When someone counts items, that person uses cardinal values. In grammatical terms, a cardinal numeral is a word used to represent such a countable quantity. The English words one, two, three, four, etc. are all examples of cardinal numerals.
In Latin, most cardinal numerals behave as indeclinable adjectives. They are usually associated with a noun that is counted, but do not change their endings to agree grammatically with that noun. The exceptions are ?nus ("one"), duo ("two"), tr?s ("three"), and multiples of centum ("hundred"), all of which decline. Additionally, although m?lle ("thousand") is an indeclinable adjective in the singular, it becomes a declinable noun in the plural. These exceptions are further explained in later sections.
|1 - 10||11 - 20||x 10||x 100|
|1||I||?nus, ?na, ?num||11||XI||?ndecim||10||X||decem||100||C||centum|
|2||II||duo, duae, duo||12||XII||duodecim||20||XX||v?gint?||200||CC||ducent?, -ae, -a|
|3||III||tr?s, tria||13||XIII||tr?decim||30||XXX||tr?gint?||300||CCC||trecent?, -ae, -a|
|4||IV||quattuor||14||XIV||quattuordecim||40||XL||quadr?gint?||400||CD||quadringent?, -ae, -a|
|5||V||qu?nque||15||XV||qu?ndecim||50||L||qu?nqu?gint?||500||D||qu?ngent?, -ae, -a|
|6||VI||sex||16||XVI||s?decim||60||LX||sex?gint?||600||DC||sescent?, -ae, -a|
|7||VII||septem||17||XVII||septendecim||70||LXX||septu?gint?||700||DCC||septingent?, -ae, -a|
|8||VIII||oct?||18||XVIII||duod?v?gint?||80||LXXX||oct?gint?||800||DCCC||octingent?, -ae, -a|
|9||IX||novem||19||XIX||?nd?v?gint?||90||XC||n?n?gint?||900||CM||n?ngent?, -ae, -a|
Inflection: The Latin ?nus ("one") inflects like an irregular first and second declension adjective. The irregularities occur in the singular genitive, which ends in -?us instead of the usual -? or -ae, and in the singular dative, which ends in -? instead of the usual -? or -ae.
The choice of ending will agree with the gender of the associated noun: ?nus equus ("one horse"), ?na cl?vis ("one key"), ?num saxum ("one stone"). The ending will also agree with the grammatical case of the associated noun: ?n?us equ? (genitive), ?nam cl?vem (accusative), ?n? sax? (dative).
Plural: Although it may seem strange at first sight, ?nus does have a set of plural forms. These forms are used when the associated noun has a plural form, but an inherently singular meaning. For example, the Latin noun castra ("camp") occurs only as a plural neuter form and takes plural endings, even though it identifies one object, hence: ?n?rum castr?rum ("of one camp").
Compounds: When ?nus is used to form compound numerals, such as ?nus et v?gint? ("twenty-one"), the case and gender agree with the associated noun, although the singular is used: v?gint? et ?nam f?min?s v?d? . Unlike duo and tr?s, the word ?nus is almost never used with m?lle ("thousand") to indicate how many thousand.
|gen||du?rum (duûm)||du?rum||du?rum (duûm)|
Inflection: The Latin duo ("two") has a highly irregular inflection, derived in part from the old Indo-European dual number. While some of the endings resemble those of a first and second declension adjective, others resemble those of a third declension adjective. The inflection of amb? ("both") is very similar.
The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: duo equ? ("two horses"), duae cl?v?s ("two keys"), duo saxa ("two stones"). The ending will also agree with the grammatical case of the associated noun: du?s equ?s (accusative), du?rum cl?vium (genitive), du?bus sax?s (dative).
Compounds: When duo is used to form compound numerals, such as duo et v?gint? or v?gint? duo ("twenty-two"), the case and gender agree with the associated noun. This is also the case when used with the plural of m?lle ("thousand") to indicate how many thousands: duo m?lia ("two thousands"), du?rum m?lium ("of two thousands").
The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: tr?s equ? ("three horses"), tr?s cl?v?s ("three keys"), tria saxa ("three stones"). The ending will also agree with the grammatical case of the associated noun: tr?s equ?s (accusative), trium cl?vium (genitive), tribus sax?s (dative).
Compounds: When tr?s is used to form compound numerals, such as tr?s et v?gint? or v?gint? tr?s ("twenty-three"), the case and gender agree with the associated noun. This is also the case when used with the plural of m?lle ("thousand") to indicate how many thousands: tria m?lia ("three thousands"), trium m?lium ("of three thousands").
|1 - 10|
|1||I||?nus, ?na, ?num|
|2||II||duo, duae, duo|
The numerals quattuor ("four") through decem ("ten") are all indeclinable, 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 as quadrangle, quintuplet, sextuple, octopus). The numerals for 7 through 10 appear in the English names of months (September, October, November, and December). These months were the seventh through tenth of the Roman calendar, since the Roman year began with m?rtius ("March").
|11 - 20|
Latin cardinals larger than decem ("ten") but less than v?gint? ("twenty") are constructed by addition. The ending -decim (a form of decem) is attached to the numerals ?n?s through novem. The resultant compound carries the same value as the mathematical sum of the components. For example quattuordecim ("fourteen") is quattuor ("four") + decem ("ten"). English does much the same by attaching -teen (a form of ten) to smaller numerals, such as the numeral fourteen which is four + ten.
