Classical Languages - Latin - Morphology - Numerals

Numerals
Cardinals, Ordinals, Counting

Numerals

Prerequisites: First and second declensions, Third declension, Adjectives, Pronouns

Next: Verbs

Latin has four kinds of number word and a system of written figures. The cardinals answer the question how many? (ūnus, duo, trēs), the ordinals the question which in order? (prīmus, secundus), the distributives the question how many each? (singulī, bīnī), and the numeral adverbs the question how many times? (semel, bis, ter). This page gives the forms of all four, the declension of ūnus, duo, trēs and mīlle, the rules for compound numbers, the Roman figures and an outline of the Roman calendar. The numerals are adjectives (the cardinals above three are indeclinable adjectives), and the use of the cases with them is treated in the syntax section.

Cardinals

1 to 20

Number Roman Cardinal Ordinal
1 I ūnus, -a, -um prīmus
2 II duo, duae, duo secundus
3 III trēs, tria tertius
4 IV quattuor quārtus
5 V quīnque quīntus
6 VI sex sextus
7 VII septem septimus
8 VIII octō octāvus
9 IX novem nōnus
10 X decem decimus
11 XI ūndecim ūndecimus
12 XII duodecim duodecimus
13 XIII tredecim tertius decimus
14 XIV quattuordecim quārtus decimus
15 XV quīndecim quīntus decimus
16 XVI sēdecim sextus decimus
17 XVII septendecim septimus decimus
18 XVIII duodēvīgintī duodēvīcēsimus
19 XIX ūndēvīgintī ūndēvīcēsimus
20 XX vīgintī vīcēsimus

Tens and hundreds

Number Roman Cardinal Ordinal
30 XXX trīgintā trīcēsimus
40 XL quadrāgintā quadrāgēsimus
50 L quīnquāgintā quīnquāgēsimus
60 LX sexāgintā sexāgēsimus
70 LXX septuāgintā septuāgēsimus
80 LXXX octōgintā octōgēsimus
90 XC nōnāgintā nōnāgēsimus
100 C centum centēsimus
200 CC ducentī, -ae, -a ducentēsimus
300 CCC trecentī, -ae, -a trecentēsimus
400 CD quadringentī, -ae, -a quadringentēsimus
500 D quīngentī, -ae, -a quīngentēsimus
600 DC sescentī, -ae, -a sescentēsimus
700 DCC septingentī, -ae, -a septingentēsimus
800 DCCC octingentī, -ae, -a octingentēsimus
900 CM nōngentī, -ae, -a nōngentēsimus
1000 M mīlle mīllēsimus

Which cardinals are declined

Numbers Declension
1: ūnus pronominal adjective: genitive ūnīus, dative ūnī
2, 3: duo, trēs irregular, in the three genders (below); ambō both is declined like duo
4 to 100: quattuor ... centum indeclinable
200 to 900: ducentī ... nōngentī like the plural of bonus, -a, -um
1000: mīlle indeclinable adjective in the singular; plural mīlia, a neuter noun

Declension of ūnus, duo, trēs, mīlle

ūnus, -a, -um one

Masculine Feminine Neuter
Nominative ūnus ūna ūnum
Genitive ūnīus ūnīus ūnīus
Dative ūnī ūnī ūnī
Accusative ūnum ūnam ūnum
Ablative ūnō ūnā ūnō

ūnus is declined like nūllus and alter (see Pronouns). It also means alone, only (ūnus omnium), and the plural ūnī, -ae, -a means alone or goes with nouns that have only a plural: ūna castra one camp, ūnae litterae one letter.

duo two and trēs three

duo m. duo f. duo n. trēs m., f. trēs n.
Nominative duo duae duo trēs tria
Genitive duōrum duārum duōrum trium trium
Dative duōbus duābus duōbus tribus tribus
Accusative duōs, duo duās duo trēs, trīs tria
Ablative duōbus duābus duōbus tribus tribus

mīlle a thousand

  • In the singular, mīlle is an indeclinable adjective and agrees with its noun in apposition: mīlle hominēs a thousand men.
  • In the plural, mīlia is a neuter noun of the 3rd declension, declined mīlia, mīlium, mīlibus, mīlia, mīlibus, and it takes the partitive genitive of what is counted: duo mīlia hominum two thousand men, tria mīlia passuum three miles.
Count Latin
one thousand men mīlle hominēs
two thousand men duo mīlia hominum
of two thousand men duōrum mīlium hominum
with two thousand men duōbus mīlibus hominum

