Standard Lemma guide

irrational

adj · noun · 6 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.

  • ĭră'sh(ə)nəl
  • /ɪˈɹæʃ.(ə.)nəl/
  • Southern-England: Recorded audio is listed in the source snapshot.
  • rhymes with -æʃənəl
  • CMU ARPABET: IH2 R AE1 SH AH0 N AH0 L Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.

1

adj

Meaning 1

Not rational; unfounded, nonsensical or wrong-headed.

Definition source: English Wiktionary via Wiktextract

Examples

  • an irrational decision
  • July 18, 2012, Scott Tobias, AV Club The Dark Knight Riseshttp://www.avclub.com/articles/the-dark-knight-rises-review-batman,82624/ Where the Joker preys on our fears of random, irrational acts of terror, Bane has an all-consuming, dictatorial agenda that’s more stable and permanent, a New World Order that’s been planned out with the precision of a military coup.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

adj

Meaning 2

Of a real number, that cannot be written as the ratio of two integers.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: arithmetic, mathematics, number-theory, sciences

Examples

  • The number π is irrational.

Meaning relationships

Synonyms: none provided

Antonyms: rational

3

noun

Meaning 3

A real number that can not be expressed as the quotient of two integers, an irrational number.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

4

adjective

Meaning 4

not consistent with or using reason

Definition source: Princeton WordNet 3.0

Examples

  • irrational fears
  • irrational animals

Meaning relationships

Synonyms: none provided

Antonyms: rational

5

adjective

Meaning 5

real but not expressible as the quotient of two integers

Definition source: Princeton WordNet 3.0

Examples

  • irrational numbers

Meaning relationships

Synonyms: none provided

Antonyms: rational

6

noun

Meaning 6

a real number that cannot be expressed as a rational number

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: irrational number

Antonyms: none provided

Broader terms: real number, real

Narrower terms: transcendental number, algebraic number

History

Etymology

From Latin irratiōnālis, from ir- + ratiōnālis.

Across languages

Translations

90 source translations are retained for this English entry.

