Latin Numbers

Latin cardinal numbers (unus through mille), ordinal numbers (primus through ultimus), distributive numerals (singuli, bini), and numeral adverbs (semel, bis, ter).

Cardinal Numbers (How Many?)

1–20 with Notes

# Latin Abbreviation Declines?
1 ūnus, ūna, ūnum I Yes (pronominal: gen. -īus, dat. -ī)
2 duo, duae, duo II Yes (see below)
3 trēs, tria III Yes (3rd decl. i-stem adj.)
4 quattuor IV (IIII) No
5 quīnque V No
6 sex VI No
7 septem VII No
8 octō VIII No
9 novem IX (VIIII) No
10 decem X No
11 ūndecim XI No
12 duodecim XII No
13 tredecim XIII No
14 quattuordecim XIV No
15 quīndecim XV No
16 sēdecim XVI No
17 septendecim XVII No
18 duodēvīgintī XVIII No
19 ūndēvīgintī XIX No
20 vīgintī XX No

Tens and Hundreds

Latin English Notes
vīgintī twenty —
trīgintā thirty —
quadrāgintā forty —
quīnquāgintā fifty —
sexāgintā sixty —
septuāgintā seventy —
octōgintā eighty —
nōnāgintā ninety —
centum one hundred indeclinable
ducentī, -ae, -a two hundred declines (1st-2nd decl. pl.)
trecentī, -ae, -a three hundred declines
quadringentī, -ae, -a four hundred declines
quīngentī, -ae, -a five hundred declines
sescentī, -ae, -a six hundred declines
septingentī, -ae, -a seven hundred declines
octingentī, -ae, -a eight hundred declines
nōngentī, -ae, -a nine hundred declines
mīlle one thousand indeclinable adjective
duo mīlia two thousand mīlia = declinable neuter noun

Which Numbers Decline and Why

Only 1, 2, 3, and the hundreds (200–900) are fully declined. All other cardinals (4–100, 1000) are indeclinable.

The logic is partly historical and partly practical:

  • ūnus declines because it functions as a pronoun-adjective (like nullus, ullus, solus) — genitive singular ūnīus, dative ūnī.
  • duo and trēs are ancient forms inherited from Proto-Indo-European that preserved their own declension patterns.
  • The hundreds (ducentī, trecentī, etc.) are adjectives formed from the numeral + centum and naturally decline in the plural.
  • Numbers from 4–10 became fixed and lost their inflection in Latin, unlike Greek which declined more of them.

Declension of ūnus, duo, trēs

ūnus, ūna, ūnum (one) — pronominal declension

Case Masc. Fem. Neut.
Nom. ūnus ūna ūnum
Gen. ūnīus ūnīus ūnīus
Dat. ūnī ūnī ūnī
Acc. ūnum ūnam ūnum
Abl. ūnō ūnā ūnō

Note: The genitive ūnīus and dative ūnī follow the same pattern as nullus, sōlus, tōtus, ipse, ille.

duo, duae, duo (two)

Case Masc. Fem. Neut.
Nom. duo duae duo
Gen. duōrum duārum duōrum
Dat. duōbus duābus duōbus
Acc. duōs (duo) duās duo
Abl. duōbus duābus duōbus

trēs, tria (three) — 3rd declension i-stem adjective

Case Masc./Fem. Neut.
Nom. trēs tria
Gen. trium trium
Dat. tribus tribus
Acc. trēs (trīs) tria
Abl. tribus tribus

Mīlle vs. Mīlia — A Critical Distinction

This is one of the most commonly confused points in Latin numerals.

mīlle (singular = 1,000):

  • Indeclinable adjective — it modifies a noun directly.
  • The noun it modifies is in the same case as the noun in the sentence (no genitive).
  • Example: mīlle mīlitēs vēnērunt — 1,000 soldiers came. (mīlitēs is nominative plural, not genitive.)

mīlia (plural = 2,000+):

