When someone counts items, that person uses cardinal values. In grammatical terms, acardinal numeral is a word used to represent such a countable quantity. The English wordsone,two,three,four, etc. are all examples of cardinal numerals.

In Latin, most cardinal numerals behave asindeclinableadjectives. They are usually associated with a noun that is counted, but do not change their endings to agree grammatically with that noun. The exceptions areūnus(“one”),duo(“two”),trēs(“three”), and multiples ofcentum(“hundred”), all of whichdecline. Additionally, althoughmīlle(“thousand”) is an indeclinable adjective in the singular, it becomes a declinable noun in the plural. These exceptions are further explained in later sections.

The smaller cardinal numerals, fromūnus(“one”) todecem(“ten”), are all simple (not made by combining two numbers).

Inflection: The Latinūnus(“one”) inflects like an irregularfirst andsecond declension adjective. The irregularities occur in the singular genitive, which ends in-īus instead of the usual-ī or-ae, and in the singular dative, which ends in-ī instead of the usual-ō or-ae.

The choice of ending will agree with the gender of the associated noun:ūnusequus ("one horse"),ūnaclāvis ("one key"),ūnumsaxum ("one stone"). The ending will also agree with the grammatical case of the associated noun:ūnīusequī (genitive),ūnamclāvem (accusative),ūnīsaxō (dative).

Plural: Although it may seem strange at first sight,ūnus does have a set ofplural forms. These forms are used when the associated noun has a plural form, but an inherently singular meaning. For example, the Latin nouncastra(“camp”) occurs only as a plural neuter form and takes plural endings, even though it identifies one object, hence:ūnōrumcastrōrum ("of one camp").

Compounds: Whenūnus is used to formcompound numerals, such asūnusetvīgintī ("twenty-one"), the case and gender agree with the associated noun, although the singular is used:vīgintīetūnamfēmināsvīdī . Unlikeduo andtrēs, the wordūnus is almost never used withmīlle(“thousand”) to indicate how many thousand.

Inflection: The Latinduo(“two”) has a highly irregular inflection, derived in part from the old Indo-Europeandual number. While some of the endings resemble those of afirst andsecond declension adjective, others resemble those of athird declension adjective. The inflection ofambō(“both”) is very similar.

The choice of ending will agree with the gender of the associated noun, which will necessarily be plural:duoequī ("two horses"),duaeclāvēs ("two keys"),duosaxa ("two stones"). The ending will also agree with the grammatical case of the associated noun:duōsequōs (accusative),duārumclāvium (genitive),duōbussaxīs (dative).

Compounds: Whenduo is used to formcompound numerals, such asduoetvīgintī orvīgintīduo ("twenty-two"), the case and gender agree with the associated noun. This is also the case when used with the plural ofmīlle(“thousand”) to indicate how many thousands:duomīlia ("two thousands"),duōrummīlium ("of two thousands").

Inflection: The Latintrēs(“three”) inflects like a pluralthird declension adjective with two endings in the nominative. Notice that the masculine and feminine endings are identical.

The choice of ending will agree with the gender of the associated noun, which will necessarily be plural:trēsequī ("three horses"),trēsclāvēs ("three keys"),triasaxa ("three stones"). The ending will also agree with the grammatical case of the associated noun:trēsequōs (accusative),triumclāvium (genitive),tribussaxīs (dative).

Compounds: Whentrēs is used to formcompound numerals, such astrēsetvīgintī orvīgintītrēs ("twenty-three"), the case and gender agree with the associated noun. This is also the case when used with the plural ofmīlle(“thousand”) to indicate how many thousands:triamīlia ("three thousands"),triummīlium ("of three thousands").

The numeralsquattuor(“four”) throughdecem(“ten”) are allindeclinable, and never change their endings to match an associated noun. Each of these numerals has a single immutable form in all situations.

Many of these numerals are mirrored in English words (such asquadrangle,quintuplet,sextuple). The numerals for 7 through 10 appear in the English names of months (September,October,November, andDecember). These months were the seventh through tenth of the Roman calendar, since the Roman year began withmārtius(“March”).

