Manhattan distance

English

WOTD – 2 January 2026

On this grid, the green line shows the diagonal straight-line distance between the two black points, while the red, blue, and yellow lines indicate equivalent Manhattan distances.

Etymology

From Manhattan +‎ distance, referring to the gridlike street geography of the borough of Manhattan in New York City, New York, United States.

Pronunciation

• (Received Pronunciation) IPA^(key): /mænˌhætn̩ ˈdɪst(ə)n(t)s/
• (General American) IPA^(key): /mænˌhætn̩ ˈdɪst(ə)n(t)s/, /mən-/

• Audio (General American); /mænˌhætn̩ ˈdɪstəns/:

  (file)

• Rhymes: -ɪstəns
• Hyphenation: Man‧hat‧tan dis‧tance

Noun

Manhattan distance (countable and uncountable, plural Manhattan distances)

1. (geometry) Synonym of taxicab distance (“the distance between two points on a grid, where the only path allowed is along horizontal and vertical lines”). [from late 1970s]

   Synonyms: blockwise distance, city block distance, taxi distance

Translations

synonym of taxicab distance — see taxicab distance

See also

• Cartesian distance, Euclidean distance (“distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points”)
• Chebyshev distance, chessboard distance (“metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension”)

Further reading

• taxicab geometry on Wikipedia.Wikipedia
• “Manhattan distance, n.”, in OED Online ⁠, Oxford: Oxford University Press, September 2025.
• “Manhattan distance, n.”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.