View source for ISBN (identifier)

{{Short description|Unique numeric book identifier since 1970}}
{{Distinguish|ISSN}}
{{For|the use of ISBNs on Wikipedia|Wikipedia:ISBN|selfref=y}}
{{pp-vandalism|small=yes}}
{{Use Oxford spelling|date=August 2022}}
{{Use dmy dates|date=July 2021}}
{{Infobox identifier
| name          = International Standard Book Number
| image         = EAN-13-ISBN-13.svg
| image_caption = A 13-digit ISBN, 978-3-16-148410-0, as represented by an [[International Article Number|EAN-13 bar code]]
| acronym       = ISBN
| start_date    = {{Start date and age|1970}}<ref name="history"/>
| organisation  = International ISBN Agency<!-- Yes, they are really called the International International Standard Book Number Agency -->
| digits        = 13 (formerly 10)
| check_digit   = Weighted sum
| example       = 978-3-16-148410-0
| website       = {{URL|https://isbn-international.org/}}
}}

The '''International Standard Book Number''' ('''ISBN''') is a numeric commercial [[book]] [[identifier]] that is intended to be unique.{{efn|Occasionally, publishers erroneously assign an ISBN to more than one title—the first edition of ''[[The Ultimate Alphabet]]'' and ''The Ultimate Alphabet Workbook'' have the same ISBN, 0-8050-0076-3. Conversely, the same book can be published with several ISBNs: A German second-language edition of {{lang|de|[[Emil and the Detectives|Emil und die Detektive]]}} has the ISBNs 87-23-90157-8 (Denmark), 0-8219-1069-8 (United States), 91-21-15628-X (Sweden), 0-85048-548-7 (United Kingdom) and 3-12-675495-3 (Germany).}}{{efn|In some cases, books sold only as a set share the same ISBN. For example, the [[Jack Vance#The Vance Integral Edition|Vance Integral Edition]] used only two ISBNs for 44 books.}} Publishers purchase or receive ISBNs from an affiliate of the International ISBN Agency.<ref>{{cite web|title=The International ISBN Agency|url=https://www.isbn-international.org/|access-date=20 February 2018|archive-date=24 February 2018|archive-url=https://web.archive.org/web/20180224032510/https://www.isbn-international.org/|url-status=live}}</ref>

A different ISBN is assigned to each separate edition and variation of a publication, but not to a simple reprinting of an existing item. For example, an [[e-book]], a [[paperback]] and a [[hardcover]] edition of the same [[book]] must each have a different ISBN, but an unchanged reprint of the hardcover edition keeps the same ISBN. The ISBN is ten digits long if assigned before 2007, and thirteen digits long if assigned on or after 1 January 2007.{{efn|name=conversion|Publishers were required to convert existing ISBNs from the 10-digit format to the 13-digit format (in their publication records) by 1&nbsp;January 2007. For ''existing'' publications, the new 13-digit ISBN would only need to be added if (and when) a publication was reprinted. During the transition period, publishers were recommended to print ''both'' the 10-digit and 13-digit ISBNs on the verso of a publication's title page, but they were required to print ''only'' the 13-digit ISBN after 1&nbsp;January 2007.<ref name="LAC FAQ" />}} The method of assigning an ISBN is nation-specific and varies between countries, often depending on how large the publishing industry is within a country.

The first version of the ISBN identification format was devised in 1967, based upon the 9-digit '''Standard Book Numbering''' ('''SBN''') created in 1966. The 10-digit ISBN format was developed by the [[International Organization for Standardization]] (ISO) and was published in 1970 as international standard ISO 2108 (any 9-digit SBN can be converted to a 10-digit ISBN by prefixing it with a zero).

Privately published books sometimes appear without an ISBN. The International ISBN Agency sometimes assigns ISBNs to such books on its own initiative.<ref>{{cite journal |last=Bradley |first=Philip |year=1992 |url=http://www.theindexer.org/files/18-1/18-1_025.pdf |title=Book numbering: The importance of the ISBN |format=PDF [245KB] |journal=The Indexer |volume=18 |issue=1 |pages=25–26 |doi=10.3828/indexer.1992.18.1.11 |s2cid=193442570 |access-date=4 September 2009 |archive-date=21 February 2021 |archive-url=https://web.archive.org/web/20210221021131/https://www.theindexer.org/files/18-1/18-1_025.pdf |url-status=dead }}</ref>

A separate identifier code of a similar kind, the [[International Standard Serial Number]] (ISSN), identifies periodical publications such as [[magazine]]s and [[newspaper]]s. The [[International Standard Music Number]] (ISMN) covers [[Sheet music|musical scores]].

=={{anchor|SBN}}History==
The Standard Book Number (SBN) is a commercial system using nine-digit [[code]] numbers to identify books. In 1965, British bookseller and stationers [[WHSmith]] announced plans to implement a standard numbering system for its books.<ref name="history">{{cite web |url= http://www.isbn.org/ISBN_history |title=ISBN History |publisher=isbn.org |date=20 April 2014 |access-date= 20 April 2014 |archive-url= https://web.archive.org/web/20140420232459/http://www.isbn.org/ISBN_history |archive-date=20 April 2014 |url-status=live }}</ref> They hired consultants to work on their behalf, and the system was devised by [[Gordon Foster]], emeritus professor of statistics at [[Trinity College Dublin]].<ref name="From Archive.org-4646971">{{cite web |url= http://www.informaticsdevelopmentinstitute.net/isbn.html |title= International Standard Book Numbering (ISBN) System original 1966 report |publisher=informaticsdevelopmentinstitute.net |date=1966 |access-date=20 April 2014 |archive-url=https://web.archive.org/web/20110430024722/http://www.informaticsdevelopmentinstitute.net/isbn.html |archive-date=30 April 2011 |url-status=dead |first= Gordon |last=Foster}}</ref> The [[International Organization for Standardization]] (ISO) Technical Committee on Documentation sought to adapt the British SBN for international use. The ISBN identification format was conceived in 1967 in the United Kingdom by [[David Whitaker (publisher)|David Whitaker]]<ref name="ktieb">{{cite book |title=Manwal ghall-Utenti tal-ISBN |url=http://ktieb.org.mt/wp-content/uploads/2016/02/Manwal-ghall-Utenti-tal-ISBN-Maltese.pdf |publisher=Kunsill Nazzjonali tal-Ktieb |edition=6th |language=mt |location=[[Malta]] |date=2016 |archive-url=https://web.archive.org/web/20160817083617/http://ktieb.org.mt/wp-content/uploads/2016/02/Manwal-ghall-Utenti-tal-ISBN |archive-date=17 August 2016 |page=5 |isbn=978-99957-889-4-0 |access-date=14 November 2016 |url-status=live }}</ref><ref>{{Cite web|url=https://www.internationalpublishers.org/standards-news/318-it-was-an-idea-whose-time-had-come-david-whitaker-on-the-birth-of-isbn|title='It was an idea whose time had come.' David Whitaker on the birth of ISBN|last=Charkin|first=Richard|author-link=Richard Charkin|date=17 July 2015|website=[[International Publishers Association]]|language=en-GB|access-date=6 August 2019|archive-url=https://web.archive.org/web/20190806111624/https://www.internationalpublishers.org/standards-news/318-it-was-an-idea-whose-time-had-come-david-whitaker-on-the-birth-of-isbn|archive-date=6 August 2019|url-status=live}}</ref> (regarded as the "Father of the ISBN")<ref name="niso.org">{{citation |url= http://www.niso.org/apps/group_public/download.php/6294/ISQ_vol8_no3_July1996.pdf |title=Emery Koltay, David Whitaker Named NISO Fellows |journal=Information Standards Quarterly |date=July 1996 |pages=12–13 |volume=8 |number=3 |publisher=National Information Standards Organization |url-status=dead |archive-url=https://web.archive.org/web/20140804153745/http://www.niso.org/apps/group_public/download.php/6294/ISQ_vol8_no3_July1996.pdf | archive-date= 4 August 2014 }}</ref> and in 1968 in the United States by Emery Koltay<ref name="ktieb" /> (who later became director of the U.S. ISBN agency [[R. R. Bowker]]).<ref name="niso.org" /><ref>{{cite web |author=US ISBN Agency |url=http://commerce.bowker.com/standards/home/isbn/about_information_standards.asp |title=Bowker.com – Products |publisher=Commerce.bowker.com |access-date=11 June 2015 |archive-date=19 December 2003 |archive-url=https://web.archive.org/web/20031219215516/http://commerce.bowker.com/standards/home/isbn/about_information_standards.asp |url-status=dead }}</ref><ref>{{cite web |first=Daniel |last=Gregory |url= http://www.printrs.com/isbn.htm |title=ISBN |publisher=PrintRS |access-date=11 June 2015 |url-status=dead |archive-url= http://arquivo.pt/wayback/20160516011735/http%3A//www.printrs.com/isbn.htm |archive-date=16 May 2016 }}</ref>

