irrational

American  

[ih-rash-uh-nl, -rash-nl] / ɪˈræʃ ə nl, -ˈræʃ nl /

adjective

1. without the faculty of reason; deprived of reason.

2. without or deprived of normal mental clarity or sound judgment.

3. not in accordance with reason; utterly illogical.

   irrational arguments.

   Synonyms:

   insensate, ridiculous, unreasonable

4. not endowed with the faculty of reason.

   irrational animals.

5. Mathematics.

   1. (of a number) not capable of being expressed exactly as a ratio of two integers.

   2. (of a function) not capable of being expressed exactly as a ratio of two polynomials.

6. Algebra. (of an equation) having an unknown under a radical sign or, alternately, with a fractional exponent.

7. Greek and Latin Prosody.

   1. of or relating to a substitution in the normal metrical pattern, especially a long syllable for a short one.

   2. noting a foot or meter containing such a substitution.

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noun

1. Mathematics. irrational number.

irrational British  

/ ɪˈræʃənəl /

adjective

1. inconsistent with reason or logic; illogical; absurd

2. incapable of reasoning

3. maths

   1. not rational

   2. ( as noun )

      an irrational

4. prosody

   1. of or relating to a metrical irregularity, usually the occurrence of a long syllable instead of a short one

   2. denoting a metrical foot where such an irregularity occurs

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Other Word Forms

• irrationally adverb
• irrationalness noun
• nonirrational adjective
• nonirrationalness noun

Etymology

Origin of irrational

First recorded in 1425–75; late Middle English, from Latin irratiōnālis; ir- ² ( def. ), rational ( def. )

Example Sentences

“In view of the current robust demand for AI cloud services, we are not concerned that Tencent’s deeper involvement in the AI cloud market would lead to irrational competition.”

From The Wall Street Journal • Mar. 23, 2026

While the motives that drive a knight are often human, political, or both, the logic is as miraculous and irrational as a muddy hedge knight crawling out from under a fallen dragon.

From Salon • Feb. 25, 2026

Freight was another sector that some analysts said was subjected to irrational AI fears last week.

From MarketWatch • Feb. 17, 2026

Mahmood has previously said the current policing structure is "irrational", announcing on Thursday that she intends to drastically cut police forces down from 43 to make way for 12 "mega" forces.

From BBC • Jan. 24, 2026

Mathematicians to this day tell of the hapless man who revealed the secret of the irrational to the world.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife

Related Words

• aberrant
• absurd
• crazy
• foolish
• incoherent
• insane
• preposterous
• ridiculous
• stupid
• unreasonable
• unsound
• unwise
• wrong