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Error detection for identification numbers
A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer generated data. It consists of one or more digits (or letters) computed by an algorithm from the other digits (or letters) in the sequence input. With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits.

The final character of a ten digit International Standard Book Number is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the : The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 + 1×1 = 99 ≡ 0 (mod 11). So the ISBN is valid. Positions can also be counted from left, in which case the check digit is multiplied by 10, to check validity: 0×1 + 2×2 + 0×3 + 1×4 + 5×5 + 3×6 + 0×7 + 8×8 + 2×9 + 1×10 = 143 ≡ 0 (mod 11).

ISBN 13 (in use January 2007) is equal to the EAN 13 code found underneath a book's barcode. Its check digit is generated the same way as the UPC.

The NOID Check Digit Algorithm (NCDA), in use since 2004, is designed for application in persistent identifiers and works with variable length strings of letters and digits, called extended digits. It is widely used with the ARK identifier scheme and somewhat used with schemes, such as the Handle System and DOI. An extended digit is constrained to betanumeric characters, which are alphanumerics minus vowels and the letter 'l' (ell). This restriction helps when generating opaque strings that are unlikely to form words by accident and will not contain both O and 0, or l and 1. Having a prime radix of R=29, the betanumeric repertoire permits the algorithm to guarantee detection of single character and transposition errors for strings less than R=29 characters in length (beyond which it provides a slightly weaker check). The algorithm generalizes to any character repertoire with a prime radix R and strings less than R characters in length.

The tenth digit of the National Provider Identifier for the US healthcare industry. The final digit of a POSTNET code. The North American CUSIP number. The final (ninth) digit of the ABA routing transit number, a bank code used in the United States. The ninth digit of a Vehicle Identification Number (VIN). Mayo Clinic patient identification numbers used in Arizona and Florida include a trailing check digit. The eleventh digit of a Customs & Border Protection entry number.

The Guatemalan Tax Number (NIT – Número de Identificación Tributaria) based on modulo 11.

The UK NHS Number uses the modulo 11 algorithm. The Spanish fiscal identification number (número de identificación fiscal, NIF) (based on modulo 23). The Dutch Burgerservicenummer (BSN) (national identifier) uses the modulo 11 algorithm. The ninth digit of an Israeli Teudat Zehut (Identity Card) number. The 13th digit of the Serbian and Former Yugoslav Unique Master Citizen Number (JMBG). (but not all of them, due to errors or non residency)
The last two digits of the 11 digit Turkish Identification Number (TC Kimlik Numarası). The ninth character in the 14 character EU cattle passport number (cycles from 1 to 7: see British Cattle Movement Service). The ninth digit in an Icelandic Kennitala (national ID number). Modulo 97 check digits in a Belgian and Serbian bank account numbers. Serbia sometimes also uses modulo 11, for reference number. The ninth digit in a Hungarian TAJ number (social insurance number). For the residents of India, the unique identity number named Aadhaar has a trailing 12th digit that is calculated with the Verhoeff algorithm. The Intellectual Property Office of Singapore (IPOS) has confirmed a new format for application numbers of registrable intellectual property (IP, e. g., trademarks, patents, registered designs). It will include a check character calculated with the Damm algorithm. The last digit of Chinese citizen ID number (second generation) is calculated by modulo 11 2 as specified in Chinese GuoBiao (aka national standard) GB11643 1999 which adopts ISO 7064:1983. 'X' is used if the calculated checking digit is 10. The 11th digit of Estonian Isikukood (Personal Identification Code). The last letter on Vehicle registration plates of Singapore.

The Australian tax file number (based on modulo 11). The seventh character of a New Zealand NHI Number. The last digit in a New Zealand locomotive's Traffic Monitoring System (TMS) number.