The 10-digit ISBN format was developed by the ISO and was published in 1970 as international standard ISO 2108.<ref name="history" /><ref name="ktieb" /> The United Kingdom continued to use the nine-digit SBN code until 1974. ISO has appointed the International ISBN Agency as the [[registration authority]] for ISBN worldwide and the ISBN Standard is developed under the control of ISO Technical Committee 46/Subcommittee 9 [[TC 46/SC 9]]. The ISO on-line facility only refers back to 1978.<ref>{{citation |format= PDF |url= https://www.iso.org/standard/6898.html |title= ISO 2108:1978 |publisher= ISO |access-date= 12 June 2020 |archive-date= 10 October 2022 |archive-url= https://web.archive.org/web/20221010155546/https://www.iso.org/standard/6898.html |url-status= live }}</ref>
[[File:Total Number of Registration ISBN 2020.png|thumb|Total number of ISBN registrations. 2020.]]
An SBN may be converted to an ISBN by prefixing the digit "0". For example, the second edition of ''[[The Guv'nor and Other Short Stories|Mr. J. G. Reeder Returns]]'', published by Hodder in 1965, has {{Nowrap|"SBN 340 01381 8"}}, where "340" indicates the [[Publishing|publisher]], "01381" is the serial number assigned by the publisher, and "8" is the [[check digit]]. By prefixing a zero, this can be converted to {{ISBN|0-340-01381-8}}; the check digit does not need to be re-calculated. Some publishers, such as [[Ballantine Books]], would sometimes use 12-digit SBNs where the last three digits indicated the price of the book;<ref>{{Cite web|url=https://archive.org/search.php?query=%22SBN+345%22&sin=TXT|title=Internet Archive Search: "SBN 345"|website=archive.org}}</ref> for example, ''Woodstock Handmade Houses'' had a 12-digit Standard Book Number of 345-24223-8-595 (valid SBN: 345-24223-8, {{text|ISBN}}: {{not a typo|0-345-24223-8}}),<ref>{{Cite book |last=Haney |first=Robert |url=https://archive.org/details/woodstockhandmad00robe |title=Woodstock handmade houses |date=1974 |publisher=Ballantine Books |others=David Ballantine, Jonathan Elliott |isbn=0-345-24223-8 |location=New York |oclc=2057258 |access-date=26 May 2021 |url-access=registration |archive-url=https://web.archive.org/web/20200625225043/http://www.worldcat.org/oclc/2057258 |archive-date=25 June 2020 |url-status=live}}</ref> and it cost {{USD|5.95}}.<ref>{{Cite book |last1=Haney |first1=Robert |url=https://archive.org/details/woodstockhandmad00robe/page/n3/mode/2up |title=Woodstock Handmade Houses |last2=Ballantine |first2=David |last3=Elliott |first3=Jonathan |via=web.archive.org |publisher=Ballantine |year=1974 |isbn=978-0-345-24223-5 |edition=1st |access-date=May 26, 2021 |url-access=registration}}</ref>

Since 1 January 2007, ISBNs have contained thirteen digits, a format that is compatible with "[[Bookland]]" [[European Article Number]]s, which have 13 digits.<ref name="LAC FAQ">{{cite web | url=http://www.lac-bac.gc.ca/iso/tc46sc9/isbn.htm | title=Frequently Asked Questions about the new ISBN standard |website=ISO TC 46/SC 9 | publisher=[[Library and Archives Canada]] |date=May 31, 2005 | url-status=dead | archive-url=https://web.archive.org/web/20070610160919/http://www.lac-bac.gc.ca/iso/tc46sc9/isbn.htm | archive-date=10 June 2007 | df=dmy-all}}</ref>

The [[United States]], with 3.9 million registered ISBNs in 2020, was by far the biggest user of the ISBN identifier in 2020, followed by the [[South Korea|Republic of Korea]] (329,582), [[Germany]] (284,000), [[China]] (263,066), the [[United Kingdom|UK]] (188,553) and [[Indonesia]] (144,793). Lifetime ISBNs registered in the United States are over 39 million as of 2020.<ref>{{Cite book |title=The Global Publishing Industry in 2020 |url=https://www.wipo.int/publications/en/details.jsp?id=4616&plang=EN |access-date=2023-11-13 |date=2022 |doi=10.34667/tind.46277 |publisher=[[WIPO]] |language=en |author1=International Publishers Association (IPa) |author2=World Intellectual Property Organization |archive-date=17 September 2024 |archive-url=https://web.archive.org/web/20240917125219/https://www.wipo.int/publications/en/details.jsp?id=4616&plang=EN |url-status=live }}</ref>

== Overview ==
A separate ISBN is assigned to each edition and variation (except reprintings) of a publication. For example, an ebook, [[audiobook]], paperback, and hardcover edition of the same book must each have a different ISBN assigned to it.<ref name="7th edition Users' Manual" />{{rp|12}} The ISBN is thirteen digits long if assigned on or after 1 January 2007, and ten digits long if assigned before 2007.{{efn|name=conversion}}<ref name="LAC FAQ" /> An International Standard Book Number consists of four parts (if it is a 10-digit ISBN) or five parts (for a 13-digit ISBN).

Section 5 of the International ISBN Agency's official user manual<ref name="7th edition Users' Manual" />{{rp|11}} describes the structure of the 13-digit ISBN, as follows:
[[File:ISBN Details.svg|thumb|The parts of a 10-digit ISBN and the corresponding EAN‑13 and barcode. Note the different check digits in each. The part of the EAN‑13 labeled "EAN" is the [[Bookland]] country code.]]

# for a 13-digit ISBN, a prefix element – a ''[[GS1]] prefix'': so far 978 or 979 have been made available by GS1,
# the ''registration group element'' (language-sharing country group, individual country or territory),{{efn|Some books have several codes in the first block: e.g. A. M. Yaglom's ''Correlation Theory...'', published by [[Springer Verlag]], has two ISBNs, {{ISBNT|0-387-96331-6|3-540-96331-6|leadout=and}}. Though Springer's 387 and 540 codes are different for English (0) and German (3); the same item number 96331 produces the same check digit for both (6). Springer uses 431 as the publisher code for Japanese (4), and 4-431-96331-? also has a check digit of 6. Other Springer books in English have publisher code 817, and 0-817-96331-? would also have a check digit of 6. This suggests that special considerations were made for assigning Springer's publisher codes, as random assignments of different publisher codes would not be expected to lead by coincidence to the same check digit every time for the same item number. Finding publisher codes for English and German, say, with this effect would amount to solving a linear equation in modular arithmetic.{{Original research inline|This note may contain original research|date=May 2019}}}}
# the ''registrant'' element,
# the ''publication element'', and
# a ''[[checksum]] character'' or [[check digit]].

