7.1 Cardinal numbers

Definition of cardinal numbers

Cardinal numbers answer the question quot? ("how many?"). In Latin, they express specific quantities: one soldier, five ships, a hundred years. They're distinct from ordinal numbers (which show position: first, second, third) and distributive numbers (which show grouping: three each).

Role in Latin

Cardinal numbers appear constantly in Latin texts for counting, dates, ages, distances, and military descriptions. They also correspond to Roman numerals in inscriptions and documents, so recognizing them helps you read both written-out Latin and numeral forms like XIV or DCII.

Relationship to ordinal numbers

Cardinal numbers tell you how many; ordinal numbers tell you which one in a sequence. Ordinals are built from their corresponding cardinals with adjusted endings (e.g., quattuor → quartus). You'll want to learn cardinals first, since ordinals depend on them.

Cardinal numbers 1–10

Here are the basic ten:

Declension patterns

The big distinction: ūnus, duo, and trēs decline (change form for gender, number, and case), while quattuor through decem are indeclinable and never change form.

• Ūnus, -a, -um follows first/second declension patterns, but only has singular forms. It also has the characteristic -īus genitive and -ī dative (like sōlus or tōtus).
• Duo has its own irregular declension with masculine duo, feminine duae, and neuter duo.
• Trēs declines as a third-declension plural adjective: masculine/feminine trēs, neuter tria.

Usage in sentences

Cardinal numbers typically function as adjectives and agree with the noun they modify (when declinable). They usually precede the noun but can follow it for emphasis.

• trēs mīlitēs — three soldiers
• ūnā cum nāve — with one ship (ablative)
• duo flūmina — two rivers (neuter nominative/accusative)

Cardinal numbers 11–100

Formation principles

Numbers 11–17 are formed by placing the unit before -decem:

• 11 = ūndecim, 12 = duodecim, 13 = trēdecim, 14 = quattuordecim, 15 = quīndecim, 16 = sēdecim, 17 = septendecim

For 18 and 19, Latin often uses subtractive forms, counting backward from 20:

• 18 = duodēvīgintī (literally "two from twenty"), though octōdecim also exists
• 19 = ūndēvīgintī ("one from twenty"), alongside nōvemdecim

The tens have their own forms: vīgintī (20), trīgintā (30), quadrāgintā (40), quīnquāgintā (50), sexāgintā (60), septuāgintā (70), octōgintā (80), nōnāgintā (90).

Compound numbers between tens connect with et: vīgintī et ūnus (21) or ūnus et vīgintī. The order can go either way.

Common variations

The subtractive pattern repeats at each tens boundary: duodētrīgintā (28), ūndēquadrāgintā (39), and so on. All numbers from 4 to 100 are indeclinable, but compounds containing ūnus, duo, or trēs may decline those elements.

Cardinal numbers 101–1000

Compound number structure

Hundreds have their own forms: centum (100), ducentī (200), trecentī (300), quadringentī (400), quīngentī (500), sescentī (600), septingentī (700), octingentī (800), nōngentī (900).

For compound numbers, combine hundreds + tens + units in descending order:

• 256 = ducentī quīnquāgintā sex
• 319 = trecentī ūndēvīgintī

Et connects tens and units but is typically not used between hundreds and tens.

Centum vs. the higher hundreds

Centum (100) is indeclinable. The hundreds from 200 to 900, however, do decline as plural first/second declension adjectives (e.g., ducentī, -ae, -a), agreeing in gender and case with their noun. This is a detail students often miss.

Indeclinable cardinal numbers

Most cardinal numbers in Latin never change form. Specifically, quattuor through centum and all the tens (vīgintī, trīgintā, etc.) stay the same no matter what noun they modify or what case that noun is in.

The special case of mīlle

Mīlle (1,000) has a split personality:

• As a singular, it's an indeclinable adjective: mīlle mīlitēs (a thousand soldiers)
• As a plural, it becomes a neuter noun mīlia that declines (genitive mīlium, etc.) and takes a genitive noun: tria mīlia mīlitum (three thousand soldiers, literally "three thousands of soldiers")

This singular/plural distinction with mīlle/mīlia is one of the trickiest points in Latin numerals, so pay close attention to it.

Declension of ūnus, duo, trēs

These three numbers are the ones you actually need to memorize declension forms for.

Ūnus, -a, -um

Declines like a first/second declension adjective, but with the -īus genitive singular and -ī dative singular across all genders (just like sōlus, tōtus, alius). Only singular forms exist.

Duo

Note the -ābus forms in the feminine dative/ablative, which help distinguish from masculine/neuter.

Trēs, tria

Declines as a third-declension adjective, plural only. Masculine and feminine share the same forms; neuter has tria in the nominative/accusative.

Hundreds (200–900)

These decline as regular first/second declension plural adjectives: ducentī, ducentae, ducenta, and so on through all cases. They agree in gender and case with the noun they modify.

Cardinal numbers in context

Expressing age

Age is typically expressed with nātus/nāta plus the accusative of duration:

• Puer decem annōs nātus — A boy ten years old (literally "born ten years")

You can also use an ablative of quality or genitive of description, but the nātus + accusative construction is the most common.

Dates and years

The Roman calendar uses cardinal numbers for counting days relative to the Kalends, Nones, and Ides. Years are often given with annō plus an ordinal (for "in the Xth year") or with cardinal numbers in phrases like ante/post constructions. Recognizing cardinals is essential for interpreting any Latin date.

Cardinal numbers vs. distributives

Semantic differences

• Cardinal: trēs librōs habent — They have three books (total)
• Distributive: ternōs librōs habent — They have three books each

Distributives (singulī, bīnī, ternī, etc.) express "X apiece" or "X at a time."

When to use distributives instead

Distributives are required in two key situations:

1. With plural-only nouns (like castra, camp, or litterae, letter): you say bīna castra (two camps), not duo castra
2. To express "each" or "apiece" in distribution contexts

With plural-only nouns, using a cardinal number would be ambiguous or ungrammatical, so the distributive fills that role.

Agreement with nouns

Gender and case rules

For declinable cardinals (1–3, 200–900, and mīlia), the number must agree with its noun in gender and case:

• duae fēminae (two women, nominative feminine)
• trecentōrum mīlitum (of 300 soldiers, genitive masculine)

Indeclinable cardinals (4–100, mīlle singular) simply sit next to the noun without changing.

Plural-only nouns

Nouns like castra (camp), arma (arms), and litterae (letter) exist only in plural forms. For numbers 1–3, you use the distributive forms instead: ūna castra doesn't work; you say bīna castra for two camps. For indeclinable cardinals (4+), this isn't an issue since they don't change form anyway.

Cardinal numbers in poetry

Metrical considerations

Latin poets sometimes choose between alternate number forms to fit the meter. For instance, a poet might prefer octōdecim over duodēvīgintī (or vice versa) depending on which syllable pattern the verse requires. Knowing that these variant forms exist helps you recognize numbers even when they appear in less common shapes.

Stylistic uses

Numbers in poetry can carry symbolic weight. Specific numbers might allude to cultural or religious significance, and poets occasionally repeat numerical patterns for rhetorical effect. Poetic license also means you may encounter unusual constructions that wouldn't appear in prose.

Common Latin expressions with cardinal numbers

Several fixed phrases use cardinal numbers in ways worth memorizing:

• ūnō animō — with one mind, unanimously
• duōbus modīs — in two ways
• centum annōs — for a hundred years (accusative of duration)

Numbers also appear in Latin proverbs and legal formulas. In many of these expressions, the number carries figurative force rather than a literal count, so context matters for accurate translation.