Number System

Irish has a rich and complex system for numbers, which differs significantly from English. This guide covers the main types of numbers you will encounter, from basic counting to more advanced forms like personal numbers and fractions. A key feature is the existence of two parallel counting systems: a modern decimal system and a traditional vigesimal (base-20) system.

The Number Systems

In Irish, there are two primary counting systems.

The Decimal System

The decimal system (an córas deachúlach) counts in steps of ten (20, 30, 40, etc.). Numbers between the tens are formed by adding units from 1 to 9. This system has been revived for modern use, especially in schools and official contexts.

• Substantival (counting): seachtó a dó - 72 (literally “70 and 2”)
• Adjectival (with a noun): dhá bhád is seachtó - 72 boats (literally “2 boats and 70”)

The Vigesimal System

The vigesimal system (an córas fichiúlach) counts in steps of twenty (20, 2x20, 3x20, etc.). Numbers between the twenties are formed by adding units from 1 to 19. This is the traditional system and is still common in the dialects.

• Substantival (counting): trí fichid a dó dhéag - 72 (literally “3x20 and 12”)
• Adjectival (with a noun): dhá bhád déag is trí fichid - 72 boats (literally “12 boats and 3x20”)

Substantival Cardinal Numbers

Substantival cardinal numbers (na maoluimhreacha) are used when counting or when the number stands alone, without a following noun.

Forms and the Number Particle a

The form of a number can change depending on whether it is used substantivally (for counting) or adjectivally (with a noun).

• The Number Particle a: When counting from 1 to 19, the numbers are usually preceded by the particle a. This particle prefixes h to numbers that start with a vowel.
  • a haon, a dó, a trí, a ceathair, a cúig, a sé, a seacht, a hocht, a naoi, a deich, a haon déag…

• Different Forms: The numbers for 2 and 4 have distinct substantival and adjectival forms.

• Numbers 11-19: These are formed by adding déag (“-teen”) after the base number. Déag is lenited to dhéag only after dó.
  • a haon déag (11), a dó dhéag (12), a trí déag (13)

• Full Tens: Numbers for full tens from 20 upwards (fiche, tríocha, etc.) are treated as nouns and do not take the particle a.

• Compound Numbers: In compound numbers like 28, the particle a reappears before the unit: fiche a hocht (28), caoga a naoi (59).

Usage of Substantival Numbers

Substantival numbers are used in specific contexts.

Counting and Enumerating

This is their primary function.

• a haon, a dó, a trí, a ceathair… - 1, 2, 3, 4…

Numbering

Used for identifying items like rooms, buses, or monarchs. The noun being numbered is considered definite, so no article is needed.

• seomra a trí - room no. 3
• bus fiche a haon - bus 21
• Eoin Pól a Dó - John Paul II

Telephone Numbers

• a náid, a dó, péire sé, a trí, a cúig, a sé, a hocht, a seacht - 0266-35687

Arithmetic

• a haon agus a dó, sin a trí - 1 and 2 is 3
• a ceathair faoina trí, sin a dó dhéag - 4 times 3 is 12
• a deich roinnte ar a cúig, sin a dó - 10 divided by 5 is 2

Years

Years from 1101 to 1999 are often read as two two-digit numbers.

• sa bhliain ocht déag dó dhéag - in the year 1812
• naoi déag fiche a trí - 1923
• cúig déag nócha a hocht - 1598

From 2000 onwards, dhá mhíle (two thousand) is used.

• dhá mhíle is a seacht - 2007
• dhá mhíle is a cúig déag - 2015

Dates

Dates can be given by numbering the day of the month.

• Iúil a ceathair, 1935 - 4th July 1935

Time

• Tá sé a haon a chlog - It is one o’clock.
• ar a trí a chlog - at 3 o’clock
• ceathrú tar éis a sé - a quarter past 6
• leathuair tar éis a seacht - half past 7

Use with Nouns (Partitive)

Substantival numbers can be used with nouns via the preposition de (of), creating a partitive sense.

• a trí déag de chapaill - 13 of the horses

Choices with nó

In phrases like “one or two”, the number dó is lenited.

