Standard Lemma guide

modulo

noun · prep · 4 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

  • Received-Pronunciation: /ˈmɒd͡ʒələʊ/
  • Received-Pronunciation: /ˈmɒdjʊləʊ/
  • General-American: /ˈmɑd͡ʒəloʊ/
  • CMU ARPABET: M AO1 JH UW0 L OW2 Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.

1

noun

Meaning 1

The operation or function that returns the remainder of one number divided by another.

Definition source: English Wiktionary via Wiktextract

Usage: uncountable

Topics: computing, engineering, mathematics, natural-sciences, physical-sciences, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: modulus

Antonyms: none provided

2

prep

Meaning 2

Given a specified modulus of.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

  • 21 and 84 are congruent to each other modulo 9, since both numbers leave the same remainder, 3, when divided by 9.
  • Thus 21 modulo 9 is 3, because when 21 is divided by 9, the remainder is 3.
  • 21 is congruent to 3 modulo 9.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

prep

Meaning 3

Except for differences accounted for by.

Definition source: English Wiktionary via Wiktextract

Topics: engineering, natural-sciences, physical-sciences, technical

Examples

  • "A is the same as B modulo C" means A is the same as B except for differences accounted for by C.

Meaning relationships

Synonyms: up to

Antonyms: none provided

4

prep

Meaning 4

With due allowance for (a specified exception or particular detail).

Definition source: English Wiktionary via Wiktextract

Qualifier: extended use

Examples

  • In the Lisp programming language, the "tail recursion modulo cons" technique allows functions that would be tail recursive but for a cons call to be transformed into a tail recursive form.
  • All mammals, modulo the monotremes, give birth to live young.

Meaning relationships

Synonyms: barring, except for, save for, apart, apart from, aside, aside from, bar, besides, but, but for, except, excepting, excluding, forby, modulo, not counting, other than, outtake, save, saving, with the exception of

Antonyms: none provided

History

Etymology

From Latin modulō, ablative of modulus (“a measure”).

Across languages

Translations

6 source translations are retained for this English entry.

  • Esperanto: module — Given a specified modulus of
  • French: modulo — Given a specified modulus of
  • German: modulo — Given a specified modulus of
  • Icelandic: mátað við — Given a specified modulus of
  • Polish: modulo — Given a specified modulus of
  • Swedish: modulo — Given a specified modulus of
Real reading context

modulo in complete knowledge articles

Pisano period Ideas & learning · Challenging · 22 uses Proofs of Fermat's little theorem Ideas & learning · Developing · 19 uses Wilson's theorem Ideas & learning · Developing · 10 uses