Compound numbers

  1. 21 to 99. The units may come first with et, or the tens first without et: vīgintī ūnus or ūnus et vīgintī (21); vīgintī duo or duo et vīgintī (22); quadrāgintā quīnque (45).
  2. 18 and 19, 28 and 29, and similar use two from and one from the next ten: duodēvīgintī (18), ūndēvīgintī (19), duodētrīgintā (28), ūndētrīgintā (29).
  3. Above 100 the larger number comes first, with or without et: centum vīgintī or centum et vīgintī (120), ducentī trīgintā quattuor (234).
  4. Agreement. The numerals that are declined agree with the noun in gender, number and case: duae legiōnēs, tribus diēbus, ūnus et vīgintī mīlitēs. The indeclinable numerals (quattuor to centum) do not change.
  5. With a partitive. A cardinal with ex or dē and the ablative gives one of: ūnus ex mīlitibus. mīlia takes the partitive genitive, as above.
  6. Fractions are expressed with pars: dīmidia pars or semis (a half), tertia pars (a third), quārta pars (a quarter), duae partēs (two thirds), trēs quārtae (three quarters).

Gallia est omnis dīvīsa in partēs trēs.

Gaul as a whole is divided into three parts. (Caesar, De Bello Gallico 1.1; trēs is feminine to agree with partēs)

Duās legiōnēs in Ītaliā cōnscrībit et trēs, quae circum Aquilēiam hiemābant, ex hībernīs ēdūcit.

He raises two legions in Italy and leads out three that were wintering around Aquileia from their winter quarters. (Caesar, De Bello Gallico 1.10; duās is feminine accusative, trēs stands for trēs legiōnēs)

Quī in longitūdinem mīlia passuum CCXL, in lātitūdinem CLXXX patēbant.

(Their territory) which extended in length 240 miles and in breadth 180. (Caesar, De Bello Gallico 1.2; mīlia passuum with a partitive genitive, and the figures CCXL and CLXXX read as ducenta quadrāgintā and centum octōgintā)

Mūrum in altitūdinem pedum sēdecim fossamque perdūcit.

He builds a wall sixteen feet high, and a ditch. (Caesar, De Bello Gallico 1.8; sēdecim is indeclinable and agrees with pedum)

Ordinals

The ordinals are adjectives of the 1st and 2nd declensions (prīmus, -a, -um) and agree with their nouns: tertiō diē on the third day, quīnta hōra the fifth hour. See the tables above for the forms.

  1. From 13 to 17 the ordinal is made of two words, both declined: tertius decimus, quārtus decimus.
  2. secundus and alter. secundus means second in a series and favourable; alter means the second of two and the other. For the first of two and the second of two Latin also uses prior and posterior.
  3. Compound ordinals are made like the cardinals: vīcēsimus prīmus (21st), centēsimus vīcēsimus (120th).
  4. Adverbs of order: prīmum first, deinde or tum then, dēnique finally; iterum a second time.

Distributives

The distributives answer the question how many each? They are adjectives of the 1st and 2nd declensions used in the plural.

Number Distributive Meaning
1 singulī, -ae, -a one each
2 bīnī, -ae, -a two each, two at a time
3 ternī, trīnī three each
4 quaternī four each
5 quīnī five each
6 sēnī six each
7 septēnī seven each
8 octōnī eight each
9 novēnī nine each
10 dēnī ten each
20 vīcēnī twenty each
100 centēnī a hundred each
1000 singula mīlia a thousand each

Uses:

Use Example (constructed) Translation
Distribution: each Singulīs mīlitibus bīna iūgera dedit. He gave two acres to each soldier.
Nouns that have only a plural bīna castra, trīnae litterae two camps, three letters
Multiplication Bis bīna quattuor sunt. Twice two is four.