A 13-digit ISBN can be separated into its parts (''prefix element'', ''registration group'', ''registrant'', ''publication'' and ''check digit''), and when this is done it is customary to separate the parts with [[hyphen]]s or spaces. Separating the parts (''registration group'', ''registrant'', ''publication'' and ''check digit'') of a 10-digit ISBN is also done with either hyphens or spaces. Figuring out how to correctly separate a given ISBN is complicated, because most of the parts do not use a fixed number of digits.{{efn|The International ISBN Agency's ''ISBN User's Manual'' says: "The ten-digit number is divided into four parts of variable length, which must be separated clearly, by hyphens or spaces", although omission of separators is permitted for internal data processing. If present, hyphens must be correctly placed.<ref name="range_file_generation">{{cite web|url=https://www.isbn-international.org/range_file_generation|title=ISBN Ranges|date=2014|publisher=International ISBN Agency|access-date=29 April 2014|archive-date=29 April 2014|archive-url=https://web.archive.org/web/20140429101326/https://www.isbn-international.org/range_file_generation|url-status=live}}</ref> The actual definition for hyphenation contains more than 220 different registration group elements with each one broken down into a few to several ranges for the length of the registrant element (more than 1,000 total). The document defining the ranges, listed by agency, is 29 pages.}}

=== Issuing process <span class="anchor" id="How ISBNs are issued"></span>===
ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for that country or territory regardless of the publication language. The ranges of ISBNs assigned to any particular country are based on the publishing profile of the country concerned, and so the ranges will vary depending on the number of books and the number, type, and size of publishers that are active. Some ISBN registration agencies are based in national libraries or within ministries of culture and thus may receive direct funding from the government to support their services. In other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded.<ref>{{Cite web|title = ISBN Canada|url = http://www.bac-lac.gc.ca/eng/services/isbn-canada/Pages/isbn-canada.aspx |date = 17 April 2013|access-date = 19 January 2016|publisher = [[Library and Archives Canada|LAC]]|archive-date = 21 April 2020|archive-url = https://web.archive.org/web/20200421235618/https://www.bac-lac.gc.ca/eng/services/isbn-canada/Pages/isbn-canada.aspx|url-status = dead }}</ref>

A full directory of ISBN agencies is available on the International ISBN Agency website.<ref>{{cite web|url=https://www.isbn-international.org/agencies|title=Find an agency |website=International ISBN Agency |access-date=6 April 2018|archive-date=20 April 2020|archive-url=https://web.archive.org/web/20200420020626/https://www.isbn-international.org/agencies|url-status=live}}</ref> A list for a few countries is given below:
* Australia – Thorpe-Bowker<ref>{{cite news|url=https://www.myidentifiers.com.au/isbn/US_isbn_agency|title=About the Australian ISBN Agency |publisher=[[R. R. Bowker|THORPE-Bowker]] &#124; Identifier Services |access-date=23 January 2016|archive-date=16 April 2020|archive-url=https://web.archive.org/web/20200416201605/https://www.myidentifiers.com.au/isbn/US_isbn_agency|url-status=live}}</ref><ref>{{cite web| title =  ISBN| publisher = Thorpe-Bowker Identifier Services | url = https://www.myidentifiers.com.au/isbn/main| access-date = 29 March 2012| archive-date = 2 April 2019| archive-url = https://web.archive.org/web/20190402074747/https://www.myidentifiers.com.au/isbn/main| url-status = live}}</ref>
* Brazil – The [[National Library of Brazil]];<ref name="ISBN BR OLD">{{cite web|title=Tabela de preços dos serviços|trans-title=Table of service prices|url=http://www.isbn.bn.br/website/tabela-de-precos|url-status=dead|access-date=8 September 2015|publisher=[[National Library of Brazil|Biblioteca Nacional do Brasil]]|language=pt|archive-date=18 October 2019|archive-url=https://web.archive.org/web/20191018035854/http://www.isbn.bn.br/website/tabela-de-precos}}</ref> (Up to 28 February 2020)<ref name="isbn-international.org">{{cite web|title=Changes in arrangements for ISBN in Brazil|url=https://www.isbn-international.org/content/changes-arrangements-isbn-brazil/333|url-status=live|access-date=20 January 2020|archive-date=28 October 2021|archive-url=https://web.archive.org/web/20211028220210/https://www.isbn-international.org/content/changes-arrangements-isbn-brazil/333}}</ref>
* Brazil – Câmara Brasileira do Livro<ref name="ISBN BR">{{cite web|url=http://www.isbn.org.br/|title=ISBN Brasil|language=pt|access-date=20 January 2020|archive-date=8 May 2020|archive-url=https://web.archive.org/web/20200508084634/https://servicos.cbl.org.br/isbn/|url-status=live}}</ref> (From 1 March 2020)<ref name="isbn-international.org"/>
* Canada – English [[Library and Archives Canada]], a government agency; French {{Lang|fr|[[Bibliothèque et Archives nationales du Québec]]|italic=no}};
* Colombia – Cámara Colombiana del Libro, an NGO
* Hong Kong – Books Registration Office (BRO), under the [[Hong Kong Public Libraries]]<ref>{{cite web|title=Introduction to Books Registration|url=https://www.hkpl.gov.hk/en/about-us/services/book-registration/introduction.html|publisher=[[Hong Kong Public Libraries|HKPL]]|access-date=12 January 2017|archive-date=20 April 2020|archive-url=https://web.archive.org/web/20200420065651/https://www.hkpl.gov.hk/en/about-us/services/book-registration/introduction.html|url-status=live}}</ref>
* Iceland – Landsbókasafn ([[National and University Library of Iceland]])
* India – The [[Raja Rammohun Roy National Agency for ISBN]] (Book Promotion and Copyright Division), under Department of Higher Education, a constituent of the [[Ministry of Human Resource Development]]<ref>{{Cite web|url=http://pib.nic.in/newsite/PrintRelease.aspx?relid=138686|title=Union HRD Minister Smt. Smriti Zubin Irani Launches ISBN Portal|date=7 April 2016|publisher=[[Ministry of Human Resource Development|MHRD]]|access-date=16 June 2016|archive-date=26 June 2019|archive-url=https://web.archive.org/web/20190626201908/http://pib.nic.in/newsite/PrintRelease.aspx?relid=138686|url-status=live}}</ref>
* Israel – The Israel Center for Libraries<ref>{{cite web|url=https://www.icl.org.il/isbn-eng|title=What is an ISBN ?|date=7 April 2015|website=ICL – מרכז הספר והספריות|access-date=13 January 2019|archive-date=13 January 2019|archive-url=https://web.archive.org/web/20190113232205/https://www.icl.org.il/isbn-eng|url-status=live}}</ref>
* Italy – ''EDISER srl'', owned by ''Associazione Italiana Editori'' (Italian Publishers Association)<ref>{{cite web | url = http://www.isbn.it/LAGENZIA.aspx | title = ISBN – Chi siamo e contatti | publisher = EDISER srl | access-date = 3 January 2015 | language = it | trans-title = ISBN – Who we are and contacts | archive-date = 24 May 2017 | archive-url = https://web.archive.org/web/20170524222541/http://www.isbn.it/LAGENZIA.aspx | url-status = dead }}</ref><ref name="ediser-tariffs">{{cite web|title=ISBN – Tariffe Servizi ISBN|trans-title=ISBN Service Tariffs|url=https://www.isbn.it/TARIFFE.aspx|url-status=live|access-date=3 January 2015|publisher=EDISER srl|language=it|archive-date=3 January 2015|archive-url=https://web.archive.org/web/20150103161540/http://www.isbn.it/TARIFFE.aspx}}</ref>
* Kenya – [[National Library Service of Kenya|National Library of Kenya]]
* Latvia - [[Latvian ISBN Agency]]
* Lebanon – [[Lebanese ISBN Agency]]
* Maldives – The [[National Bureau of Classification (NBC)]]
* Malta – The [[National Book Council]] ({{lang-mt|Il-Kunsill Nazzjonali tal-Ktieb|link=no}})<ref>{{cite web|title=ISBN|url=http://ktieb.org.mt/?page_id=22|date=2016|publisher=Kunsill Nazzjonali tal-Ktieb|archive-url=https://web.archive.org/web/20161023123140/http://ktieb.org.mt/?page_id=22|archive-date=23 October 2016}}</ref><ref>{{cite book|title=Manwal ghall-Utenti tal-ISBN|url=http://ktieb.org.mt/wp-content/uploads/2016/02/Manwal-ghall-Utenti-tal-ISBN-Maltese.pdf|publisher=Kunsill Nazzjonali tal-Ktieb|language=mt|location=[[Malta]]|edition=6th|date=2016|archive-url=https://web.archive.org/web/20160817083617/http://ktieb.org.mt/wp-content/uploads/2016/02/Manwal-ghall-Utenti-tal-ISBN|archive-date=17 August 2016|pages=1–40|isbn=978-99957-889-4-0|access-date=14 November 2016|url-status=live}}</ref><ref>{{cite web|title=Gazzetta tal-Gvern ta' Malta|url=https://govcms.gov.mt/en/Government/Government%20Gazette/Documents/2015/01/Government%20Gazette%20-%2023%20January.pdf|publisher=Government Gazette|date=23 January 2015|page=582|archive-url=https://web.archive.org/web/20161123220053/https://govcms.gov.mt/en/Government/Government%20Gazette/Documents/2015/01/Government%20Gazette%20-%2023%20January.pdf|archive-date=23 November 2016}}</ref>
* Morocco – The National Library of Morocco
* New Zealand – The [[National Library of New Zealand]]<ref name=NLNZ>{{cite web|title=ISBNs, ISSNs, and ISMNs|url=http://natlib.govt.nz/publishers-and-authors/isbns-issns-and-ismns|publisher=[[National Library of New Zealand]]|access-date=19 January 2016|archive-date=23 April 2020|archive-url=https://web.archive.org/web/20200423113348/https://natlib.govt.nz/publishers-and-authors/isbns-issns-and-ismns|url-status=live}}</ref>
* Nigeria – [[National Library of Nigeria]]
* Pakistan – [[National Library of Pakistan]]
* Philippines – [[National Library of the Philippines]]<ref>{{cite web|url=http://web.nlp.gov.ph/nlp/?q=node%2F645|title=International Standard Book Number|publisher=[[National Library of the Philippines|NLP]]|access-date=25 December 2017|archive-date=19 April 2020|archive-url=https://web.archive.org/web/20200419212749/http://web.nlp.gov.ph/nlp/?q=node%2F645|url-status=live}}</ref>
* South Africa – [[National Library of South Africa]]
* Spain – [https://www.agenciaisbn.es/ Spanish ISBN Agency – Agencia del ISBN]
* Turkey – General Directorate of Libraries and Publications, a branch of the [[Ministry of Culture and Tourism (Turkey)|Ministry of Culture]]<ref>{{cite web|url=http://ekygm.gov.tr/isbn.html|title=ISBN – Kültür ve Turizm Bakanlığı Kütüphaneler ve Yayımlar Genel Müdürlüğü OS|website=ekygm.gov.tr|access-date=29 March 2018|archive-date=19 April 2020|archive-url=https://web.archive.org/web/20200419234147/http://ekygm.gov.tr/isbn.html|url-status=dead}}</ref>
* United Kingdom and Republic of Ireland – ''Nielsen Book Services Ltd'', part of [[NielsenIQ|NIQ]]<ref>{{cite web | url = https://www.nielsenisbnstore.com/ | title = Nielsen UK ISBN Agency | publisher = Nielsen UK ISBN Agency | access-date = 2 January 2015 | archive-date = 29 October 2019 | archive-url = https://web.archive.org/web/20191029082349/http://www.nielsenisbnstore.com/ | url-status = live }}</ref>
* United States – [[R. R. Bowker]]<ref name="ktieb"/><ref>{{cite web| title = Bowker – ISBN| date = 8 March 2013| publisher = R. R. Bowker| url = http://www.bowker.com/en-US/products/servident_isbn.shtml| access-date = 8 March 2013| archive-date = 31 March 2015| archive-url = https://web.archive.org/web/20150331032631/http://www.bowker.com/en-US/products/servident_isbn.shtml| url-status = live}}</ref>

