Title: city-block distance
Long Title: IUPAC Gold Book - city-block distance
DOI: 10.1351/goldbook.10120
Status: current

Definition
Distance (\(d_{i,j}\)) between two objects (\(i\) and \(j\)) calculated as the sum of the absolute difference between \(k\) variables (\(x\)) that describe the objects. \[d_{i,j} = \sum\limits_{k\,=\,1}^{k\,=\,N} \vert x_{i,k} - x_{j,k}\vert\]

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 427 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10120/html
- json: https://goldbook.iupac.org/terms/view/10120/json
- xml: https://goldbook.iupac.org/terms/view/10120/xml

Citation: Citation: 'city-block distance' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10120
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Disclaimer: The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.
Accessed: 2026-07-26T14:54:13+00:00