One camp is ūna castra and two camps is bīna castra: the distributive replaces the cardinal with a plural-only noun, except for ūnus, which takes the plural ūna.

Numeral adverbs

Number Adverb Meaning
1 semel once
2 bis twice
3 ter three times
4 quater four times
5 quīnquiēs five times
6 sexiēs six times
7 septiēs seven times
8 octiēs eight times
9 noviēs nine times
10 deciēs ten times
20 vīciēs twenty times
100 centiēs a hundred times
1000 mīlliēs a thousand times
how many times? quotiēns how often
so many times totiēns so often

The forms from 5 to 10 end in -iēs, which is also found written -iēns. Other words in the series: the multiplicative adjectives simplex (single), duplex (double), triplex (triple), and the proportionals duplus, triplus.

Roman figures

Symbols

Symbol I V X L C D M
Value 1 5 10 50 100 500 1000

Rules

  1. Add the values when a symbol of smaller or equal value follows: VI = 6, XVIII = 18, MDC = 1600.
  2. Subtract when a smaller symbol stands before a larger one: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900.
  3. Repeat a symbol up to three times in a row: III, XXX, CCC, MMM. The ancients also wrote IIII for 4, which is still found on clock faces.
  4. A bar over a symbol multiplies it by 1000.
Roman Value Roman Value
XIV 14 CDXLIV 444
XLIX 49 MCMXCIX 1999
XCIX 99 MMXXVI 2026

The Roman calendar in outline

The Romans counted days backwards from three fixed days of each month:

Fixed day Name Date
the first of the month Kalendae, Kalendārum f. pl. (the Kalends) the 1st
the Nones Nōnae, Nōnārum f. pl. the 5th, but the 7th in March, May, July and October
the Ides Īdūs, Īduum f. pl. the 13th, but the 15th in March, May, July and October
  1. On the day itself the date is in the ablative: Kalendīs Mārtiīs on the Kalends of March, Īdibus Mārtiīs on the Ides of March.
  2. The day before a fixed day is prīdiē with the accusative: prīdiē Īdūs Mārtiās on the day before the Ides of March (14 March).
  3. The other days are counted back inclusively from the next fixed day: ante diem tertium Nōnās Mārtiās on the third day before the Nones of March (5 March). The abbreviation is a. d. III Non. Mart.
  4. The number is found with a formula. After the Ides, the number is the number of days in the month + 2 − the date, counted back to the next Kalends. For example, 25 December is ante diem VIII Kalendās Iānuāriās, since 31 + 2 − 25 = 8. Before the Ides (or before the Nones), count back from the Ides (or the Nones) with the number the date of the fixed day + 1 − the date: 10 March is ante diem VI Īdūs Mārtiās, since 15 + 1 − 10 = 6.
Month Adjective Nones Ides Days
January Iānuārius 5th 13th 31
February Februārius 5th 13th 28
March Mārtius 7th 15th 31
April Aprīlis 5th 13th 30
May Māius 7th 15th 31
June Iūnius 5th 13th 30
July Iūlius 7th 15th 31
August Augustus 5th 13th 31
September September 5th 13th 30
October Octōber 7th 15th 31
November November 5th 13th 30
December December 5th 13th 31

The year was named after the consuls, often in the ablative absolute (Cicerōne cōnsule, see Infinitive and participle constructions), or counted from the foundation of the city: ab urbe conditā (abbreviated a.u.c.).

Summary

Kind Question Examples
Cardinal how many? ūnus, duo, trēs, quattuor, centum, mīlle
Ordinal which in order? prīmus, secundus, tertius, centēsimus
Distributive how many each? singulī, bīnī, ternī, dēnī
Adverb how many times? semel, bis, ter, quater

Parsing practice

Give the number, the kind of numeral and the agreement.

