(number);
6 int checksum = 0;
7 boolean isEven = true;
8 for (int i = digits.length() - 1; i >= 0; i--) {
9 int digit = Character.getNumericValue(digits.charAt(i));
10 if (isEven) {
11 digit *= 2;
12 if (digit > 9) digit -= 9;
13 }
14 checksum += digit;
15 isEven = !isEven;
16 }
17 return checksum % 10 == 0;
18 }
19
20 public static long generateValidNumber(int length) {
21 Random random = new Random();
22 long[] digits = new long[length - 1];
23 for (int i = 0; i < length - 1; i++) {
24 digits[i] = random.nextInt(10);
25 }
26 long checksum = 0;
27 for (int i = digits.length - 1; i >= 0; i--) {
28 long digit = digits[i];
29 if ((length - 1 - i) % 2 == 0) {
30 digit *= 2;
31 if (digit > 9) digit -= 9;
32 }
33 checksum += digit;
34 }
35 long checkDigit = (10 - (checksum % 10)) % 10;
36 long result = 0;
37 for (long digit : digits) {
38 result = result * 10 + digit;
39 }
40 return result * 10 + checkDigit;
41 }
42
43 public static void main(String[] args) {
44 System.out.println(luhnValidate(4532015112830366L)); // true
45 System.out.println(luhnValidate(4532015112830367L)); // false
46 System.out.println(generateValidNumber(16)); // Generates a valid 16-digit number
47 }
48}
49When implementing the Luhn algorithm, consider the following edge cases and special considerations:
Input Validation: Ensure that the input is a valid number string. Non-digit characters should be handled appropriately (either removed or treated as invalid input).
Leading Zeros: The algorithm should work correctly with numbers that have leading zeros.
Large Numbers: Be prepared to handle very long numbers that might exceed the capacity of standard integer types in some programming languages.
Empty Input: Define how your implementation should handle empty strings or null inputs.
Non-Standard Character Sets: In some applications, you might encounter numbers represented with characters outside the standard 0-9 range. Define how these should be handled.
Performance Considerations: For applications that need to validate large numbers of inputs quickly, consider optimizing the algorithm implementation.
Valid Credit Card Number:
Invalid Credit Card Number:
Valid Canadian Social Insurance Number:
Invalid IMEI Number:
To verify the implementation of the Luhn algorithm, you can use the following test cases:
1def test_luhn_algorithm():
2 assert luhn_validate(4532015112830366) == True
3 assert luhn_validate(4532015112830367) == False
4 assert luhn_validate(79927398713) == True
5 assert luhn_validate(79927398714) == False
6
7 # Test generated numbers
8 for _ in range(10):
9 assert luhn_validate(generate_valid_number(16)) == True
10
11 print("All tests passed!")
12
13test_luhn_algorithm()
14The Luhn algorithm is primarily used to validate identification numbers like credit card numbers, IMEI numbers (mobile devices), Canadian Social Insurance Numbers, and National Provider Identifier numbers in healthcare. It detects accidental errors such as mistyped digits or transposed adjacent numbers.
To validate a credit card number with the Luhn algorithm: 1) Starting from the rightmost digit, double every second digit moving left, 2) Subtract 9 from any doubled result greater than 9, 3) Sum all digits, 4) If the sum is divisible by 10 (ends in 0), the credit card number is valid.
No, the Luhn algorithm cannot detect all errors. It catches most single-digit errors and many transposition errors, but it's not foolproof. The algorithm was designed to catch accidental errors, not intentional fraud. It will not detect twin errors (like 22 to 55) or jump transpositions (like 101 to 404).
The Luhn algorithm is not a security measure—it's only an error-detection mechanism. While it validates that a number follows the correct format, it doesn't verify if the credit card is active, has sufficient funds, or belongs to the person using it. Always use additional security measures like CVV codes and payment gateway verification.
The Luhn algorithm can be implemented in virtually any programming language including Python, JavaScript, Java, C++, C#, PHP, Ruby, and Go. The algorithm is simple enough to code in just 10-20 lines in most languages.
The Luhn algorithm is called the "modulus 10" or "mod 10" algorithm because the final validation step checks if the sum of all processed digits is divisible by 10 (sum mod 10 = 0). This modulo operation is the key to determining whether a number is valid.
Yes, you can generate numbers that pass the Luhn check, but these are not valid, active credit card numbers. They simply follow the correct mathematical format. Generating actual valid credit cards for unauthorized use is illegal. Luhn-valid numbers are useful for testing payment systems in development environments.
The Luhn algorithm is simpler than alternatives like the Verhoeff algorithm or Damm algorithm, but less comprehensive. While Luhn catches most single-digit errors and some transposition errors, the Verhoeff algorithm detects all single-digit errors and most transpositions. The Damm algorithm catches all single-digit and adjacent transposition errors.
This Luhn algorithm calculator provides instant validation and generation of numbers that comply with the mod 10 checksum formula. Whether you're a developer testing payment systems, verifying identification numbers, or learning about algorithmic validation, this tool simplifies the process with real-time visualization and accurate results.
Start using the calculator above to validate credit card numbers, generate test data, or understand how the Luhn algorithm processes each digit in your number sequences.