  • Declinable neuter noun — it takes a partitive genitive.
  • Example: duo mīlia mīlitum vēnērunt — 2,000 soldiers came. (mīlitum is genitive plural.)
  • Example: sex mīlia passuum — 6,000 paces = 6 Roman miles. (passuum = genitive of passus)
Expression Latin Construction
1,000 soldiers mīlle mīlitēs mīlle + noun in same case
2,000 soldiers duo mīlia mīlitum mīlia + genitive plural
6,000 paces (6 miles) sex mīlia passuum mīlia + genitive plural
1,001 mīlle et ūnum —

Forming Compound Numbers

Numbers 21–99

Latin places the larger number first with et, or the smaller number first without et:

  • vīgintī ūnus or ūnus et vīgintī — 21
  • trīgintā duo or duo et trīgintā — 32
  • quīnquāgintā sex — 56

With nouns, the noun agrees with the final (smaller) element if that element is declinable: vīgintī ūnus mīles (21 soldiers, sg.); duo et vīgintī mīlitēs (22 soldiers, pl.).

Subtraction Compounds: duodē- and undē-

Latin forms 18 and 19 (and their multiples) by subtraction, not addition:

  • duodēvīgintī = 18 = two-from-twenty (2 away from 20)
  • ūndēvīgintī = 19 = one-from-twenty (1 away from 20)

This pattern extends to other tens:

Number Latin Literally
18 duodēvīgintī two-from-twenty
19 ūndēvīgintī one-from-twenty
28 duodētrīgintā two-from-thirty
29 ūndētrīgintā one-from-thirty
38 duodēquadrāgintā two-from-forty
48 duodēquīnquāgintā two-from-fifty
98 duodēcentum two-from-hundred
99 ūndēcentum one-from-hundred

Ordinal Numbers (Which in Order?)

All ordinals decline as 1st-2nd declension adjectives (prīmus, -a, -um). They agree with their noun in gender, number, and case.

# Latin Notes
1st prīmus, -a, -um "first" (superlative of prior)
2nd secundus, -a, -um also alter (the other of two)
3rd tertius, -a, -um
4th quārtus, -a, -um
5th quīntus, -a, -um
6th sextus, -a, -um
7th septimus, -a, -um
8th octāvus, -a, -um
9th nōnus, -a, -um
10th decimus, -a, -um
11th ūndecimus, -a, -um
12th duodecimus, -a, -um
13th tertius decimus
14th quārtus decimus
15th quīntus decimus
16th sextus decimus
17th septimus decimus
18th duodēvīcēsimus
19th ūndēvīcēsimus
20th vīcēsimus (vīgēsimus) both spellings found
21st vīcēsimus prīmus
30th trīcēsimus
100th centēsimus, -a, -um
1000th mīllēsimus, -a, -um
last ultimus / postrēmus

Common usage: prīmō annō (in the first year), rēx tertius (the third king), diē quārtō (on the fourth day).

Distributive Numerals (How Many Each?)

Distributive numerals express how many apiece or are used with pluralia tantum (nouns that exist only in the plural form).

Three main uses:

  1. Distributive sense: mīlitibus singula tēla data sunt — single spears were given to the soldiers (one each).
  2. With pluralia tantum: Since castra (camp), lītterae (letter), nūptiae (wedding) only have plural forms, cardinals cannot be used for "one." Singula castra = "one camp."
  3. Multiplication: bis bīna sunt quattuor — twice two is four.

All distributives are 1st-2nd declension adjectives (plural only).

# each Latin Notes
1 each singulī, -ae, -a also used in distributive / pluralia tantum context
2 each bīnī, -ae, -a
3 each ternī (trīnī), -ae, -a
4 each quaternī, -ae, -a
5 each quīnī, -ae, -a
6 each sēnī, -ae, -a
7 each septēnī, -ae, -a
8 each octōnī, -ae, -a
9 each novēnī, -ae, -a
10 each dēnī, -ae, -a
11 each ūndēnī
12 each duodēnī
20 each vīcēnī
100 each centēnī

Examples:

  • singula castra — one camp (not ūna castra, since castra is always plural)
  • bīnās lītterās accēpī — I received two letters (lītterae is always plural)
  • milites bīna tēla ferēbant — the soldiers were carrying two spears each

Numeral Adverbs (How Many Times?)