=== Registration group element ===
{{anchor|Registration Group identifier}}
{{anchor|ISBN format}}
The ISBN [[list of ISBN identifier groups|registration group element]] is a 1-to-5-digit number that is valid within a single prefix element (i.e. one of 978 or 979),<ref name="7th edition Users' Manual" />{{rp|11}} and can be separated between hyphens, such as {{nobr|"978-1-..."}}. Registration groups have primarily been allocated within the 978 prefix element.<ref name="ISBN Ranges">{{cite web |url= https://www.isbn-international.org/range_file_generation |title= ISBN Ranges |website=isbn-international.org |at=Select the format you desire and click on the Generate button |date= 29 April 2014 |access-date= 29 April 2014 |archive-url= https://web.archive.org/web/20140429101326/https://www.isbn-international.org/range_file_generation |archive-date= 29 April 2014 |url-status=live  }}</ref> The single-digit registration groups within the 978-prefix element are: 0 or 1 for English-speaking countries; 2 for French-speaking countries; 3 for German-speaking countries; 4 for Japan; 5 for Russian-speaking countries; and 7 for People's Republic of China. Example 5-digit registration groups are 99936 and 99980, for Bhutan. The allocated registration groups are: 0–5, 600–631, 65, 7, 80–94, 950–989, 9910–9989, and 99901–99993.<ref>See [https://www.isbn-international.org/range_file_generation a complete list of group identifiers] {{Webarchive|url=https://web.archive.org/web/20140429101326/https://www.isbn-international.org/range_file_generation |date=29 April 2014 }}. ISBN.org sometimes calls them ''group numbers''. Their table of identifiers now refers to ''ISBN prefix ranges'', which must be assumed to be group identifier ranges.</ref> Books published in rare languages typically have longer group elements.<ref>{{cite book |last=Hailman |first=Jack Parker |date=2008 |title=Coding and redundancy: man-made and animal-evolved signals |publisher=Harvard University Press |page=209 |isbn=978-0-674-02795-4}}</ref>

Within the 979 prefix element, the registration group 0 is reserved for compatibility with [[International Standard Music Number]]s (ISMNs), but such material is not actually assigned an ISBN.<ref name="6th edition Users' Manual">{{cite book |url=https://www.isbn-international.org/sites/default/files/ISBN%20Manual%202012%20-corr.pdf |title=ISBN Users' Manual, International Edition |edition=6th |date=2012 |page=23 |publisher=International ISBN Agency |location=London |isbn=978-92-95055-02-5 |access-date=29 April 2014 |archive-date=29 April 2014 |archive-url=https://web.archive.org/web/20140429101742/https://www.isbn-international.org/sites/default/files/ISBN%20Manual%202012%20-corr.pdf |url-status=live }}</ref> The registration groups within prefix element 979 that have been assigned are 8 for the United States of America, 10 for France, 11 for the Republic of Korea, and 12 for Italy.<ref name="C4WDefault-5691881">{{cite web |url=https://www.isbn-international.org/export_rangemessagebyprefix.pdf |title=International ISBN Agency – Range Message (pdf sorted by prefix) |page=29 |website=isbn-international.org |date=5 December 2014 |access-date=15 December 2014 |author=International ISBN Agency |archive-date=29 December 2014 |archive-url=https://web.archive.org/web/20141229084400/https://www.isbn-international.org/export_rangemessagebyprefix.pdf |url-status=live }}</ref>

The original 9-digit standard book number (SBN) had no registration group identifier, but prefixing a zero to a 9-digit SBN creates a valid 10-digit ISBN.

=== Registrant element ===
The national ISBN agency assigns the registrant element ([[cf.]] [[:Category:ISBN agencies]]) and an accompanying series of ISBNs within that registrant element to the publisher; the publisher then allocates one of the ISBNs to each of its books. In most countries, a book publisher is not legally required to assign an ISBN, although most large bookstores only handle publications that have ISBNs assigned to them.<ref>{{cite web |title=Independent Publishers |url=https://www.waterstones.com/help/independent-publishers/48 |website=Waterstones |access-date=2 February 2020 |quote=Before submitting any titles to our central buying team for consideration, your book must have the following: An ISBN... |archive-date=9 January 2020 |archive-url=https://web.archive.org/web/20200109085858/https://www.waterstones.com/help/independent-publishers/48 |url-status=live }}</ref><ref>{{cite web |title=How to obtain an ISBN |url=https://help.barnesandnoble.com/app/answers/detail/a_id/1262/~/how-to-obtain-an-isbn |website=Barnes & Noble |access-date=2 February 2020 |quote=We use ISBNs to track inventory and sales information.  All books Barnes & Noble transacts on must have an ISBN. |archive-date=2 February 2020 |archive-url=https://web.archive.org/web/20200202204227/https://help.barnesandnoble.com/app/answers/detail/a_id/1262/~/how-to-obtain-an-isbn |url-status=live }}</ref><ref>{{cite web |title=Product ID (GTIN) requirements for Books |url=https://sellercentral.amazon.com/gp/help/external/200786200 |website=Amazon.com |access-date=2 February 2020 |quote=Effective June 1, 2017, you must provide an ISBN, EAN, or JAN to list a book in the Amazon catalog, regardless of the book's publication date. |archive-date=2 February 2020 |archive-url=https://web.archive.org/web/20200202211553/https://sellercentral.amazon.com/gp/help/external/200786200 |url-status=live }}</ref>

The International ISBN Agency maintains the details of over one million ISBN prefixes and publishers in the [https://grp.isbn-international.org Global Register of Publishers].<ref>{{cite web |url=https://www.isbn-international.org/content/global-register-publishers |title=Global Register of Publishers |author=<!--Not stated--> |publisher=International ISBN Agency |access-date=15 November 2022 |archive-date=15 November 2022 |archive-url=https://web.archive.org/web/20221115070135/https://www.isbn-international.org/content/global-register-publishers |url-status=dead }}</ref> This database is freely searchable over the internet.

