What the Luhn algorithm is and how to use it | Stripe (2024)

The Luhn algorithm, also known as the “modulus 10” or “mod 10” algorithm, is a simple checksum formula used to validate identification numbers. The algorithm—developed by IBM engineer Hans Peter Luhn—can be used to validate credit card numbers, International Mobile Equipment Identity (IMEI) numbers, and other numerical data. Businesses today frequently use it to increase the accuracy and reliability of their data entry processes, especially when handling sensitive information such as payment data.

Below, we’ll share what businesses need to know about the Luhn algorithm: what it is, why it’s so important, and how to use it to boost the security of your customer payments.

What’s in this article?

• Why is the Luhn algorithm so important?
  
• What kinds of numbers does the Luhn algorithm validate?
  
• How do different industries use the Luhn algorithm?
  
• Luhn algorithm formula
  
• Luhn algorithm limitations
  

Why is the Luhn algorithm so important?

The Luhn algorithm has been a game changer to the world of data validation and fraud prevention for the following reasons:

• Improved data accuracy: The Luhn algorithm is a straightforward method for detecting common types of input errors such as single-digit errors or transposition errors that invert two digits, which is especially important in industries such as finance and banking.

• Ease of implementation: The algorithm is simple to understand and implement in various programming languages without substantial computational resources, making it accessible for a wide range of applications.

• Real-time capabilities: The Luhn algorithm can be applied in real time to verify the correctness of numerical data as it’s entered, and it has become an important check for systems that require instant data validation.

• Fraud prevention: While not foolproof against sophisticated fraud attempts, the Luhn algorithm helps screen out invalid numbers before a transaction or operation proceeds, which can deter fraud attempts and reduce the incidence of errors that could lead to fraud or security breaches.

• Cost efficiency: By detecting errors early in the process, the algorithm helps avoid costs associated with incorrect data processing such as financial losses, customer dissatisfaction, and the administrative costs of correcting errors.

• Global influence: Because of its effectiveness and simplicity, the Luhn algorithm has been widely adopted across the globe and has set a standard for practices such as credit card and ID number validation.

What kinds of numbers does the Luhn algorithm validate?

In any system where numbers are manually entered, the Luhn algorithm can be used as a real-time validation tool to immediately detect and highlight errors, improving data quality and operational efficiency. Here’s an overview of the types of number sequences it typically verifies.

• Credit card numbers: The most common use of the Luhn algorithm is for verifying credit card numbers. Before a credit card transaction is processed, the card number can be checked using the Luhn algorithm to confirm that it’s a valid sequence. This step helps detect accidental input errors or incomplete numbers.

• Identification numbers: The Luhn algorithm is used to validate identification numbers such as social security numbers, IMEI numbers for mobile phones, or national identification numbers. This validation checks that these numbers have been entered and processed correctly.

• Financial identifiers: Banks use the Luhn algorithm to verify account numbers and other financial identifiers before processing transactions such as fund transfers.

• Barcodes: Some barcode formats incorporate a check digit that’s calculated using the Luhn algorithm. Scanners use the algorithm to verify that barcodes are scanned correctly for more accurate inventory tracking, retail checkout, and logistical operations.

How do different industries use the Luhn algorithm?

Here’s a quick look at some common ways the Luhn algorithm works in practice:

• Online shopping: When you make a purchase online, the payment system uses the Luhn algorithm to verify that you entered a valid credit card number before processing the transaction.

• Banking systems: Banks use the Luhn algorithm to validate account numbers and routing numbers to ensure that funds are transferred to the correct accounts.

• Mobile phones: International Mobile Equipment Identity (IMEI) numbers uniquely identify mobile devices and include a check digit calculated from the other digits using the Luhn algorithm. This helps verify the integrity of the IMEI number, aiding in fraud prevention and device identification when buying a used phone.

• Government documents: In some countries, identification numbers such as social security numbers or national ID numbers incorporate a check digit that’s calculated using the Luhn algorithm. This helps government agencies verify the accuracy of these numbers during data entry and processing.

• Utility companies: Utility service providers often use the Luhn algorithm to validate customer account numbers. This ensures that billing and payment information is associated with the correct accounts, reducing billing errors and customer service issues.

• Ticketing systems: Airlines and other transportation companies use the Luhn algorithm to validate booking reference numbers or ticket numbers, ensuring that data is entered correctly and reducing the risk of ticket fraud.

Luhn algorithm formula

The Luhn algorithm doesn’t have a formula in the conventional mathematical sense. Rather, it’s constituted by a series of steps.

• Step 1: Starting from the right, double the value of the second-to-last digit and continue doing the same for every second digit. If the result of any doubling operation is greater than 9, then add the digits of the result to obtain a single-digit number.
  Example: 6 × 2 = 12; 1 + 2 = 3

• Step 2: Sum all the digits you didn’t double and the new values you got from doubling.

• Step 3: Determine if the total sum is a multiple of 10. The number is considered valid according to the Luhn algorithm if the total ends in 0.

To illustrate, let’s verify the number 79927398713 using the Luhn algorithm formula.

Double every second digit from the right:

1 x 2 = 2

8 x 2 = 16 (1 + 6 = 7)

3 × 2 = 6

2 × 2 = 4

9 x 2 = 18 (1 + 8 = 9)

Add all the digits together, including the undoubled digits:

7 + 9 + 9 + 4 + 7 + 6 + 9 + 7 + 7 + 2 + 3 = 70

The number 79927398713 is valid according to the Luhn algorithm because the result is 70, which is a multiple of 10.

These steps form the “formula” or procedure that the Luhn algorithm follows to validate or generate numbers.

Luhn algorithm limitations

While the Luhn algorithm is a powerful tool for error detection and numerical validation, it has certain limitations. When it comes to fraud detection or data validation, the Luhn algorithm is typically just one part of a more extensive set of checks and balances, and relying solely on it for these practices is not advisable.

The Luhn algorithm’s limitations in data validation are outlined below.

• Complex error detection: The algorithm is designed to catch common errors such as single-digit misentries or adjacent digit transpositions (e.g., 67 becoming 76), but it does not detect more complex errors such as nonadjacent digit swapping (e.g., 197 becoming 971).

• Fraud detection: The Luhn algorithm can verify that a sequence of numbers is potentially valid, but it cannot determine if it corresponds to a legitimate account or identity or protect against deliberate fraudulent activities, where the fraudulent actor has a valid number sequence.

• Non-numeric data: The algorithm applies only to numeric data and cannot be used to validate data that includes letters or symbols.

• Data integrity: The algorithm only checks numerical validity, not data integrity. It cannot detect if the data has been altered intentionally or identify which part of the data is incorrect.

• Predictability: The algorithm is a well-known, standard method and anyone with knowledge of the algorithm can generate numbers that pass the Luhn check. This predictability can be a drawback in situations where a higher level of security is required.

Despite these limitations, the Luhn algorithm remains a widely used tool for preliminary checks of numerical sequences in various applications, particularly in financial services.