Times Latin Notes
once semel irregular
twice bis irregular
three times ter irregular
four times quater irregular
five times quīnquiēs (-ēns)
six times sexiēs
seven times septiēs
eight times octiēs
nine times noviēs
ten times deciēs
eleven times ūndeciēs
twenty times vīciēs
one hundred times centiēs
one thousand times mīliēs

In arithmetic: bis ternī sunt sex — twice three is six. Semel centum = centum — 1 × 100 = 100.

In compound interest and finance: Romans calculated interest using centēsimae (hundredths per month = 12% annually). Cicero's letters refer to bīnae centēsimae (24% per year).

Multiplication with distributives: quīnquiēs centēnī = 500 (five times a hundred each). This construction appears in Livy for large army counts.

Roman Numerals

Basic Symbols

Symbol Value
I 1
V 5
X 10
L 50
C 100
D 500
M 1,000

Reading Rules

  1. Additive: symbols are normally added left to right (larger to smaller): VIII = 8, XVI = 16, MDCCC = 1800.
  2. Subtractive notation: a smaller symbol before a larger one is subtracted: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900.
  3. Repetition: a symbol may be repeated up to three times: III = 3, XXX = 30, CCC = 300. (Some inscriptions use IIII instead of IV.)
  4. No zero: Romans had no symbol for zero. The word nūllus (none) was used in context.

Examples of Roman Numerals

Roman Value Common context
XIV 14 Caesar's Bellum Gallicum Book XIV
XLII 42 Year of reign
MCMXCIX 1999 Modern usage
MMXXVI 2026 Current year
MDCCCXII 1812 Historical date

Numerals in Inscriptions

Latin inscriptions often use Roman numerals for dates, ages, and years. The formula AN(NIS) VIXIT + numeral records the age at death: VIXIT ANNIS XLII — "he lived 42 years."

Dates are reckoned from the founding of Rome (ab urbe conditā, AUC): 753 BCE = Year 1 AUC. Caesar's death (44 BCE) = 709 AUC = anno DCC nonō ab urbe conditā.

The Latin Date System

The Romans did not number days of the month sequentially (1st, 2nd, 3rd...). Instead, each month had three fixed reference days, and other days were counted backward to the next reference day.

The Three Reference Days

Name Meaning Day in March, May, July, October Day in all other months
Kalendae Kalends 1st 1st
Nōnae Nones 7th 5th
Īdūs Ides 15th 13th

Mnemonic: "In March, July, October, May, the Nones fall on the 7th day."

Counting Backward

Days are counted inclusively (counting both the starting day and the reference day).

Formula: ante diem + ordinal + reference day name (in accusative)

  • prīdiē (the day before) is used for the day immediately before a reference day.
  • postrīdiē (the day after) refers to the day after.

Examples for March:

Modern date Latin expression
March 1 Kalendīs Mārtīīs (Ablative — "on the Kalends")
March 6 prīdiē Nōnās Mārtias (the day before the Nones)
March 7 Nōnīs Mārtīīs
March 14 prīdiē Īdūs Mārtias
March 15 Īdibus Mārtīīs (the Ides of March — Īdibus Mārtīīs)
March 16 ante diem XVII Kalendās Aprīlēs (17 days before the April Kalends, inclusive)
March 31 prīdiē Kalendās Aprīlēs

Caesar was assassinated on Īdibus Mārtīīs — the Ides of March (March 15, 44 BCE).

Counting Formula Explained

To find a date: ante diem [N] Kalendās/Nōnās/Īdūs [Month]

Example: March 10 = ? days before the Ides (March 15)?