In some of these compounds, a spelling and pronunciation change occurs during the attachment, so that sex + decem drops the -x and lengthens the e to yield s?decim. This kind of change also occurs in English, as in five + ten which softens the sound of the v and drops the e to yield fifteen.
Exceptions: There are two exceptions to the general pattern for forming the teens. In Classical Latin, the numerals for 18 and 19 are more frequently written as subtractive compounds. So, although 18 may be written as oct?decim, it is more often written as duod?v?gint? (literally "two from twenty"). Likewise, the numeral for 19 may be written as novemdecim, but is more often encountered as ?nd?v?gint? ("one from twenty").
For more information about the subtractive pattern of construction, see the section on "counting backwards".
|Multiples of ten|
|Multiples of one hundred|
|100||C||centum 1||600||DC||sescent?, -ae, -a|
|200||CC||ducent?, -ae, -a||700||DCC||septingent?, -ae, -a|
|300||CCC||trecent?, -ae, -a||800||DCCC||octingent?, -ae, -a|
|400||CD||quadringent?, -ae, -a||900||CM||n?ngent?, -ae, -a|
|500||D||qu?ngent?, -ae, -a||1000||M||m?lle, m?lia (m?llia) 2|
|1centum does not inflect.|
2 see the following section on m?lle.
|C (adj.)||NN (noun)|
The Latin m?lle ("thousand") is irregular in that it has two forms. In the singular, it is an indeclinable adjective, but in the plural it is a noun that declines like a third declension neuter i-stem. Notice that the genitive plural ending is -ium.
Singular: In the singular, m?lle ("thousand") functions as an adjective. This singular form is indeclinable, so its ending will remain the same rather than agree with the case or gender of the associated noun. However, the associated noun will necessarily be plural: m?lle equ? ("thousand horses"), m?lle cl?v?s ("thousand keys"), m?lle saxa ("thousand stones"). This is true regardless of the case or gender of the associated noun.
Plural: In the plural, m?lia functions as a noun, and will inflect according to how it is used in the sentence (subject, direct object, etc.). The associated noun being counted will necessarily be in the genitive plural, and so will not agree with the grammatical case of m?lia. Note that, if the numeral before m?lia is duo or tr?s, then it will take a neuter form in the same grammatical case as m?lia: oct? m?lia equ?rum (nominative, "eight thousand of horses"), cum tribus m?libus cl?vium (ablative, "with three thousand of keys"), du?rum m?lium sax?rum (genitive, "of two thousand of stones").
Latin cardinal numerals larger than v?gint? ("twenty"), that are not multiples of ten, are assembled as compound words. The components of these compounds are the numerals ?nus ("one") through novem ("nine") and the multiples of decem ("10"), the multiples of centum ("100"), and m?lle ("1000").
Compound numerals in Latin are assembled by one of two basic methods: additive or subtractive. Most compound numerals are additive, meaning that the value of the compound numeral is calculated by adding the values of the component words. However, a few Latin compound numerals are subtractive, meaning that the value of the compound numeral is calculated by subtracting the values of the component words. A large-valued compound numeral may incorporate both additive and subtractive components.
|Tens +8 ( or -2 )||Tens +9 ( or -1 )|
|98||XCVIII||n?n?gint? oct?||99||XCIX||n?n?gint? novem|
Of the Latin compound numerals less than centum ("100"), sixteen are normally subtractive. 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 the compound numerals for 98 and 99 are not among the special cases, but instead are formed in the usual additive way. Subtractive compounds normally are written as single words (with no spaces) and are indeclinable.
Numerals representing cardinal values that are eight more (two less) than a multiple of ten are constructed literally as:
Thus, the numeral for 48 is normally written as duod?qu?nqu?gint? ("two from fifty"), rather than as the expected quadr?gint? oct? ("forty-eight") or oct? et quadr?gint? ("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:
Thus, the numeral for 49 is normally written as ?nd?qu?nqu?gint? ("one from fifty"), rather than as the expected quadr?gint? novem ("forty-nine") or novem et quadr?gint? ("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 as substantive nouns, but as most are indeclinable, this tends to be ambiguous. Mille behaves differently; in the plural, as milia, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be "duo milia militum" (literally, "two thousands of soldiers). Thus a mile is mille pass?s (literally, "a thousand paces"), but two miles is duo milia passuum (literally, "two thousands of paces").
To denote one's age, which in English is expressed in the construction I am ... years old, in Latin one would most commonly say Habeo ... annos (literally, "I have ... years"). The numeral is in the accusative plural, if it declines.