Check Digit Calculator

A check digit is a form of redundancy check used for error detection on identification numbers, such as credit card numbers, book ISBNs, or bank account numbers. It is a single digit computed from the other digits in the number sequence. This calculator allows you to generate a check digit for a given number using popular algorithms.

What is a Check Digit For?

The primary purpose of a check digit is to detect simple errors in data entry. When a long number is typed manually, common mistakes include:

• Single-digit errors: Mistyping one digit (e.g., 4 becomes 5).
• Transposition errors: Swapping two adjacent digits (e.g., 34 becomes 43).

A well-designed check digit algorithm can catch a high percentage of these common errors. When a number is entered into a system, the system can recalculate the check digit and compare it to the one provided. If they don't match, the system flags the number as potentially incorrect.

Algorithms Explained

1. The Luhn Algorithm (MOD 10)

The Luhn algorithm is one of the most widely used check digit formulas, famously used for credit card numbers and many other identification numbers.

How it works:

1. Starting from the rightmost digit of the base number (excluding the space for the check digit), double the value of every second digit.
2. If doubling a digit results in a two-digit number, add the two digits together to get a single-digit number (e.g., 14 becomes 1 + 4 = 5).
3. Sum up all the digits (the doubled-and-summed digits and the untouched digits).
4. The check digit is the number that must be added to this sum to make it a multiple of 10. (Calculated as (10 - (sum % 10)) % 10).

Example (for number 7992739871): The Luhn algorithm will process this and produce a check digit of 3.

2. MOD 11 (Modulo 11)

The MOD 11 algorithm is another common method, often used for ISBN-10 numbers and various other identifiers. It uses a weighted sum.

How it works (common variant):

1. Starting from the rightmost digit of the base number, assign a weight to each digit. The weights typically cycle through a sequence, such as 2, 3, 4, 5, 6, 7.
2. Multiply each digit by its corresponding weight.
3. Sum the results of all the multiplications.
4. Divide the sum by 11 and find the remainder.
5. Subtract the remainder from 11. This is the check digit.
6. If the result is 10, it's often represented by 'X'. If it's 11, it becomes 0.