How does ISBN-10 become ISBN-13?

You drop the ISBN-10 check digit, prefix the EAN code 978 to the remaining 9 digits, then compute a fresh ISBN-13 check digit. The first nine significant digits are otherwise unchanged.

Why does the new check digit differ from the old one?

ISBN-10 uses a modulo-11 checksum with weights 10 down to 1, while ISBN-13 uses a modulo-10 checksum with alternating weights 1 and 3. Different schemes over different digits produce different check digits.

What does the X in an ISBN-10 mean?

The ISBN-10 check digit can be 0 through 10, and 10 is written as the letter X because it needs a single character. The tool accepts X and treats it as the value 10 when validating.

Can every ISBN-10 be converted?

Yes. Every valid ISBN-10 maps to exactly one ISBN-13 using the 978 prefix. The reverse is not true, because newer ISBN-13 numbers using the 979 prefix have no ISBN-10 equivalent.

Is the hyphenation accurate?

The hyphenated grouping shown is illustrative. Correct group, registrant, and publication boundaries depend on the registration agency and vary by length, so always use the publisher's official hyphenation for print.

ISBN-10 to ISBN-13 Converter

ISBN-13 replaced the older 10-digit ISBN in 2007, and every ISBN-10 has an exact 13-digit equivalent. This converter validates your ISBN-10, then performs the standard transformation: keep the meaningful digits, add the 978 prefix, and recompute the check digit under the newer scheme.

How it works

The conversion is mechanical once the original number is verified:

1. Validate ISBN-10:  sum of digit × (10,9,...,1) is divisible by 11 (X = 10)
2. Drop the ISBN-10 check digit, keep the first 9 digits
3. Prefix "978" to make a 12-digit body
4. ISBN-13 check = (10 − (sum of digit×[1,3,1,3,...]) mod 10) mod 10

The first nine information digits carry the registration group, publisher, and title and are preserved unchanged; only the prefix and check digit are new. Because the two formats use different checksum algorithms, the check digit almost always changes during conversion.

Example and notes

The ISBN-10 0-306-40615-2 validates (its weighted sum is divisible by 11) and converts to ISBN-13 978-0-306-40615-7. Notice the trailing digit changed from 2 to 7 because the modulo-10 algorithm replaces the modulo-11 one. The tool will not convert a number whose ISBN-10 check digit is wrong, which catches typos before they propagate. Note that ISBN-13 numbers beginning with 979 are genuinely new and have no ISBN-10 form, so conversion only ever runs in the ISBN-10 to 978 direction.