How the checksums work
ISBN-10
Each of the 10 characters is weighted from 10 down to 1. Positions 1 through 9 must be digits. Position 10 may be a digit or the letter X (which stands for the value 10). The weighted sum must be a multiple of 11. The expected last character is the value that makes the sum divisible by 11.
ISBN-13
ISBN-13 uses the EAN-13 algorithm. Odd-position digits keep their value and even-position digits are multiplied by 3. The sum must be a multiple of 10. The expected last digit is the value that makes the sum divisible by 10. ISBN-13 must start with the bookland prefix 978 or 979.
Convert ISBN-10 to ISBN-13
Drop the ISBN-10 check character, prepend 978, and compute the EAN-13 check digit on the new 12-digit body. Every valid ISBN-10 has a unique ISBN-13 equivalent under this rule.
Convert ISBN-13 to ISBN-10
Only defined for ISBN-13 values whose prefix is 978. Drop the prefix and the check digit, then compute the ISBN-10 check character on the 9-digit body. ISBN-13 values starting with 979 are intentionally outside ISBN-10 space and cannot be represented as an ISBN-10.
The dashed display format uses a generic group split for readability. Registrant-accurate hyphenation requires the International ISBN Agency ranges file; the validator does not embed that snapshot because it changes when new ranges are allocated.