Publishers receive blocks of ISBNs, with larger blocks allotted to publishers expecting to need them; a small publisher may receive ISBNs of one or more digits for the registration group identifier, several digits for the registrant, and a single digit for the publication element. Once that block of ISBNs is used, the publisher may receive another block of ISBNs, with a different registrant element. Consequently, a publisher may have different allotted registrant elements. There also may be more than one registration group identifier used in a country. This might occur once all the registrant elements from a particular registration group have been allocated to publishers.

By using variable block lengths, registration agencies are able to customise the allocations of ISBNs that they make to publishers. For example, a large publisher may be given a block of ISBNs where fewer digits are allocated for the registrant element and many digits are allocated for the publication element; likewise, countries publishing many titles have few allocated digits for the registration group identifier and many for the registrant and publication elements.<ref>{{Cite book|last=Splane|first=Lily|url=https://www.worldcat.org/oclc/54527545|title=The book book : a complete guide to creating a book on your computer|date=2002|publisher=Anaphase II|isbn=0-945962-14-2|edition=2nd|location=San Diego, Calif.|oclc=54527545}}</ref> Here are some sample <nowiki>ISBN-10</nowiki> codes, illustrating block length variations.
{| class="wikitable" style="width:100%; max-width:40em;"
|-
! ISBN || Country or area || Publisher
|-
| <code>99921-58-10-7</code><!--ISBN 978-99921-58-10-4--> || Qatar || NCCAH, Doha
|-
| <code>9971-5-0210-0</code><!--ISBN 978-9971-5-0210-2--> || Singapore || World Scientific
|-
| <code>960-425-059-0</code><!--ISBN 978-960-425-059-2--> || Greece || Sigma Publications
|-
| <code>80-902734-1-6</code><!--ISBN 978-80-902734-1-2--> || Czech Republic; Slovakia || Taita Publishers
|-
| <code>85-359-0277-5</code><!--ISBN 978-80-902734-1-2--> || Brazil || Companhia das Letras
|-
| <code>1-84356-028-3</code><!--ISBN 978-0-14-015098-8--> || English-speaking area || Simon Wallenberg Press
|-
| <code>0-684-84328-5</code><!--ISBN 978-0-684-84328-5--> || English-speaking area || Scribner
|-
| <code>0-8044-2957-X</code><!--ISBN 978-0-8044-2957-3--> || English-speaking area || Frederick Ungar
|-
| <code>0-85131-041-9</code><!--ISBN 978-0-85131-041-1--> || English-speaking area || J. A. Allen & Co.
|-
| <code>93-86954-21-4</code><!--ISBN 978-93-86954-21-3--> || English-speaking area || Edupedia Publications Pvt Ltd.
|-
| <code>0-943396-04-2</code><!--ISBN 978-0-943396-04-0--> || English-speaking area || Willmann–Bell
|-
| <code>0-9752298-0-X</code><!--ISBN 978-0-9752298-0-4--> || English-speaking area || KT Publishing
|}

==== English-language pattern <span class="anchor" id="Pattern for English language ISBNs"></span> ====
English-language registration group elements are 0 and 1 (2 of more than 220 registration group elements). These two registration group elements are divided into registrant elements in a systematic pattern, which allows their length to be determined, as follows:<ref name="range_file_generation"/>

{| class="wikitable" style="text-align:right;"
|-
! rowspan="2" | Publication<br />element length
! colspan="3" | 0 – Registration group element
! colspan="3" | 1 – Registration group element
! rowspan="2" | Total<br />Registrants
|-
! From !! To !! Registrants !! From !! To !! Registrants
|-
! 6 digits
| style="font-family:monospace;" | 0-00-xxxxxx-x
| style="font-family:monospace;" | 0-19-xxxxxx-x
| 20
| style="font-family:monospace;" | 1-01-xxxxxx-x<br />1-05-xxxxxx-x
| style="font-family:monospace;" | 1-02-xxxxxx-x<br />1-05-xxxxxx-x
|  3
| 23
|-
! 5 digits
| style="font-family:monospace;" | 0-200-xxxxx-x<br />0-229-xxxxx-x<br />0-370-xxxxx-x<br />0-640-xxxxx-x<br />0-646-xxxxx-x<br />0-649-xxxxx-x<br />0-656-xxxxx-x
| style="font-family:monospace;" | 0-227-xxxxx-x<br />0-368-xxxxx-x<br />0-638-xxxxx-x<br />0-644-xxxxx-x<br />0-647-xxxxx-x<br />0-654-xxxxx-x<br />0-699-xxxxx-x
| 494
| style="font-family:monospace;" | 1-000-xxxxx-x<br />1-030-xxxxx-x<br />1-040-xxxxx-x<br />1-100-xxxxx-x<br />1-714-xxxxx-x
| style="font-family:monospace;" | 1-009-xxxxx-x<br />1-034-xxxxx-x<br />1-049-xxxxx-x<br />1-397-xxxxx-x<br />1-716-xxxxx-x
| 326
| 820
|-
! 4 digits
| style="font-family:monospace;" | 0-2280-xxxx-x<br />0-3690-xxxx-x<br />0-6390-xxxx-x<br />0-6550-xxxx-x<br />0-7000-xxxx-x
| style="font-family:monospace;" | 0-2289-xxxx-x<br />0-3699-xxxx-x<br />0-6397-xxxx-x<br />0-6559-xxxx-x<br />0-8499-xxxx-x
| 1,538
| style="font-family:monospace;" | 1-0350-xxxx-x<br />1-0700-xxxx-x<br />1-3980-xxxx-x<br />1-6500-xxxx-x<br />1-6860-xxxx-x<br />1-7170-xxxx-x<br />1-7620-xxxx-x<br />1-7900-xxxx-x<br />1-8672-xxxx-x<br />1-9730-xxxx-x
| style="font-family:monospace;" | 1-0399-xxxx-x<br />1-0999-xxxx-x<br />1-5499-xxxx-x<br />1-6799-xxxx-x<br />1-7139-xxxx-x<br />1-7319-xxxx-x<br />1-7634-xxxx-x<br />1-7999-xxxx-x<br />1-8675-xxxx-x<br />1-9877-xxxx-x
| 2,867
| 4,405
|-
! 3 digits
| style="font-family:monospace;" | 0-85000-xxx-x
| style="font-family:monospace;" | 0-89999-xxx-x
|  5,000
| style="font-family:monospace;" | 1-55000-xxx-x<br />1-68000-xxx-x<br />1-74000-xxx-x<br />1-76500-xxx-x<br />1-77540-xxx-x<br />1-77650-xxx-x<br />1-77830-xxx-x<br />1-80000-xxx-x<br />1-83850-xxx-x<br />1-86760-xxx-x
| style="font-family:monospace;" | 1-64999-xxx-x<br />1-68599-xxx-x<br />1-76199-xxx-x<br />1-77499-xxx-x<br />1-77639-xxx-x<br />1-77699-xxx-x<br />1-78999-xxx-x<br />1-83799-xxx-x<br />1-86719-xxx-x<br />1-86979-xxx-x
| 22,010
| 27,010
|-
! 2 digits
| style="font-family:monospace;" | 0-900000-xx-x<br />0-900372-xx-x
| style="font-family:monospace;" | 0-900370-xx-x<br />0-949999-xx-x
|  49,999
| style="font-family:monospace;" | 1-869800-xx-x<br />1-916506-xx-x<br />1-916908-xx-x<br />1-919655-xx-x<br />1-987800-xx-x<br />1-991200-xx-x
| style="font-family:monospace;" | 1-915999-xx-x<br />1-916869-xx-x<br />1-919599-xx-x<br />1-972999-xx-x<br />1-991149-xx-x<br />1-998989-xx-x
| 113,741
| 163,740
|-
! 1 digit
| style="font-family:monospace;" | 0-6398000-x-x<br />0-6450000-x-x<br />0-6480000-x-x<br />0-9003710-x-x<br />0-9500000-x-x
| style="font-family:monospace;" | 0-6399999-x-x<br />0-6459999-x-x<br />0-6489999-x-x<br />0-9003719-x-x<br />0-9999999-x-x
| 522,010
| style="font-family:monospace;" | 1-0670000-x-x<br />1-7320000-x-x<br />1-7635000-x-x<br />1-7750000-x-x<br />1-7764000-x-x<br />1-7770000-x-x<br />1-8380000-x-x<br />1-9160000-x-x<br />1-9168700-x-x<br />1-9196000-x-x<br />1-9911500-x-x<br />1-9989900-x-x
| style="font-family:monospace;" | 1-0699999-x-x<br />1-7399999-x-x<br />1-7649999-x-x<br />1-7753999-x-x<br />1-7764999-x-x<br />1-7782999-x-x<br />1-8384999-x-x<br />1-9165059-x-x<br />1-9169079-x-x<br />1-9196549-x-x<br />1-9911999-x-x<br />1-9999999-x-x
| 164,590
| 686,600
|-
! colspan="3" style="text-align:right;" | Total
| 579,061
! colspan="2" style="text-align:right;" | Total
| 303,537
| 882,598
|}

