Concepts

Big O Notation

big O, read as the letter O, not the numeral zero

Also Known As Landau Notation

Notation

Citation Formats

General Reference

Computing Atlas. "Big O Notation." Accessed August 30, 2026. https://computing.interactiveatlas.org/concepts/big-o-notation.

APA Style

Computing Atlas. (n.d.). Big O Notation. Retrieved August 30, 2026, from https://computing.interactiveatlas.org/concepts/big-o-notation

BibTeX

@misc{computingatlas-big-o-notation,
  author = {Computing Atlas},
  title = {Big O Notation},
  year = {2026},
  url = {https://computing.interactiveatlas.org/concepts/big-o-notation},
  note = {Accessed August 30, 2026}
}

Big O notation is a mathematical notation used to describe the limiting behavior of a function as its argument grows toward a particular value or infinity. In computer science it classifies algorithms by how their running time or space requirements grow as input size grows, providing an upper bound on that growth.

Facts

Origin Year

1894 1

Proposed by Paul Bachmann in 1894 in a number theory context and extended by Edmund Landau in 1909; its use to classify algorithm running time came later.

Core Principle

Expresses that a function's growth is bounded above by another, usually simpler, function times a constant for sufficiently large inputs, letting algorithms be compared by growth rate rather than exact operation counts. 1

Cross-Tradition Connections