  1. duae legiōnēs
  2. tribus diēbus
  3. mīlle mīlitēs
  4. duo mīlia mīlitum
  5. ūnīus
  6. bīna castra
  7. semel et bis
  8. tertiō diē
  9. CCXL (Caesar, De Bello Gallico 1.2)
  10. MMXXVI
  11. a. d. VIII Kal. Ian.
  12. sēdecim pedēs (Caesar, De Bello Gallico 1.8)
  13. quīngentī and nōngentī
  14. vīcēsimus prīmus

Answers

  1. Cardinal 2, feminine nominative or accusative plural to agree with legiōnēs: two legions.
  2. Cardinal 3, ablative to agree with diēbus: in three days, on three days.
  3. mīlle as an indeclinable adjective in apposition: a thousand soldiers.
  4. mīlia, a neuter plural noun, with the partitive genitive mīlitum: two thousand soldiers.
  5. Genitive singular of ūnus (all genders): of one.
  6. Distributive with a plural-only noun: two camps.
  7. Numeral adverbs: once and twice.
  8. Ordinal 3rd in the ablative of time: on the third day.
  9. The figures for 240, read ducenta quadrāgintā: 240 (with mīlia passuum, miles).
  10. The Roman figures for 2026: 2000 + 20 + 6.
  11. ante diem octāvum Kalendās Iānuāriās: 25 December.
  12. An indeclinable cardinal 16 with pedēs (or pedum in Caesar): sixteen feet.
  13. Cardinals 500 and 900, declined like the plural of bonus.
  14. Compound ordinal: the 21st.

Common pitfalls

  • Declining quattuor to centum. They are indeclinable.
  • Forgetting that duo and trēs agree. duae legiōnēs, tribus diēbus.
  • Using the genitive of ūnus in -ī. It is ūnīus.
  • Using mīlle with a partitive genitive in the singular, or mīlia without one. mīlle hominēs, but duo mīlia hominum.
  • Misspelling the thousands. mīlle and mīllēsimus have two l; the plural mīlia has one.
  • Counting ūna castra for two camps. It is bīna castra, the distributive.
  • Making 18 and 19 as octōdecim and novendecim. The usual forms are duodēvīgintī and ūndēvīgintī.
  • Using the cardinal for the ordinal. The third day is tertius diēs, not trēs diēs.
  • Confusing the Nones and the Ides in March, May, July and October. In these four months the Nones are on the 7th and the Ides on the 15th.
  • Counting the Roman date backwards without including the fixed day. The count is inclusive: prīdiē is the 2nd day.
  • Repeating a Roman symbol four times in standard use. Write IV, IX, XL, XC, CD and CM; IIII is a variant found on clock faces.

Self-test

  1. Decline duo in the feminine and trēs in the masculine.
  2. Give the genitive and the dative of ūnus.
  3. How do you say a thousand men, two thousand men and with two thousand men?
  4. Write in Latin: 18, 21, 45, 120, 234.
  5. Give the ordinals from 1st to 10th.
  6. How do you say two camps, and why?
  7. Translate Singulīs mīlitibus bīna iūgera dedit.
  8. Read as a Latin date: 25 December, 14 March, 5 March.
  9. Write in Roman figures: 14, 49, 99, 444, 1999, 2026.
  10. Read CCXL and CLXXX in Caesar, De Bello Gallico 1.2.

Answers

  1. duae, duārum, duābus, duās, duābus; trēs, trium, tribus, trēs, tribus.
  2. ūnīus; ūnī.
  3. mīlle hominēs; duo mīlia hominum; duōbus mīlibus hominum.
  4. duodēvīgintī; vīgintī ūnus or ūnus et vīgintī; quadrāgintā quīnque; centum vīgintī; ducentī trīgintā quattuor.
  5. prīmus, secundus, tertius, quārtus, quīntus, sextus, septimus, octāvus, nōnus, decimus.
  6. bīna castra: castra has only a plural, so the distributive replaces the cardinal.
  7. He gave two acres to each soldier.
  8. ante diem VIII Kalendās Iānuāriās; prīdiē Īdūs Mārtiās; ante diem III Nōnās Mārtiās.
  9. XIV; XLIX; XCIX; CDXLIV; MCMXCIX; MMXXVI.
  10. ducenta quadrāgintā and centum octōgintā: 240 and 180.

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