• bád nó dhó - one boat or two
• uair nó dhó - once or twice

If a partitive de phrase follows, dó is not lenited.

• ceann nó dó de bháid - one or two boats
• trí nó ceathair de bháid - three or four boats

Counting Items

An exception is the full tens (e.g., fiche, tríocha), which are nouns and can stand alone.

Substantival Numbers with the Article

Number words can take the definite article an. When they do, they become fully-fledged nouns with genitive and plural forms.

• an t-aon - the one
• na haonta - the ones
• an fiche - the twenty
• an fhichead - of the twenty

This is used for:

• Naming numbers: an deich - the number ten
• Decades: na fichidí - the twenties; sna seascaidí - in the 60s
• Centuries and Millennia: i dtús an chéid seo - at the beginning of this century
• Large quantities: na céadta de na fir - hundreds of men
• Numbered objects: an t-ocht déag - the 18 (e.g., bus number 18)
• Playing cards: an trí hart - the 3 of hearts

Adjectival Cardinal Numbers

Adjectival cardinal numbers (na bunuimhreacha) are used with a noun to specify a quantity. They stand before the noun they modify.

• trí bhád - 3 boats

Forms and Basic Rules

• One: To say “one boat”, you must use amháin (only, alone).
  • bád amháin - one boat
  • aon bhád amháin - one boat

• People: For counting people, special personal numbers are usually preferred over adjectival numbers (e.g., triúr fear instead of trí fhear for “3 men”).

Mutations and Noun Forms

The number determines the mutation and the form (singular or plural) of the noun that follows.

• 1 (aon): Causes lenition and is followed by the singular noun.

  • aon bhád amháin - one boat

• 2 (dhá): Causes lenition and is followed by the singular or dual form of the noun. (The dual form is identical to the dative singular).

  • dhá bhád - 2 boats (singular)
  • dhá láimh - 2 hands (dual of lámh)

• 3-6: Cause lenition and are followed by the singular noun in modern standard Irish.

  • trí bhád - three boats
  • sé chat - six cats

• 7-10: Cause eclipsis and are followed by the singular noun in modern standard Irish.

  • seacht mbád - seven boats
  • deich gcat - ten cats

The Counting Plural

An older but still common practice, especially with units of measurement and frequently counted items, is to use a special plural form of the noun after numbers 3-10. This is often called the “counting plural”.

• After 3-6: The noun is in the plural and is not lenited. Vowel-initial nouns get an h-prefix.

  • trí bliana - three years (compare standard: trí bhliain)
  • trí huibhe - three eggs

• After 7-10: The noun is in the plural and is eclipsed.

  • seacht mbliana - seven years

This counting plural is mandatory for certain words, including:

• Years: trí bliana, seacht mbliana
• The general noun ceann (piece): trí cinn (3 pieces), seacht gcinn (7 pieces)
• Multiples of twenty: trí fichid (60, or 3 x 20)

Numbers 11-19

For numbers 11-19, the word déag comes after the noun. The initial number (1-9) follows its normal mutation rules.

• trí bhád déag - 13 boats
• seacht mbád déag - 17 boats
• naoi mbliana déag - 19 years

The form of déag itself can change:

• It is lenited (dhéag) after a singular noun ending in a vowel.
  • trí chóta dhéag - 13 coats
• It is lenited (dhéag) after a plural noun ending in a slender consonant (but not after cinn).
  • trí mhic dhéag - 13 sons
• It is not lenited in other cases.
  • trí bhád déag - 13 boats
  • trí bliana déag - 13 years

Numbers Above 20

Numbers above 20 combine the lower number and noun with the ten or twenty.

• Decimal System: trí bhád is seachtó - 73 boats (“3 boats and 70”)
• Vigesimal System: trí bhád déag is trí fichid - 73 boats (“13 boats and 3x20”)

The full tens and twenties (fiche, tríocha, caoga, etc.) are nouns, so the following noun is in the singular and is not mutated.

