ISBN Check Digit Calculator

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.