15 Digit Check Digit Calculator

What is a Check Digit?

A check digit is an extra digit added to a number to verify its accuracy. It's commonly used in barcodes, credit cards, and other identification systems to detect errors during data entry or transmission.

Check digits work by applying a mathematical algorithm to the original number, producing a single digit that can be appended to the original number. When the number is later used, the check digit can be recalculated and compared to the stored check digit to verify the number's integrity.

How to Calculate a 15-Digit Check Digit

Calculating a 15-digit check digit involves these steps:

1. Assign weights to each digit position (typically 1 through 15)
2. Multiply each digit by its corresponding weight
3. Sum all the products
4. Calculate the remainder when the sum is divided by 10
5. The check digit is 10 minus this remainder (or 0 if the remainder is 0)

This method ensures that the check digit can detect single-digit errors in any position of the original number.

Formula Used

Worked Example

Let's calculate the check digit for the 15-digit number: 123456789012345

1. Assign weights 1 through 15 to each digit
2. Multiply each digit by its weight:
   • 1×1 = 1
   • 2×2 = 4
   • 3×3 = 9
   • 4×4 = 16
   • 5×5 = 25
   • 6×6 = 36
   • 7×7 = 49
   • 8×8 = 64
   • 9×9 = 81
   • 0×10 = 0
   • 1×11 = 11
   • 2×12 = 24
   • 3×13 = 39
   • 4×14 = 56
   • 5×15 = 75
3. Sum all products: 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 0 + 11 + 24 + 39 + 56 + 75 = 435
4. Calculate 435 mod 10 = 5
5. Check digit = (10 - 5) mod 10 = 5

The complete number with check digit is: 1234567890123455