📖 ISBN Check Digit Calculator
Calculate, validate & verify ISBN-10 and ISBN-13 check digits with step-by-step workings
| Position | Digit | Weight | Product | Notes |
|---|---|---|---|---|
| 1 | d₁ | 10 | 10 × d₁ | First digit |
| 2 | d₂ | 9 | 9 × d₂ | Second digit |
| 3 | d₃ | 8 | 8 × d₃ | Third digit |
| 4–9 | d₄–d₉ | 7–2 | w × d | Continuing weights |
| 10 | CHECK | 1 | — | CHECK = (11 – (sum mod 11)) mod 11 |
| Position | Digit | Weight | Product | Notes |
|---|---|---|---|---|
| 1, 3, 5, 7, 9, 11 | Odd | 1 | 1 × d | Odd positions × 1 |
| 2, 4, 6, 8, 10, 12 | Even | 3 | 3 × d | Even positions × 3 |
| 13 | CHECK | — | — | CHECK = (10 – (sum mod 10)) mod 10 |
| ISBN | Format | Check Digit | Valid? |
|---|---|---|---|
| 0-306-40615-2 | ISBN-10 | 2 | ✅ Valid |
| 978-0-306-40615-7 | ISBN-13 | 7 | ✅ Valid |
| 0-8044-2957-X | ISBN-10 | X (=10) | ✅ Valid |
| 978-3-16-148410-0 | ISBN-13 | 0 | ✅ Valid |
| 979-1-0669-8640-7 | ISBN-13 | 7 | ✅ Valid |
| 0-306-40615-3 | ISBN-10 | 3 (wrong) | ❌ Invalid |
| ISBN-10 | Strip Check | Add 978 Prefix | New ISBN-13 |
|---|---|---|---|
| 0306406152 | 030640615 | 978030640615 | 9780306406157 |
| 0804429570 | 080442957 | 978080442957 | Check: 978-0-8044-2957-X → 9780804429573 |
| 0316148415 | 031614841 | 978031614841 | 9780316148412 |
| 0195153448 | 019515344 | 978019515344 | 9780195153446 |
Every book has a unique name called ISBN. The ISBN Check Digit forms the end of that number as the last single sign. It helps to catch mistakes during entry or copying of the ISBN.
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Both the ISBN-10 and ISBN-13 use such an ISBN Check Digit to close the number.
How the ISBN check digit works
The ISBN Check Digit is calculated using a special method that builds on all the earlier signs. Its main task is to check that no one made a mistake for instance swapping two signs. When the ISBN Check Digit does not match the expected result of the formula, the ISBN fails.
That closing sign protects well against wrong keys and mistakes during sharing.
In ISBN-10 the ISBN Check Digit can be something between zero and nine. It is also possible to use the letter “X”, which means ten, similar to Roman style. So sometimes an ISBN ends with X. No other non-number element shows anywhere in the code.
To count, one multiplies every sign by its weight and later adds them. The first is multiplied by ten, the second by nine, and so down. Later the whole is divided by eleven.
Without rest the ISBN counts. One somtimes calls it a check sum.
ISBN-13 works quite differently. It commonly starts with “978”. The ISBN Check Digit stays the closing sign, even though it is calculated using another method from the first twelve signs.
When converting ISBN-10 too ISBN-13, one must recalculate the ISBN Check Digit. Because of that the two kinds have different closing signs.
Before the appearance of ISBNs there were standard book numbers with only nine signs. They lacked an ISBN Check Digit. Old SBN one can easily make into ISBN simply by adding zero at the start.
For instance “SBN 340 01381 8” changes to “ISBN 0-340-01381-8” without need to recalculate the ISBN Check Digit.
ISBNs consist only of editions and have either ten or thirteen signs. ISBN does not show whether a book is paperback or hard cover. It exactly identifies a certain publication and type, but no part of the number encodes such details.
Also nothing in it shows the date of the publication.
Sometimes wrong ISBNs appear on the covers of books. One case was a printing mistake, where “882523” came instead of “882513” and the ISBN Check Digit still matched. Online tools are available to quickly count and check ISBN Check Digits for both types, with automatic detection of the format.
The ISBN usually sits on the page of copyright or theback cover of the book.
