ISBN-10 / ISBN-13 Check Digit & Converter

Understanding the ISBN check digit calculator — concept and principle

The International Standard Book Number (ISBN) identifies an edition of a book, and its last digit is a check digit that catches typing and scanning errors. ISBNs have had 13 digits since 2007; older books carry 10-digit ISBNs. Enter the first 12 digits of an ISBN-13 or the first 9 digits of an ISBN-10, and the calculator completes the number and converts it to the other format where possible.

How it is calculated

• ISBN-13: multiply the 12 digits alternately by 1 and 3, starting with 1, and add the products to get S. Check digit = (10 − S mod 10) mod 10.
• ISBN-10: multiply the 9 digits by 10, 9, 8, … 2 and add them to get S. Check digit = (11 − S mod 11) mod 11; a value of 10 is written as X.
• Conversion: an ISBN-10 becomes an ISBN-13 by adding the prefix 978 and recomputing the check digit. An ISBN-13 can be converted back only if it starts with 978; numbers starting with 979 have no ISBN-10.

The principle

Both schemes make the weighted sum of all digits, including the check digit, a multiple of the modulus (10 or 11). ISBN-13 is the same as the EAN-13 product barcode, which is why it uses the 1-3 weights of retail barcodes. Those weights catch every single-digit error, and they catch a swap of two adjacent digits unless the two digits differ by 5. ISBN-10 uses 11, a prime, with all different weights, so it detects every single-digit error and every adjacent swap; the price is an eleventh symbol, X.

Worked example

1. Input: 978030640615 (12 digits).
2. Weights 1, 3, 1, 3 …: 9 + 21 + 8 + 0 + 3 + 0 + 6 + 12 + 0 + 18 + 1 + 15 = 93.
3. Check digit = (10 − 93 mod 10) mod 10 = (10 − 3) mod 10 = 7, so the full ISBN is 9780306406157.
4. The prefix is 978, so drop it: 030640615. Weights 10 … 2: 0 + 27 + 0 + 42 + 24 + 0 + 24 + 3 + 10 = 130.
5. 130 mod 11 = 9, and 11 − 9 = 2, so the ISBN-10 is 0306406152.

How to read the result

If the check digit you have differs from the computed one, at least one digit is wrong. Within an ISBN, the first block after 978 or 979 is the registration group (a country or language area), then come the registrant (publisher), the publication and the check digit. Korean ISBNs begin with 978-89 or 979-11.

Common mistakes

• Entering all 13 digits: the tool recalculates the last one from the first 12, so compare it yourself.
• Writing the ISBN-10 check value 10 as "10" instead of X.
• Converting by copying the old check digit; the ISBN-13 check digit almost always differs from the ISBN-10 one.

Frequently asked questions

Do e-books and audiobooks need a separate ISBN?

Each format of a publication is normally given its own ISBN, so print, e-book and audio editions usually differ.

Is the ISBN-13 the same as the barcode number?

Yes, the EAN-13 barcode on the back cover encodes the ISBN-13 digits.

Why can ISBN-10 end in X?

The mod 11 check can give 10, which needs a single symbol, so the Roman numeral X is used.

Sources: ISO 2108, Information and documentation — International standard book number (ISBN) · International ISBN Agency, ISBN Users' Manual