ISBN check digits explained, and why a wrong ISBN is refused

An ISBN is not just a number printed on the back of a book. Its last character is a check digit, calculated from all the others, so that a mistyped digit almost always shows up. That is why BooksPOS can tell you an ISBN is wrong the moment you type it, and why it refuses one rather than saving it. This guide shows the arithmetic, with a worked example, so you can check an ISBN by hand if you ever need to. You can also try it in the ISBN checker on the home page.

Two forms: ISBN-10 and ISBN-13

Older books carry a 10-character ISBN; newer ones a 13-digit ISBN. The 13-digit form is the 10-digit one with 978 in front and a new check digit at the end. ISBNs that start with 979 exist only in the 13-digit form.

The worked example used in most explanations of the standard is the same book in both forms:

• ISBN-10: 0-306-40615-2
• ISBN-13: 978-0-306-40615-7

Hyphens and spaces do not matter to the check; they only group the parts of the number for people. BooksPOS searches an ISBN with or without them.

The ISBN-10 check digit

Take the first nine digits and multiply them by 10, 9, 8, 7, 6, 5, 4, 3 and 2 in turn. For 0 3 0 6 4 0 6 1 5:

The products add up to 130. Divide by 11: the remainder is 9. The check digit is what brings the total to the next multiple of 11: 11 − 9 = 2. So the ISBN-10 is 0306406152.

When the answer is 10, the check "digit" is written as X, which is why some ISBN-10s end in an X. An X anywhere else in an ISBN is an error. When the remainder is 0, the check digit is 0.

The ISBN-13 check digit

Take the first twelve digits and multiply them alternately by 1 and 3. For 9 7 8 0 3 0 6 4 0 6 1 5:

• The digits in the odd positions (9, 8, 3, 6, 0, 1) add up to 27.
• The digits in the even positions (7, 0, 0, 4, 6, 5) add up to 22, times 3 is 66.

27 + 66 = 93. The check digit brings that to the next multiple of 10: 100 − 93 = 7. So the ISBN-13 is 9780306406157. When the total is already a multiple of 10, the check digit is 0.

This is the same calculation as an EAN-13 barcode, which is why an ISBN-13 prints as a normal retail barcode.

Converting between the two

• ISBN-10 to ISBN-13: put 978 in front of the first nine digits, drop the old check digit, and calculate a new one with the 1-3 rule.
• ISBN-13 to ISBN-10: only for ISBNs starting 978. Drop the 978 and the last digit, and calculate a new check digit with the 10-to-2 rule. A 979 ISBN has no ISBN-10.

You cannot convert by just adding or removing 978: the check digit almost always changes.

Why BooksPOS refuses a wrong ISBN

When an ISBN is typed, scanned or imported, BooksPOS verifies its check digit. If it does not match, the ISBN is refused and you are asked for it again. It never "corrects" it, for a simple reason: the check digit tells you that a digit is wrong, not which one. Changing the last digit to make the sum work would produce a valid-looking ISBN for a different book, or for no book at all.

The same goes for books without an ISBN. Many local and school books have none. BooksPOS does not make one up; the item gets an internal code instead, which can be printed as a Code 128 barcode label so it scans at the till. Items with a valid ISBN or EAN get an EAN-13 label. Labels are built and checked with barcode-reading software, but have not yet been printed on a real printer.

Where the check happens in BooksPOS

• Adding or editing an item in the Catalog: the ISBN field is verified before the item is saved.
• Importing your item list from CSV: each row's ISBN is verified, and a wrong one is listed as an error with its row number (how the import works).
• Searching at the till: an ISBN finds its item with or without hyphens.

Common questions

Why does my ISBN end in X?

It is an ISBN-10 whose check calculation came to 10. X stands for 10, and it can only be the last character.

Is a barcode on a book always its ISBN?

A barcode starting 978 or 979 is an ISBN-13. Other 13-digit barcodes are EAN-13 retail barcodes, common on stationery; they pass the same check but are not ISBNs. BooksPOS keeps them as barcodes on the item.

Can the check digit catch every mistake?

It catches every single mistyped digit, and the ISBN-10 check also catches two neighbouring digits swapped. The ISBN-13 check misses a few swaps. Neither can tell you that a valid ISBN belongs to a different book, so check the title as well.

Does every book need an ISBN in BooksPOS?

No. ISBN is optional. A book without one gets an internal code for scanning.

Will BooksPOS fix a wrong ISBN for me?

No. It refuses it and asks again, because a guessed correction could be the ISBN of a different book. Check the number on the book itself.

More about how BooksPOS keeps books and their editions straight: book inventory and ISBN.