factorial

/fækˈtɔːɹi.əl/

//fækˈtɔːɹi.əl// noun

By · According to Wiktionary data (CC BY-SA) ·

"factorial" is a 9-letter English headword indexed on PlainSpell.

The verdict

“factorial” is uncommon English (frequency #51,697 among 2,507 “F” headwords), classed as a noun. The kind of spelling people second-guess.

#51,697
frequency rank, English
2,507
“F” headwords

According to Wiktionary data (CC BY-SA, analyzed September 3, 2026) - The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.

Corpus desk

Index EN-factorial · factorial · English

factorial · rank #51,697 · 0 variants · 0 confusables

  • FREQ-RARE #51,697
  • LEN-LONG 9 letters
  • VOW-4 4 vowels
  • CONFUS-0 No pairs
  • VAR-0 0 variants
  • BOOK-MID 2,507
  • PHOTO-FINISH facepalm

Nearest frequency peer: facepalm (-1 rank slots)

Read with this headword: Spelling guide for this pattern

Desk codes from Wiktionary headword shape, FrequencyWords rank tier, confusable-pair count, generated misspelling depth, letter-cohort book size, and photo-finish peer. Not a difficulty grade.

Long-tail ranks near “factorial”

Sparse band: bars invert rank so rarer forms read shorter

corpus weight

What this shows Long-tail view: where “factorial” sits against similarly uncommon English ranks.

Source FrequencyWords open word-frequency list As of September 3, 2026
Key facts for factorial
PropertyValue
Headwordfactorial
LanguageEnglish
Part of speechNoun
IPA/fækˈtɔːɹi.əl/
Letters9
Frequency rank#51,697
Misspellings tracked0
Confusable pairs0
SourceWiktionary (kaikki.org)

Long-tail rank of “factorial” in English

Word frequency stretches from the small set of words we reach for constantly (left) out to the long tail barely used once in a while (right).factorialfalls in this rarity band:

#1#100#1K#10K#100K
← used constantlyrarely used →

The axis is logarithmic, with each marked tick roughly ten times rarer than the last. Rare peers in the same band: “facepalm” (#51,696), “Fanta” (#51,699), “exude” (#51,694). Among 2,507 “F” headwords, “factorial” is #51,697. Source: FrequencyWords open word-frequency list.

Rare enough to double-check

factorial is uncommon English at frequency #51,697 among 2,507 “F” headwords, classed as anoun, transcribed /fækˈtɔːɹi.əl/. Rarity is why readers land here mid-draft. Gloss: "The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.".

No generated misspelling entries exist for factorial in our index, a sign its spelling follows regular English conventions. It is not paired with a close-neighbour confusable in our dataset, which tends to mean the word is visually distinctive enough to stand on its own.

Etymologically, the entry records: From factor + -ial. The correct English form is factorial, spelled F-A-C-T-O-R-I-A-L.

Definition

  1. 1
    The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.

Recorded use

Wiktionary examples

These source excerpts show how factorial appears in context. They illustrate usage; the definition above remains the entry’s reference meaning.

  1. The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inc…
  2. This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#92;prod#95;#123;k#61;1#125;ⁿk#61;1#92;cdot 2#92;cdot 3#92;cdotsn.But what does this equal? Well, of course we can say that it is equal to n factorial and write#92;prod#95;#123;k#61;…

Etymology

From factor + -ial.

This word in other languages

factorial(Español)factorielle(Français)Fakultät(Deutsch)fatorial(Português)

Definitions, pronunciation, and etymology for this entry are drawn from Wiktionary via the kaikki.org structured extract (CC BY-SA); frequency ordering uses the FrequencyWords open word-frequency list (2018 English corpus, MIT). See the methodology for how each field is sourced and updated.

Frequently Asked Questions

How do you spell "factorial"?
"factorial" is spelled F-A-C-T-O-R-I-A-L. The IPA pronunciation is /fækˈtɔːɹi.əl/.
What does "factorial" mean?
As a noun, "factorial" means: The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
How do you pronounce "factorial"?
The IPA (International Phonetic Alphabet) transcription for "factorial" is /fækˈtɔːɹi.əl/. Click the speaker icon on the pronunciation badge above to hear it spoken aloud where audio is available.
What is the origin of the word "factorial"?
From factor + -ial. See the full etymology section above for more details.
Is PlainSpell free to use?
Yes, PlainSpell is a completely free word reference. You can look up definitions, pronunciations, confusable pairs, homophones, and spelling corrections across 5 languages without any sign-up or subscription.

Similar English words by spelling shape

Same letter count and similar misspelling depth for "factorial", not the corpus desk frequency band.

Same letter count

Frequency-ranked English headwords with 9 letters (nearest by frequency rank).

Fergusson#51,702expending#51,691fireballs#51,703firebrand#51,704

Source: Wiktionary (via kaikki.org) Structured Wiktionary extract

Source: FrequencyWords open word-frequency list