Latin cardinals larger thandecem(“ten”) but less thanvīgintī(“twenty”) are constructed by addition. The ending-decim (a form ofdecem) is attached to the numeralsūnus throughnovem. The resultant compound carries the same value as the mathematical sum of the components. For examplequattuordecim(“fourteen”) isquattuor(“four”) +decem(“ten”). English does much the same by attaching-teen (a form often) to smaller numerals, such as the numeralfourteen which isfour +ten.

In some of these compounds, a spelling and pronunciation change occurs during the attachment, so thatsex +decem drops the-x and lengthens thee to yieldsēdecim. This kind of change also occurs in English, as infive +ten, in which thev is devoiced under the influence of the followingt (and the purely orthographice is dropped) to yieldfifteen.

Exceptions: There are two exceptions to the general pattern for forming theteens. In Classical Latin, the numerals for 18 and 19 are more frequently written as subtractive compounds. So, although 18 may be written asoctōdecim, it is more often written asduodēvīgintī (literally "two from twenty"). Likewise, the numeral for 19 may be written asnovemdecim, but is more often encountered asūndēvīgintī(“one from twenty”).

For more information about the subtractive pattern of construction, see the section on "counting backwards".

Numbers inbetween multiples of 10 can be formed by two different ways. Let us take 22 as example:

• vīgintī duo
• duo et vīgintī

The numeralcentum(“100”) is the only "hundred" that isindeclinable.

All multiples ofcentum up tonōngentī(“900”), e.g.ducentī(“200”),trecentī(“300”), etc., decline as a plural adjective of thefirst andsecond declension.

The Latinmīlle(“thousand”) is irregular in that it can function both as a numeral (adjective) and as anoun. When used as anoun, itdeclines like athird declension neuteri-stem with the genitive plural ending-ium, and even possesses a rare distinct singular ablative formmīllī.

Singular: In the singular,mīlle(“thousand”) can mimic other numerals by functioning as anindeclinable adjective whose ending will remain the same rather than agree with the case, gender or number of the associated head (such as a noun). The head itself declines for case and gender, but is always plural:mīlleequī (nominative masculine, "thousand horses"),mīlleclāvibus (ablative feminine, "with a thousand keys"),hōrummīllesaxōrum (genitive neuter, "of these thousand stones"). This use agrees with thepredicate in the plural:mīllemīlitēsvēnērunt ("a thousand soldiers came").

Alternatively it can function as a neuter singular noun, which is also indeclinable with the exception of the existence of a rare ablativemīllī. In this usage it governs apartitive genitive and agrees with the predicate in the singular:mīllemīlitumvēnit ("a thousand soldiers came").

A third and less preferred option combines the two uses by functioning as a neuter noun with plural predicate agreement, as inmīllemīlitumvēnērunt, perhaps in a partitive sense "a thousand men from among the soldiers".

Plural: The plural form,mīlia, normally behaves as adeclinable neuter noun of the third declension, inflects according to its grammatical function in the sentence (subject, direct object, etc.) and agrees with the predicate in the neuter plural. The associated noun being counted will necessarily be governed bymīlia in thegenitiveplural instead of agreeing with it as an adjective would:totmīliamīlitumcapta ("that many thousand of soldiers were captured"). If further modified by thecardinal numeralsduo ortrēs ("two/three thousand"), or bydistributive numerals likesingulī anddēnī ("one/ten each"), or any other declinable adjective, the latter will appear in the same gender (neuter) and grammatical case asmīlia:fuērunttriamīliaequōrum (nominative, "there were three thousand horses"),crepitusduōrummīliumsaxōrum (genitive, "the rumbling of two thousand stones"),insingulīsmīlibusnummumcollocātīs (ablative, "in every thousand sesterces invested" - notice the irregular genitive plural).

However, if part of a compound numeral ("one thousand five hundred"), and/or when used with personal reference in the absence of a dependent genitive, it again functions as an adjective (either substantivized or dependent on the other numeral), and the predicate takes masculine agreement unless the personal reference is an exclusively feminine group:duomīliacaptī ("two thousand were captured"),duomīliaquīngentīmīlitēscaptī ("two thousand five hundred soldiers were captured"),triamīliaquīngentae (mīlitēs)captae ("three thousand five hundred women (soldiers) were captured").

Latin cardinal numerals larger thanvīgintī(“twenty”), that are not multiples of ten, are assembled as compound words. The components of these compounds are the numeralsūnus(“one”) throughnovem(“nine”) and the multiples ofdecem(“10”), the multiples ofcentum(“100”), andmīlle(“1000”).

