# Converting between ISBN-10 and ISBN-13 (aka EAN-13)

ISBN stands for International Standard Book Number. Originally this was a 10 digit number known as ISBN-10, but has been replaced with a 13 digit version known as ISBN-13 (aka EAN-13) to better fit in with the industry standard product numbering system.

The ISBN system offers a unique numbering system for books and publications of various types. ISBN offers 9 identification digits for each book or publication and one check digit. ISBN-13 expands the available number set by doubling the available numbers. You might think that the extra three digits would more than double the available numbers but ISBN is limited within the EAN-13 numbering system and will always start with 978 or 979 as the first three digits, leaving only 9 more digits for the actual identification digits and again the last digit is the check digit.

Any ISBN-10 number can be converted to ISBN-13. Any ISBN-13 number that starts with 978 can be converted back to ISBN-10. ISBN-13 numbers that start with 979 cannot be converted to ISBN-10.

The conversion process from ISBN-10 to ISBN-13 is a rather simple one. Start with the first 9 digits of the ISBN-10 number, place 978 in front and calculate the new check digit using the standard EAN check digit calculation.

If you want to calculate the check digit for ISBN-10, that is done using a MOD-11 calculation that is very different than the EAN check digit process.

- Lets start with ISBN-10 number 1-5905-9332-?
- Each digit is multiplied by its position for digits 1-9
- 1x1 + 5x2 + 9x3 + 0x4 + 5x5 + 9x6 + 3x7 + 3x8 + 2x9 = 180
- Now get the remainder 180 mod 11 = 4
- Now return the mod 11 again... 4 mod 11 = 4
- If the results is 10, return the letter X otherwise return the digit.
- For our example, the final number is 1-5905-9332-4

**ISBN-1-5905-9332-4**

Look at the number above and below the barcode. You will see that except for the last digit in the ISBN number, all of the digits exist in the 13 digit version shown under the barcode right after the 978 and just before the new check digit of 5.

Now you can see how easy it is to convert between ISBN-10 and ISBN-13.