ISBN Validator

What is an ISBN check digit?

An ISBN is a book's identifier, and its last character is not part of the number in any meaningful sense — it is a checksum, computed from the digits before it, whose only job is to catch mistakes when somebody types or scans the number. If the last character does not match what the others imply, the ISBN is wrong and the software can say so before ordering the wrong book.

There are two schemes. ISBN-10, used until 2007, weights its ten digits 10, 9, 8 down to 1 and requires the total to divide by eleven. ISBN-13, used since, weights its thirteen digits alternately 1 and 3 and requires the total to divide by ten.

That difference of moduli looks like a detail and is the whole story of this page. Eleven is prime and ten is not, and the consequences run in both directions: one gives ISBN-10 a check character that is sometimes the letter X, and the other leaves ISBN-13 with a blind spot that ISBN-10 did not have.

How to use it

1. Paste an ISBN in any format. Hyphens, spaces and a leading “ISBN:” are stripped before checking, so anything you copy from a book's back cover, a library catalogue or an invoice will work as-is.
2. Read the verdict and, if it fails, the reason. A rejection names its cause — wrong length, a stray letter, an X in a place X cannot go, a prefix that is a barcode but not a book — and when only the check digit is wrong it tells you which digit the rest of the number implies.
3. Take whichever form you need. Valid numbers are shown in both the ten- and thirteen-digit forms with copy buttons. Underneath, the tool says whether that particular number has the weakness described below.

Why some ISBNs end in X

A checksum modulo eleven has eleven possible values, and there are only ten digits to write them with. The eleventh is written X, the Roman ten, and it appears in exactly the cases where the arithmetic demands it. Over a million ten-digit prefixes, the check character comes out X 9.091% of the time — which is 1 in 11, to three decimal places, exactly as the modulus requires.

X is only ever the last character, and only ever in an ISBN-10. It is not a digit and it never appears anywhere else in the number, which is why this tool rejects it in any other position rather than trying to interpret it.

ISBN-13 has no X at all. Its checksum is modulo ten, so ten values need ten digits and there is nothing left over. We checked every check digit it produces across two hundred thousand prefixes: they cover 0 through 9 and never exceed 9. That was one of the goals of the 2007 change — an ISBN-13 is also a valid EAN-13 barcode, and a barcode cannot encode a letter.

The typo ISBN-13 cannot catch

The commonest typing mistake after a wrong digit is swapping two adjacent ones — writing 12 for 21. A good check digit catches that, and ISBN-10 does: we generated valid ISBN-10s, swapped every adjacent pair in each, and tested 161,557 of them. Not one slipped through. Every single transposition broke the checksum.

The same sweep over ISBN-13 tested 168,833 transpositions and 17,244 passed — 10.21% of them. Swapping those digits produces a different number that the check digit still accepts, so nothing downstream will notice.

The misses are not random, and this is the part worth knowing. They are exactly the five pairs of digits that differ by five: 0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9. No other pair is ever missed, and those five are missed every time.

The reason is a line of arithmetic. The weights alternate 1 and 3, so swapping two adjacent digits changes the weighted total by twice their difference. Two times five is ten, and ten is zero modulo ten — so a difference of exactly five vanishes from the checksum by construction. ISBN-10 has no equivalent blind spot because its weights differ by one and eleven is prime: a difference can only disappear when there was no difference to begin with.

So the standard that replaced ISBN-10 is, on this specific measure, worse than the one it replaced. That was a deliberate trade: compatibility with the world's barcode infrastructure was worth more than catching one class of typo. The tool tells you when the number in front of you happens to contain one of those adjacent pairs.

Honest limits

A valid check digit means the number is well-formed, not that the book exists. ISBNs are assigned by national agencies and there is no way to know from the digits alone whether one has ever been issued. This page does arithmetic; it does not have a catalogue, and any tool that claims to validate an ISBN without querying a database is doing the same thing.

Conversion runs one way more freely than the other. Every ISBN-10 becomes an ISBN-13 by prefixing 978 and recomputing the check digit. Going back only works for numbers that start 978 — a 979 prefix numbers a range created after the ten-digit standard was retired, so those books have no ISBN-10 and never did. The tool says so rather than producing something that looks like one.

Hyphens are stripped rather than checked. Their positions encode the registration group and publisher, and the split varies by agency and by the length of the publisher's allocation, so the same digits can be hyphenated several ways. Getting that right needs the agency's range tables, which change; validating the arithmetic does not.

The transposition figures come from sweeping generated numbers rather than a corpus of real books, because the property being measured is arithmetic and does not depend on which ISBNs were actually issued. The blind pairs are provable from the weights, and the page states that proof rather than resting on the sample.

Why is it free?

Because it is multiplication and a remainder. There is no dataset, nothing to download, and no server involved — everything runs in your browser and nothing you paste is uploaded or stored.

So there is no account, no sign-up and nothing held back. The engine and its 131-assertion test suite are in the repository beside the page. The transposition claim is settled by brute force rather than by citation: a sweep of every adjacent swap in tens of thousands of valid numbers, with the ISBN-10 result as the control that makes the ISBN-13 figure mean something.