EAN13 is a barcode system used to label products. "EAN" stands for European article number and 13 refers to the number of digits in the code. However, the actual information that is transmitted by the barcode is contained within only the first 12 of these digits. The final digit of the code is what is referred to as the check digit. This number does not contain information but is meant to confirm that the barcode was scanned correctly. This is done by having the 13th digit be the mathematical result of a formula dealing with the previous 12 numbers. The formula used in this process is referred to as the modulo 10 algorithm. To calculate an EAN13 barcode is to determine the 13th number of the code by applying this modulo 10 algorithm to the previous 12 digits.

Locate the 12th digit in the barcode. If the check digit is not yet in place, this is the last digit from the left. If the check digit is in place, this is the second to last digit from the left.
For example, if your EAN13 was 97 35940 56482 4, the 12th digit is the No. 2. 
Starting with this 12th digit, move from right to left across the code adding every second digit to it. Using our example code of 97 35940 56482 4, this means starting with the No. 2 and adding to it the numbers 4, 5, 4, 5 and 7, giving a total of 27.

Multiply the sum obtained in Step 2 by 3. Using our example above, this means the multiplying of 27 by 3, giving a total of 81.

Locate the 11th digit in the code. Using our example code of 97 35940 56482 4, this would be the No. 8.

Starting with the 11th digit, move from right to left across the code adding every second digit to it. Using our example of 97 35940 56482 4, this means starting with the No. 8 and adding to it 6, 0, 9, 3 and 9, giving a total of 35.

Add the results from Step 3 and Step 5. In our example this means adding 81 and 35, giving a total of 116.

Round the result of Step 6 up to the nearest multiple of 10. In our example, this means rounding 116 up to 120.

Subtract the result of Step 7 from the result of Step 6. In our example, this is 120116, giving us a difference of 4. This 4 should be the 13th number in the EAN13, otherwise known as the check digit.
Tips & Warnings
 If you do not feel like doing the calculation manually, you can use the automatic check digit calculator found in the Resources section of this article.
References
 Photo Credit http://www.codeproject.com/KB/graphics/EAN_13_Barcodes/EAN13NumericSections.gif