== Check digits ==
A [[check digit]] is a form of redundancy check used for [[error detection]], the decimal equivalent of a binary [[check bit]]. It consists of a single digit computed from the other digits in the number. The method for the 10-digit ISBN is an extension of that for SBNs, so the two systems are compatible; an SBN prefixed with a zero (the 10-digit ISBN) will give the same check digit as the SBN without the zero. The check digit is base eleven, and can be an integer between 0 and 9, or an 'X'. The system for 13-digit ISBNs is not compatible with SBNs and will, in general, give a different check digit from the corresponding 10-digit ISBN, so does not provide the same protection against transposition. This is because the 13-digit code was required to be compatible with the [[European Article Number|EAN]] format, and hence could not contain the letter 'X'.

=== <nowiki>ISBN-10</nowiki> check digits ===
According to the 2001 edition of the International ISBN Agency's official user manual,<ref>{{cite web|url=http://www.isbn.org/standards/home/isbn/international/html/usm4.htm |title=ISBN Users' Manual (2001 edition) – 4. Structure of ISBN |publisher=International ISBN Agency |url-status=dead |archive-url=https://web.archive.org/web/20130522043458/http://www.isbn.org/standards/home/isbn/international/html/usm4.htm |archive-date=22 May 2013 }}</ref> the <nowiki>ISBN-10</nowiki> check digit (which is the last digit of the 10-digit ISBN) must range from 0 to 10 (the symbol 'X' is used for 10), and must be such that the sum of the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11. That is, if {{var|x}}{{sub|{{var|i}}}} is the {{var|i}}th digit, then {{var|x}}{{sub|10}} must be chosen such that:
{{block indent|<math>\sum_{i = 1}^{10} (11-i)x_i \equiv 0 \pmod{11}.</math>}}
For example, for an <nowiki>ISBN-10</nowiki> of 0-306-40615-2:
{{block indent|<math>
\begin{align}
 s &= (0\times 10) + (3\times 9) + (0\times 8) + (6\times 7) + (4\times 6) + (0\times 5) + (6\times 4) + (1\times 3) + (5\times 2) + (2\times 1) \\
   &=    0 + 27 +   0 +  42 +  24 +   0 + 24  +   3 + 10 + 2\\
   &= 132 = 12\times 11.
\end{align}
</math>}}

Formally, using [[modular arithmetic]], this is rendered
{{block indent|<math>(10x_1+9x_2+8x_3+7x_4+6x_5+5x_6+4x_7+3x_8+2x_9+x_{10})\equiv 0 \pmod{11}.</math>}}

It is also true for <nowiki>ISBN-10</nowiki>s that the sum of all ten digits, each multiplied by its weight in ''ascending'' order from 1 to 10, is a multiple of 11. For this example:
{{block indent|<math>
\begin{align}
 s &= (0\times 1) + (3\times 2) + (0\times 3) + (6\times 4) + (4\times 5) + (0\times 6) + (6\times 7) + (1\times 8) + (5\times 9) + (2\times 10) \\
   &=    0 + 6 +   0 +  24 +  20 +   0 + 42  +   8 + 45 + 20\\
   &= 165 = 15\times 11.
\end{align}
</math>}}

Formally, this is rendered
{{block indent|<math>(x_1 + 2x_2 + 3x_3 + 4x_4 + 5x_5 + 6x_6 + 7x_7 + 8x_8 + 9x_9 + 10x_{10})\equiv 0 \pmod{11}.</math>}}

The two most common errors in handling an ISBN (e.g. when typing it or writing it down) are a single altered digit or the transposition of adjacent digits. It can be proven mathematically that all pairs of valid <nowiki>ISBN-10</nowiki>s differ in at least two digits. It can also be proven that there are no pairs of valid <nowiki>ISBN-10</nowiki>s with eight identical digits and two transposed digits (these proofs are true because the ISBN is less than eleven digits long and because 11 is a [[prime number]]). The ISBN check digit method therefore ensures that it will always be possible to detect these two most common types of error, i.e., if either of these types of error has occurred, the result will never be a valid ISBN—the sum of the digits multiplied by their weights will never be a multiple of 11. However, if the error were to occur in the publishing house and remain undetected, the book would be issued with an invalid ISBN.<ref>For example, ''I'saka: a sketch grammar of a language of north-central New Guinea.'' Pacific Linguistics. ISBN "0-85883-554-4".</ref>

In contrast, it is possible for other types of error, such as two altered non-transposed digits, or three altered digits, to result in a valid ISBN (although it is still unlikely).

=== <nowiki>ISBN-10</nowiki> check digit calculation ===
<!-- "Damm algorithm" links here -->
Each of the first nine digits of the 10-digit ISBN—excluding the check digit itself—is multiplied by its (integer) weight, descending from 10 to 2, and the sum of these nine products found. The value of the check digit is simply the one number between 0 and 10 which, when added to this sum, means the total is a multiple of 11.

For example, the check digit for an <nowiki>ISBN-10</nowiki> of 0-306-40615-''?'' is calculated as follows:
{{block indent|<math>
\begin{align}
 s &= (0\times 10)+(3\times 9)+(0\times 8)+(6\times 7)+(4\times 6)+(0\times 5)+(6\times 4)+(1\times 3)+(5\times 2)\\
   &= 130.
\end{align}
</math>}}
Adding 2 to 130 gives a multiple of 11 (because 132 = 12×11)—this is the only number between 0 and 10 which does so. Therefore, the check digit has to be 2, and the complete sequence is <nowiki>ISBN 0-306-40615-2</nowiki>. If the value of <math>x_{10}</math> required to satisfy this condition is 10, then an 'X' should be used.

Alternatively, [[modular arithmetic]] is convenient for calculating the check digit using modulus 11. The [[remainder]] of this sum when it is divided by 11 (i.e. its value modulo 11), is computed. This remainder plus the check digit must equal either 0 or 11. Therefore, the check digit is (11 minus the remainder of the sum of the products modulo 11) modulo 11. Taking the remainder modulo 11 a second time accounts for the possibility that the first remainder is 0. Without the second modulo operation, the calculation could result in a check digit value of {{nobr|11 − 0 {{=}} 11}}, which is invalid. (Strictly speaking, the ''first'' "modulo 11" is not needed, but it may be considered to simplify the calculation.)

For example, the check digit for the <nowiki>ISBN</nowiki> of 0-306-40615-''?'' is calculated as follows:
{{block indent|<math>
\begin{align}
 s &= (11 - ( ( (0\times 10)+(3\times 9)+(0\times 8)+(6\times 7)+(4\times 6)+(0\times 5)+(6\times 4)+(1\times 3)+(5\times 2) ) \,\bmod\, 11 ) ) \,\bmod\, 11\\
   &=    (11 - ( (0 + 27 +   0 +  42 +  24 +   0 + 24  +   3 + 10 ) \,\bmod\, 11) ) \,\bmod\, 11\\
   &= (11-((130) \,\bmod\, 11))\,\bmod\, 11 \\
   &= (11-(9))\,\bmod\, 11 \\
   &= (2)\,\bmod\, 11 \\
   &= 2
\end{align}
</math>}}

Thus the check digit is 2.