Compound numerals in Latin are assembled by one of two basic methods: additive or subtractive. Most compound numerals areadditive, meaning that the value of the compound numeral is calculated byadding the values of the component words. However, a few Latin compound numerals aresubtractive, meaning that the value of the compound numeral is calculated bysubtracting the values of the component words. A large-valued compound numeral may incorporate both additive and subtractive components.

Of the Latin compound cardinal numerals less thancentum(“100”), sixteen are normallysubtractive. All of these special cases represent values that are one or two less than a multiple of ten, and have names that subtract from a starting value rather than adding to that value. These sixteen exceptions are displayed in the table at right. Note that in Classical Latin, the compound cardinal numerals for 98 and 99 are not among the special cases (with one counterexample in Pliny the Elder), but instead are formed in the usual additive way. Subtractive compounds normally are written as single words (with no spaces) and areindeclinable.

Numerals representing cardinal values that are eight more (two less) than a multiple of ten are constructed literally as:

duo(“two”) +dē(“from”) +multiple of ten

Thus, the numeral for 48 is normally written asduodēquīnquāgintā(“two from fifty”), rather than as the expectedquadrāgintāoctō(“forty-eight”) oroctōetquadrāgintā(“eight and forty”). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.

Numerals representing cardinal values that are nine more (one less) than a multiple of ten are constructed literally as:

ūn-(“one”) +dē(“from”) +multiple of ten

Thus, the numeral for 49 is normally written asūndēquīnquāgintā(“one from fifty”), rather than as the expectedquadrāgintānovem(“forty-nine”) ornovemetquadrāgintā(“nine and forty”). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.

Numbers are almost always treated as adjectives, and often come before the noun. They may be used alone assubstantive nouns, but as most are indeclinable, this tends to be ambiguous.Mīlle behaves differently; in the plural, asmīlia, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be "duomīliamīlitum" (literally, "two thousands of soldiers). Thus a mile ismīllepassūs (literally, "a thousand paces"), but two miles isduo mīlia passuum (literally, "two thousands of paces").

To denote one's age, which in English is expressed in the constructionI am ... years old, in Latin one would most commonly sayHabeō ...annōs (literally, "I have ... years"). The numeral is in the accusative plural, if it declines. One may also express it through a genitive construction... annōrum (of ... years) with the number declined in genitive, e.g.Andreāsvīgintīūnīusannōrumest (Andrew is of twenty-one years, meaningAndrew is 21 years old). The following unique words are however used for infants:

• hornōtinus, a, um: 0-years-old^[1]
  • mēnsuālis, e: 1-month-old^[2]
  • bimēstris, e: 2-months-old^[3]
  • trimēstris, e: 3-months-old^[4]
  • quadrimēstris, e: 4-months-old^[5]
  • quīnquemēstris, e: 5-months-old^[6]
  • semēstris, e: 6-months-old^[7]
  • (Late Latin)septemmēstris, e: 7-months-old^[8]
  • (*octōmēstris?): 8-months-old
  • (New Latin)novemmēstris, e: 9-months-old^[9]
  • decemmēstris, e: 10-months-old^[10]
  • (*undecemmēstris?): 11-months-old
• anniculus, a, um: 1-year-old,yearling^[11]
• bīmus, a, um: 2-years-old^[12]
• trīmus, a, um: 3-years-old^[13]
• quadrīmus, a, um: 4-years-old^[14]
• (rare,Medieval Latin)quīnquīmus, a, um: 5-year-old^[15]

After that, one may also create a one-word adjective with the suffix-ennis, derived fromannus, yielding toquīnquennis,sexennis, etc. Please note that all these words are adjectives on their own and thus need to agree with the name they refer to: e.g.,Duōshabeōlīberōs,maiornātūestRichardustrīmus,minornātūestMarīaannicula. (I have two children, the eldest named Richard is three-years-old, the youngest Mary is one-year-old; more literally,the eldest is the three-year-old Richard, the youngest is the one-year-old Mary).

• Appendix:Roman numerals
• Roman numerals on Wikipedia.Wikipedia

• Numerical appendices
• Latin appendices
• Latin numerals

• Latin links with redundant target parameters