Calculate numeric or X check characters.
Initialising algorithm engine for ISBN-10 Check Digit Calculator...
How ISBN-10 Check Digit Calculator Works?
The ISBN-10 Check Digit Calculator works by multiplying the 9 payload digits by weights 10 down to 2, dividing the sum by 11, and writing the remaining check value as 0–9 or X.
- 1Enter the first 9 digits of the International Standard Book Number (ISBN-10), ignoring hyphens.
- 2Multiply the 1st digit by 10, the 2nd by 9, and so on down to the 9th digit by 2.
- 3Add the 9 products to get S.
- 4Compute the check value as (11 − (S mod 11)) mod 11.
- 5Write a check value of 10 as the Roman numeral X.
ISBN-10 Check Digit Calculator Formula
The ISBN-10 formula is d₁₀ = (11 − (Σ (11 − i)·dᵢ mod 11)) mod 11, with 10 written as X.
S = 10·d₁ + 9·d₂ + 8·d₃ + 7·d₄ + 6·d₅ + 5·d₆ + 4·d₇ + 3·d₈ + 2·d₉ d₁₀ = (11 − (S mod 11)) mod 11, 10 → X Validation: (S + 1·d₁₀) mod 11 = 0
dᵢis the i-th ISBN digit from the left.Xrepresents the value 10.
0 × 10 = 0 3 × 9 = 27 0 × 8 = 0 6 × 7 = 42 4 × 6 = 24 0 × 5 = 0 6 × 4 = 24 1 × 3 = 3 5 × 2 = 10 S = 130 S mod 11 = 9 Check = (11 − 9) mod 11 = 2 → 2 ISBN-10 = 0-306-40615-2
ISBN-10 Check Digit Calculator Conversion Table
The ISBN-10 conversion table maps remainders of S mod 11 to check characters with sample payloads.
| S mod 11 | Check character | Sample payload | Computed check | ISBN-10 |
|---|---|---|---|---|
| 0 | 0 | 030640615 | 2 | 0306406152 |
| 1 | X | 080442957 | X | 080442957X |
| 2 | 9 | 043942089 | X | 043942089X |
| 3 | 8 | 007063546 | 3 | 0070635463 |
| 4 | 7 | 019853453 | 1 | 0198534531 |
| 5 | 6 | 014044913 | 2 | 0140449132 |
| 6 | 5 | 067972331 | 5 | 0679723315 |
| 7 | 4 | 185326041 | X | 185326041X |
| 8 | 3 | 155860832 | X | 155860832X |
| 9 | 2 | 093999602 | 2 | 0939996022 |
| 10 | 1 | 039480001 | X | 039480001X |
The first 2 columns are the remainder lookup. The sample columns show real-format payloads computed with the same rule.
What is ISBN-10 Check Digit Calculator?
An ISBN-10 Check Digit Calculator is a tool that computes the 10th character of a 10-digit International Standard Book Number. ISBN-10 was the book numbering standard until 1 January 2007, when ISBN-13 replaced it.
The modulus 11 check detects 100% of single-digit errors and 100% of adjacent transpositions. The check character X appears in about 1 of every 11 ISBN-10 numbers.
What are the uses of ISBN-10 Check Digit Calculator?
There are 4 main uses of the ISBN-10 Check Digit Calculator, including backlist cataloguing, library records, and used-book listings.
- Backlist cataloguing: Publishers verify ISBNs of titles printed before 2007.
- Library records: Librarians check MARC records that store ISBN-10 values.
- Used-book listings: Second-hand sellers confirm ISBNs printed on older books.
- Data migration: Developers clean ISBN-10 fields before converting to ISBN-13.