It is possible to avoid the multiplications in a software implementation by using two accumulators. Repeatedly adding <code>t</code> into <code>s</code> computes the necessary multiples:
<syntaxhighlight lang="C">
// Returns ISBN error syndrome, zero for a valid ISBN, non-zero for an invalid one.
// digits[i] must be between 0 and 10.
int CheckISBN(int const digits[10]) {
  int i, s = 0, t = 0;

  for (i = 0; i < 10; ++i) {
    t += digits[i];
    s += t;
  }
  return s % 11;
}
</syntaxhighlight>
The modular reduction can be done once at the end, as shown above (in which case <code>s</code> could hold a value as large as 496, for the invalid <nowiki>ISBN 99999-999-9-X</nowiki>), or <code>s</code> and <code>t</code> could be reduced by a conditional subtract after each addition.

=== <nowiki>ISBN-13</nowiki> check digit calculation ===

Appendix 1 of the International ISBN Agency's official user manual<ref name="7th edition Users' Manual">{{cite book |url=https://www.kb.se/download/18.71dda82e160c04f1cc412bc/1531827912246/ISBN%20International%20Users%20Manual%20-%207th%20edition.pdf |via=Kungliga biblioteket  |title=ISBN Users' Manual, International Edition |edition=7th |date=2017 |publisher=International ISBN Agency |location=London |isbn=978-92-95055-12-4 |access-date=9 June 2019 |archive-date=11 December 2019 |archive-url=https://web.archive.org/web/20191211194637/https://www.kb.se/download/18.71dda82e160c04f1cc412bc/1531827912246/ISBN%20International%20Users%20Manual%20-%207th%20edition.pdf |url-status=live }}</ref>{{rp|33}} describes how the 13-digit ISBN check digit is calculated. The <nowiki>ISBN-13</nowiki> check digit, which is the last digit of the ISBN, must range from 0 to 9 and must be such that the sum of all the thirteen digits, each multiplied by its (integer) weight, alternating between 1 and 3, is a multiple of [[10 (number)|10]]. As ISBN-13 is a subset of [[International Article Number#Check digit|EAN-13]], the algorithm for calculating the check digit is exactly the same for both.

Formally, using [[modular arithmetic]], this is rendered:
{{block indent|<math>(x_1 + 3x_2 + x_3 + 3x_4 + x_5 + 3x_6 + x_7 + 3x_8 + x_9 + 3x_{10} + x_{11} + 3x_{12} + x_{13} ) \equiv 0 \pmod{10}.</math>}}

The calculation of an <nowiki>ISBN-13</nowiki> check digit begins with the first twelve digits of the 13-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed [[modular arithmetic|modulo]] 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero replaces a ten, so, in all cases, a single check digit results.

For example, the <nowiki>ISBN-13</nowiki> check digit of 978-0-306-40615-''?'' is calculated as follows:
<!-- This is what we'd like to do, but it is far too wide.
:<math>\textstyle \begin{array}{rlllllllllllll}
s &{}= 1 \times 9 &{}+ 3 \times 7 &{}+ 1 \times 8 &{}+ 3 \times 0 &{}+ 1 \times 3 &{}+ 3 \times 0 &{}+ 1 \times 6 &{}+ 3 \times 4 &{}+ 1 \times 0 &{}+ 3 \times 6 &{}+ 1 \times 1 &{}+ 3 \times 5 \\
 &{}= 9 &{}+21 &{}+ 8 &{}+ 0 &{}+ 3 &{}+ 0 &{}+ 6 &{}+ 12 &{}+ 0 &{}+ 18 &{}+ 1 &{}+ 15 \\
 &{}= 93
\end{array}</math>
-->
 s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3
   =   9 +  21 +   8 +   0 +   3 +   0 +   6 +  12 +   0 +  18 +   1 +  15
   = 93
 93 / 10 = 9 remainder 3
 10 –  3 = 7

Thus, the check digit is 7, and the complete sequence is <nowiki>ISBN 978-0-306-40615-7</nowiki>.

In general, the <nowiki>ISBN</nowiki> check digit is calculated as follows.

Let
{{block indent|<math>r = 10 - \big(\big(x_1 + 3x_2 + x_3 + 3x_4 + \cdots + x_{11} + 3x_{12}\big) \bmod 10\big).</math>}}

Then
{{block indent|<math>
 x_{13} = \begin{cases}
  r, & r < 10, \\
  0, & r = 10.
\end{cases}
</math>}}

This check system—similar to the [[Universal Product Code|UPC]] check digit formula—does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes {{nobr|3 × 6 + 1 × 1 {{=}} 19}} to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be {{nobr|3 × 1 + 1 × 6 {{=}} 9}}. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The <nowiki>ISBN-10</nowiki> formula uses the [[prime number|prime]] modulus 11 which avoids this blind spot, but requires more than the digits 0–9 to express the check digit.

Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0).

=== <nowiki>ISBN-10</nowiki> to <nowiki>ISBN-13</nowiki> conversion ===
A 10-digit ISBN is converted to a 13-digit ISBN by prepending "978" to the  <nowiki>ISBN-10</nowiki> and recalculating the final checksum digit using the <nowiki>ISBN-13</nowiki> algorithm. The reverse process can also be performed, but not for numbers commencing with a prefix other than 978, which have no 10-digit equivalent.

=== {{anchor|Cancelled ISBN}}Errors in usage ===
[[Publishing|Publishers]] and [[library|libraries]] have varied policies about the use of the ISBN check digit. Publishers sometimes fail to check the correspondence of a book title and its ISBN before publishing it; that failure causes book identification problems for libraries, booksellers, and readers.<ref>{{Cite book|title=Book Publishing I|last1=Lorimer|first1=Rowland|last2=Shoichet|first2=Jillian|last3=Maxwell|first3=John W.|publisher=CCSP Press|year=2005|isbn=978-0-9738727-0-5|pages=299}}</ref> For example, {{ISBN|0-590-76484-5}} is shared by two books—''Ninja gaiden: a novel based on the best-selling game by Tecmo'' (1990) and ''Wacky laws'' (1997), both published by [[Scholastic Corporation|Scholastic]].

Most libraries and booksellers display the book record for an invalid ISBN issued by the publisher. The [[Library of Congress]] catalogue contains books published with invalid ISBNs, which it usually tags with the phrase "Cancelled ISBN".<ref>{{cite web |url=https://www.loc.gov/marc/bibliographic/bd020.html |title=020 – International Standard Book Number (R) – MARC 21 Bibliographic – Full |date=September 2013 |publisher=[[Library of Congress]] |access-date=29 December 2017 |archive-date=5 January 2018 |archive-url=https://web.archive.org/web/20180105045654/http://www.loc.gov/marc/bibliographic/bd020.html |url-status=live }}</ref> The International Union Library Catalog (a.k.a., [[WorldCat]] [[OCLC]]—Online Computer Library Center system) often indexes by invalid ISBNs, if the book is indexed in that way by a member library.<ref>{{cite web|url=http://xisbn.worldcat.org/xisbnadmin/xoclcnum/index.htm|title=xISBN (Web service)|publisher=Xisbn.worldcat.org|access-date=27 May 2013|archive-url=https://web.archive.org/web/20110501074452/http://xisbn.worldcat.org/xisbnadmin/xoclcnum/index.htm|archive-date=1 May 2011|url-status=dead}}</ref>

=== eISBN ===
{{Multiple issues |section=yes |
{{POV section|date=May 2024}}
{{Unreliable sources|section|date=May 2024}}
}}