  • Armenian: իռացիոնալ (iṙacʻional) — unfounded or nonsensical
  • Asturian: irracional — unfounded or nonsensical
  • Bulgarian: неразумен (nerazumen) — unfounded or nonsensical
  • Bulgarian: безразсъден (bezrazsǎden) — unfounded or nonsensical
  • Catalan: bèstia — unfounded or nonsensical
  • Catalan: irracional — unfounded or nonsensical
  • Chinese Mandarin: 不合理 (bùhélǐ) — unfounded or nonsensical
  • Danish: irrationel — unfounded or nonsensical
  • Dutch: irrationeel — unfounded or nonsensical
  • Dutch: irrationele — unfounded or nonsensical
  • Dutch: onzinnig — unfounded or nonsensical
  • Dutch: onzinnige — unfounded or nonsensical
  • Dutch: onredelijk — unfounded or nonsensical
  • Dutch: onredelijke — unfounded or nonsensical
  • Esperanto: malracia — unfounded or nonsensical
  • Finnish: epälooginen — unfounded or nonsensical
  • Finnish: irrationaalinen — unfounded or nonsensical
  • French: irrationnel — unfounded or nonsensical
  • Galician: irracional — unfounded or nonsensical
  • German: irrational — unfounded or nonsensical
  • German: irrationell — unfounded or nonsensical
  • German: unvernünftig — unfounded or nonsensical
  • Ancient Greek: ἄλογος (álogos) — unfounded or nonsensical
  • Hungarian: észszerűtlen — unfounded or nonsensical
  • Hungarian: irracionális — unfounded or nonsensical
  • Irish: aingiallta — unfounded or nonsensical
  • Italian: irrazionale — unfounded or nonsensical
  • Japanese: 不合理な (fugōri na) — unfounded or nonsensical
  • Japanese: 無理な (muri na) — unfounded or nonsensical
  • Japanese: 理不尽な (rifujin na) — unfounded or nonsensical
  • Japanese: ばかげた (bakageta) — unfounded or nonsensical
  • Japanese: 筋違いな (sujichigai na) — unfounded or nonsensical
  • Korean: 불합리한 (bulhamnihan) — unfounded or nonsensical
  • Macedonian: нера́зумен (nerázumen) — unfounded or nonsensical
  • Macedonian: безра́суден (bezrásuden) — unfounded or nonsensical
  • Manx: neuresoonagh — unfounded or nonsensical
  • Māori: heahea — unfounded or nonsensical
  • Norwegian Bokmål: irrasjonell — unfounded or nonsensical
  • Norwegian Nynorsk: irrasjonell — unfounded or nonsensical
  • Plautdietsch: onveninftich — unfounded or nonsensical
  • Polish: nieracjonalny — unfounded or nonsensical
  • Polish: irracjonalny — unfounded or nonsensical
  • Portuguese: irracional — unfounded or nonsensical
  • Romanian: irațional — unfounded or nonsensical
  • Romanian: nerațional — unfounded or nonsensical
  • Russian: нерациона́льный (neracionálʹnyj) — unfounded or nonsensical
  • Russian: иррациона́льный (irracionálʹnyj) — unfounded or nonsensical
  • Serbo-Croatian: и̏рациона̄лан — unfounded or nonsensical
  • Serbo-Croatian: не̏разӯман — unfounded or nonsensical
  • Serbo-Croatian: ȉracionālan — unfounded or nonsensical
  • Serbo-Croatian: nȅrazūman — unfounded or nonsensical
  • Spanish: irracional — unfounded or nonsensical
  • Swedish: irrationell — unfounded or nonsensical
  • Tagalog: atbang — unfounded or nonsensical
  • Tagalog: maatbang — unfounded or nonsensical
  • Telugu: అసంబద్ధము (asambaddhamu) — unfounded or nonsensical
  • Vietnamese: bất hợp lý — unfounded or nonsensical
  • Armenian: իռացիոնալ (iṙacʻional) — mathematics: of a number
  • Bulgarian: ирационален (iracionalen) — mathematics: of a number
  • Catalan: irracional — mathematics: of a number
  • Chinese Mandarin: 無理數 /无理数 (wúlǐshù) — mathematics: of a number
  • Czech: iracionální — mathematics: of a number
  • Danish: irrational — mathematics: of a number
  • Dutch: irrationaal — mathematics: of a number
  • Dutch: irrationale — mathematics: of a number
  • Esperanto: neracionala — mathematics: of a number
  • Finnish: irrationaalinen — mathematics: of a number
  • French: irrationnel — mathematics: of a number
  • German: irrational — mathematics: of a number
  • Greek: άρρητος (árritos) — mathematics: of a number
  • Ancient Greek: ἄρρητος (árrhētos) — mathematics: of a number
  • Hindi: अपरिमेय (aprimey) — mathematics: of a number
  • Hungarian: irracionális — mathematics: of a number
  • Icelandic: óræður — mathematics: of a number
  • Japanese: 無理数 (murisū) — mathematics: of a number
  • Korean: 무리수 (murisu) — mathematics: of a number
  • Māori: kewha — mathematics: of a number
  • Norwegian Bokmål: irrasjonal — mathematics: of a number
  • Norwegian Nynorsk: irrasjonal — mathematics: of a number
  • Polish: niewymierny — mathematics: of a number
  • Portuguese: irracional — mathematics: of a number
  • Russian: иррациона́льный (irracionálʹnyj) — mathematics: of a number
  • Swedish: irrationell — mathematics: of a number
  • Tagalog: ditagwayin — mathematics: of a number
  • Vietnamese: số vô tỉ — mathematics: of a number
  • Bulgarian: ирационално число (iracionalno čislo) — irrational number
  • Icelandic: óræð tala — irrational number
  • Korean: 무리수 (murisu) — irrational number
  • Polish: liczba niewymierna — irrational number
  • Tagalog: bilang na ditagwayin — irrational number
Real reading context

irrational in complete knowledge articles