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ISBN Check Digit Calculator

Compute and verify the ISBN-13 check digit

How it is calculated

The tool removes everything that is not a digit, so hyphens and spaces are fine, and accepts either 12 or 13 digits. It multiplies the first 12 digits alternately by 1 and 3 (digits in odd positions by 1, in even positions by 3), adds the products, and takes check digit = (10 − (sum mod 10)) mod 10.

With 12 digits it only computes the missing check digit and says so. With 13 digits it compares the last digit with the computed one and reports Valid or Invalid. Any other length, including the older 10-digit ISBN-10, gives no result. A valid check digit means the number is well-formed; it does not confirm that a book with that ISBN exists or has been assigned.

Worked example

The ISBN 978-0-306-40615-7.

The first 12 digits are 9 7 8 0 3 0 6 4 0 6 1 5. Weighted: 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3 = 9 + 21 + 8 + 0 + 3 + 0 + 6 + 12 + 0 + 18 + 1 + 15 = 93. 93 mod 10 = 3, so the check digit is 10 − 3 = 7. The 13th digit is 7, so the status is Valid. If the last digit were 8, it would read Invalid.

Try this example →

Common mistakes

  • Entering an ISBN-10. It has 10 digits and a different formula, so the tool returns nothing; convert it to ISBN-13 by adding the 978 prefix and recalculating the check digit.
  • Including the check digit and expecting it to be recalculated. With 13 digits the tool validates the last one; enter only 12 to get the digit.
  • Treating Valid as proof that the book exists. Any number with the right check digit passes.
  • Reading a barcode with extra digits, such as the 5-digit price add-on, and entering all of them. Use only the 13 digits of the main code.
  • Typing a letter O for a zero or an I for a one. Letters are stripped, which can leave you with 11 or 12 digits and a wrong result.

About this calculator

Every ISBN-13 ends in a check digit computed from the 12 digits before it using alternating weights of 1 and 3: each digit is multiplied by 1 or 3 in turn, the products are summed, and the check digit is whatever value — from 0 to 9 — makes that total a multiple of 10, following the formula Check digit = (10 − (sum mod 10)) mod 10.

This is the same modular-arithmetic checksum baked into every barcode on a published book, since ISBN-13 shares its check-digit algorithm with the EAN-13/UPC barcode standard used across retail; it exists specifically so that a single mistyped or misscanned digit — the most common data-entry error — gets caught immediately rather than silently pointing to the wrong book.

Publishers and librarians validating batches of ISBNs, bookstore and library systems checking barcodes at the point of scan, and developers building cataloging or inventory software all use this exact algorithm to verify an ISBN is well-formed before it's stored or printed.

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