Only the term "ISBN" should be used; the terms "eISBN" and "e-ISBN" have historically been sources of confusion and should be avoided. If a book exists in one or more digital ([[e-book]]) formats, each of those formats must have its own ISBN. In other words, each of the three separate [[EPUB]], [[Amazon Kindle]], and [[PDF]] formats of a particular book will have its own specific ISBN. They should not share the ISBN of the paper version, and there is no generic "eISBN" which encompasses all the e-book formats for a title.<ref>{{Cite news|url=http://www.sellbox.com/myth-eisbn-every-ebook-edition-needs-unique-number/|title=The Myth of the eISBN Why Every eBook Edition Needs a Unique Number – Publishing services for self publishing authors and businesses|date=28 June 2013|work=Publishing services for self publishing authors and businesses|language=en-US|access-date=16 January 2017|archive-date=10 October 2022|archive-url=https://web.archive.org/web/20221010155538/https://www.sellbox.com/myth-eisbn-every-ebook-edition-needs-unique-number/|url-status=live}}</ref>

== EAN format used in barcodes, and upgrading ==
The [[barcode]]s on a book's back cover (or inside a mass-market [[paperback]] book's front cover) are [[European Article Number|EAN-13]]; they may have a separate barcode encoding five digits called an [[EAN-5]] for the [[currency]] and the [[recommended retail price]].<ref>{{Citation |title= Frequently asked questions |publisher=ISBN |place= [[U.S.|US]] |date= 12 March 2014 |url= http://www.isbn-us.com/blog/2014/03/12/isbn-information-frequently-asked-questions/ |url-status=dead |archive-url= https://web.archive.org/web/20140416211950/http://www.isbn-us.com/blog/2014/03/12/isbn-information-frequently-asked-questions/ |archive-date= 16 April 2014 |df= dmy-all }} – including a detailed description of the EAN-13 format.</ref> For 10-digit ISBNs, the number "978", the [[Bookland]] "country code", is prefixed to the ISBN in the barcode data, and the check digit is recalculated according to the EAN-13 formula (modulo 10, 1× and 3× weighting on alternating digits).

Partly because of an expected shortage in certain ISBN categories, the [[International Organization for Standardization]] (ISO) decided to migrate to a 13-digit ISBN (<nowiki>ISBN-13</nowiki>). The process began on 1 January 2005 and was planned to conclude on 1 January 2007.<ref>{{Citation |publisher= Collections |contribution-url= http://www.collectionscanada.ca/iso/tc46sc9/isbn.htm |type= FAQ |title= ISO TC49SC9 |contribution= ISBN |place= [[Canada|CA]] |access-date= 22 September 2004 |archive-date= 10 April 2007 |archive-url= https://web.archive.org/web/20070410204507/http://www.collectionscanada.ca/iso/tc46sc9/isbn.htm |url-status= dead }}</ref> {{as of|2011}}, all the 13-digit ISBNs began with 978. As the 978 ISBN supply is exhausted, the 979 prefix was introduced. Part of the 979 prefix is reserved for use with the [[Bookland|Musicland]] code for musical scores with an [[ISMN]]. The 10-digit ISMN codes differed visually as they began with an "M" letter; the bar code represents the "M" as a zero, and for checksum purposes it counted as a 3. All ISMNs are now thirteen digits commencing {{Not a typo|979-0}}; {{Not a typo|979-1}} to {{not a typo|979-9}} will be used by ISBN.

Publisher identification code numbers are unlikely to be the same in the 978 and 979 ISBNs, likewise, there is no guarantee that language area code numbers will be the same. Moreover, the 10-digit ISBN check digit generally is not the same as the 13-digit ISBN check digit. Because the GTIN-13 is part of the [[Global Trade Item Number]] (GTIN) system (that includes the GTIN-14, the GTIN-12, and the GTIN-8), the 13-digit ISBN falls within the 14-digit data field range.<ref>{{Citation | title = Standards | contribution-url = http://www.isbn.org/standards/home/isbn/transition.asp | contribution = Are You Ready for <nowiki>ISBN-13</nowiki>? | publisher = ISBN | access-date = 14 October 2005 | archive-date = 31 August 2008 | archive-url = https://web.archive.org/web/20080831082318/http://www.isbn.org/standards/home/isbn/transition.asp | url-status = live }}</ref>

Barcode format compatibility is maintained, because (aside from the group breaks) the <nowiki>ISBN-13</nowiki> barcode format is identical to the EAN barcode format of existing 10-digit ISBNs. So, migration to an EAN-based system allows booksellers the use of a single numbering system for both books and non-book products that is compatible with existing ISBN based data, with only minimal changes to [[information technology]] systems. Hence, many [[bookstore|booksellers]] (e.g., [[Barnes & Noble]]) migrated to EAN barcodes as early as March 2005. Although many American and Canadian booksellers were able to read EAN-13 barcodes before 2005, most general retailers could not read them. The upgrading of the [[Universal Product Code|UPC]] [[barcode system]] to full EAN-13, in 2005, eased migration to the <nowiki>ISBN</nowiki> in North America.

== See also ==
* [[Amazon Standard Identification Number|ASIN]] (Amazon Standard Identification Number)
* [[Book Item and Component Identifier|BICI]] (Book Item and Component Identifier)
* [[Special:BookSources|Book sources search]]&nbsp;– a Wikipedia resource that allows search by ISBNs
* [[CODEN]] (serial publication identifier currently used by libraries; replaced by the ISSN for new works)
* [[Digital object identifier|DOI]] (Digital Object Identifier)
* [[English Short Title Catalogue|ESTC]] (English Short Title Catalogue)
* [[International Standard Audiovisual Number|ISAN]] (International Standard Audiovisual Number)
* [[International Standard Recording Code|ISRC]] (International Standard Recording Code)
* [[International Standard Text Code|ISTC]] (International Standard Text Code)
* [[International Standard Musical Work Code|ISWC]] (International Standard Musical Work Code)
* [[ISSN]] (International Standard Serial Number)
* [[ISWN]] (International Standard Wine Number)
* [[Library of Congress Control Number|LCCN]] (Library of Congress Control Number)
* [[License number (East German books)]] (Book identification system used between 1951 and 1990 in the former GDR)
* [[List of group-0 ISBN publisher codes]]
* [[List of group-1 ISBN publisher codes]]
* [[List of ISBN registration groups]]
* [[Serial Item and Contribution Identifier|SICI]] (Serial Item and Contribution Identifier)
* [[VD 16]] (''Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des 16. Jahrhunderts'', "Bibliography of Books Printed in the German Speaking Countries of the Sixteenth Century")
* [[VD 17]] (''Verzeichnis der im deutschen Sprachraum erschienenen Drucke des 17. Jahrhunderts'', "Bibliography of Books Printed in the German Speaking Countries of the Seventeenth Century")

== Explanatory notes ==
{{Notelist}}

== References ==
{{Reflist}}

== External links ==
{{Wikidata property |P957|P212}}
{{sister project links|d=Q33057|mw=Manual:ISBN|species=no|voy=no|wikt=ISBN|n=no|q=no|s=no|b=no|v=no|c=Category:ISBN}}
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* [https://www.iso.org/standard/65483.html ISO 2108:2017 – International Standard Book Number (ISBN)]
* [https://www.isbn-international.org/ International ISBN Agency]&nbsp;– coordinates and supervises the worldwide use of the ISBN system
** [https://www.isbn-international.org/range_file_generation Numerical List of Group Identifiers]&nbsp;– List of language/region prefixes
** [https://www.isbn.org/ISBN_converter Free conversion tool: <nowiki>ISBN-10</nowiki> to <nowiki>ISBN-13</nowiki> & <nowiki>ISBN-13</nowiki> to <nowiki>ISBN-10</nowiki>] from the [http://www.isbn.org/ ISBN agency]. Also shows correct hyphenation & verifies if ISBNs are valid or not.
* {{Cite web |title=Guidelines for the Implementation of 13-Digit ISBNs |url=http://isbn-international.org/en/download/implementation-guidelines-04.pdf |url-status=dead |archive-url=https://web.archive.org/web/20040912203458/http://www.isbn-international.org/en/download/implementation-guidelines-04.pdf |archive-date=12 September 2004 |df=dmy-all }}
* {{IETF RFC|3187}}&nbsp;– Using International Standard Book Numbers as [[Uniform Resource Name]]s (URN)
* [https://www.loc.gov/programs/preassigned-control-number/isbn-converter/ Worldwide Auto-Converter at Library of Congress]

{{Audiovisual works|state=uncollapsed}}
{{ISO standards}}
{{Books}}
{{Authority control}}

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