Bookdigit

Method and boundaries

Twelve weighted digits, one check digit

Bookdigit checks one complete thirteen-digit entry. It does not request book metadata, contact a library service or consult current publisher ranges. The distinction matters: a checksum can agree even when a number has never been assigned.

Start at the left

  1. Multiply the first digit by 1, the second by 3, and continue alternating through digit twelve.
  2. Add those twelve products. Call the sum S.
  3. Find the remainder when S is divided by 10.
  4. The required final digit is (10 − remainder) mod 10. In particular, a remainder of zero needs a final zero.
  5. Compare this expected digit with the thirteenth digit actually entered.

Equivalently, add the supplied final digit to S. A matching checksum makes that total divisible by ten. All arithmetic here uses small whole numbers exactly; there is no rounding or display tolerance.

Example: the sum is 93

For 9780306406157, the first twelve products are 9, 21, 8, 0, 3, 0, 6, 12, 0, 18, 1 and 15. Their sum is 93. The remainder is 3, so the expected final digit is 7. The entered final 7 agrees.

Input rules

Use ASCII digits, ASCII spaces and plain ASCII hyphens, up to 64 characters in total. Spaces and hyphens are removed before counting digits. No labels, tabs, line breaks, other dash characters, non-ASCII digits or punctuation are silently discarded. Exactly thirteen digits must remain. Leading zeroes within the identifier are retained.

The supported prefix is 978 or 979. The 979-0 range identifies printed music through ISMN and is excluded from this ISBN-only checker. This tool does not check how hyphens divide registration groups or publisher elements. The separators are treated only as input spacing.

What agreement leaves unanswered

A matching checksum does not prove assignment, availability, title, author, edition, publisher, format, ownership or purchase legitimacy. Current range allocation and book metadata are not checked. Some transposed digit pairs can also leave the weighted sum unchanged modulo ten. Treat the result as evidence about the checksum, not a certificate for the whole number.

A mismatch does not locate the original error. The displayed expected final digit follows from the first twelve digits, which could themselves contain a typo. Bookdigit never replaces your entry automatically. ISBN-10 conversion, barcodes and identifier allocation are outside this tool.

Calculation sources

The stable checksum formula is described in Appendix 1 of the International ISBN Agency's historical users' manual. For current structure, see the agency's ISBN explanation. The Library of Congress ISMN structure explains the 979-0 music prefix. These sources describe the numbering systems; they do not endorse this independent tool.