  • Count: March 10, 11, 12, 13, 14, 15 = 6 days
  • So: ante diem VI Īdūs Mārtias (6th day before the Ides of March)

Time Expressions in Latin

Expressing the Year

The year is expressed with the ablative of time when:

Construction Example Translation
Consular dating M. Cicerone cōnsule when Marcus Cicero was consul
AUC year annō septingentēsimō in the 700th year (from Rome's founding)
Ablative + abhinc abhinc decem annīs ten years ago

Expressing the Day

  • Specific day: use the calendar formula above.
  • diē tertiō — on the third day (ablative of time).
  • diē quīntō post — on the fifth day afterward.
  • post diem tertium — on the third day after (accusative of extent of time).

Expressing the Hour

The Roman day (sunrise to sunset) was divided into 12 equal hours (hōrae), which varied in length by season.

  • hōrā prīmā — at the first hour (dawn)
  • hōrā sextā — at the sixth hour (midday/noon)
  • hōrā nōnā — at the ninth hour (mid-afternoon; the origin of the English word "noon")

Age Expressions

Latin offers several equivalent ways to express age:

Construction Example Translation
nātus + accusative + annōs nātus XVII annōs born 17 years ago = aged 17
annōs nātus + number annōs nātus XVII aged 17
Genitive of description homō annōrum XVII a man of 17 years
Ablative of description homō decem et octō annīs a man of 18 years
annīs + ablative number vigintī annīs maior older by 20 years

Inscriptions frequently use: VIXIT ANNIS XX — "he/she lived for 20 years."

Caesar writes of Vercingetorix as being in the prime of life; Cicero notes Pompey's age relative to his consulship using quō annō (in which year) constructions.

Mathematical Operations in Latin

Latin expressed arithmetic in a distinctive way:

Operation Latin Meaning
Addition trēs et quattuor sunt septem 3 + 4 = 7
Subtraction septem minus trēs sunt quattuor 7 − 3 = 4
Multiplication bis bīna (sunt) quattuor 2 × 2 = 4
Multiplication ter quīnī (sunt) quīndecim 3 × 5 = 15
Large multiplication quīnquiēs centēnī (sunt) quīngentī 5 × 100 = 500
Fractions dīmidia pars / semis one half
Three-quarters dodrans ¾ (from dē-quadrans "minus a quarter")

The distributive + adverb construction (bis bīna) was the standard way to express multiplication tables.

Numbers in Classical Latin Texts

Caesar's Bellum Gallicum — Army Sizes

Caesar frequently uses large numbers: mīlia + genitive for troop counts.

  • Helvētii numerum... CCLXIII mīlia — the Helvetii (counted) 263,000.
  • Equitēs octō mīlia — 8,000 cavalry.
  • Legiōnēs sex — six legions (simple cardinal, no genitive since legiōnēs is the main noun).

Livy's Historical Dates

Livy uses both consular dating and AUC years:

  • annō trecentēsimō sexāgēsimō quārtō ab urbe conditā — in the 364th year from the city's founding.
  • T. Quinctio C. Iuliō cōnsulibus — when Titus Quinctius and Gaius Julius were consuls.

Inscriptions (CIL Corpus Inscriptionum Latinarum)

Inscriptions compress information heavily and use standard abbreviations:

  • D.M. = Dīs Mānibus (to the divine shades)
  • VIX. AN. = vīxit annīs (he/she lived N years)
  • H.S.E. = hīc situs/a est (here lies)
  • ANN. LXXXII = annōrum octōgintā duōrum or annīs octōgintā duōbus (aged 82)
  • KAL. IAN. = Kalendīs Iānuāriīs (on the Kalends of January = January 1st)

A typical epitaph: D.M. / LUCIAE CORNELIAE / VIX. AN. XLII / MARITUS FECIT — "To the divine shades of Lucia Cornelia, who lived 42 years; her husband made (this tomb)."

Reference