• fiche bliain - 20 years
• tríocha bád - 30 boats

There are several ways to connect the units to fiche (20):

• is fiche (“and 20”): trí bhád is fiche - 23 boats
• fichead (“of 20”): trí bhád fichead - 23 boats
• ar fhichid (“on 20”): trí bhád ar fhichid - 23 boats

Adjectives with Numbers

The form of an adjective depends on the number and the noun.

• After aon (1): Adjective is singular. It is lenited after a feminine noun.
  • aon fhear mór amháin - one big man
  • aon bhean mhór amháin - one big woman
• After dhá (2): Adjective is plural and lenited.
  • dhá bhád mhóra - two big boats
• After 3-10 + singular noun: Adjective is plural and lenited.
  • trí bhád mhóra - three big boats
• After 3-10 + plural noun: Adjective is plural. It is lenited after a noun ending in a slender consonant, but not after one ending in a vowel.
  • trí bliana móra - three big years
  • trí cinn mhóra - three big pieces
• With déag (11-19): déag comes between the noun and the adjective. The adjective is always plural.
  • trí bhád déag bheaga - 13 small boats
• After full tens (20, 30…): Adjective is singular. It is lenited after a feminine noun.
  • fiche fear mór - 20 big men
  • fiche bean mhór - 20 big women

Numbers with the Article

• an t-aon (the one): The singular article an is used. It always becomes an t-aon in the nominative.
  • an t-aon bhád amháin - the one/only boat
• an dá (the two): The dual article an is used, and dhá becomes dá.
  • an dá láimh - the two hands
• na trí, na ceithre… (the 3, the 4…): The plural article na is used.
  • na trí bhád - the three boats
  • na hocht mbád - the eight boats
• an fiche (the 20): The singular article an is used before full tens.
  • an fiche bliain - the 20 years

In the genitive case, these forms change:

• Genitive of “the one”: an aon (masc.), na haon (fem.).
• Genitive of “the two”: an dá (unchanged).
• Genitive of “the three”, etc.: The article becomes na and causes eclipsis on the number: seolta na dtrí bhád (the sails of the three boats).
• Genitive of “the twenty”, etc.: The article becomes an and causes lenition on the number: i rith an fhiche bliain (during the 20 years).

Counting with ceann

A common way to count things is to use the word ceann (piece) or its plural cinn, followed by the preposition de and the noun in the plural.

• dhá cheann de chaoirigh - 2 sheep
• trí cinn de chaoirigh - 3 sheep
• seacht gcinn déag de chaoirigh - 17 sheep

Variants and Notes

• daichead (40) is a compressed form of dá fhichead (two twenties).
• scór is an alternative word for fiche (twenty).
• leathchéad (“half-hundred”) is an alternative for caoga (50).
• dosaen (dozen) can be used: doiséinne uibheacha (a dozen eggs).
• When writing numbers as digits, a simplified grammar is often used in writing, where the noun remains in the singular nominative without mutations: 23 buidéal folamh. However, it would be pronounced fully: trí bhuidéal fholmha is fiche.

Personal Numbers

Personal numbers (na huimhreacha pearsanta) are special nouns used for counting people. They exist for numbers 2-10 and 12.

For other numbers (1, 11, 13+), the standard cardinal numbers are used with duine (person) or another noun.

Grammar of Personal Numbers

• They are nouns, not adjectives. beirt is feminine; the others are masculine.
• A following noun is usually in the genitive plural.
  • beirt fhear - two men
  • triúr ban - three women
• The noun is lenited after beirt, but not after the others.
• They can stand alone: Bhí triúr ann - There were three people there.
• They can be used in apposition with pronouns: siad triúr - the three of them.

Ordinal Numbers

Ordinal numbers (na horduimhreacha) indicate position in a sequence (first, second, third, etc.). They are used with the definite article and a noun.

Grammar of Ordinal Numbers

• an chéad (1st) always lenites the following noun.
• an dara (2nd) and higher do not cause lenition, but they prefix h to a following vowel-initial noun.
  • an dara hoíche - the second night
• Vowel-initial ordinals like ochtú (8th) and aonú (1st part of 11th, 21st, etc.) take a t-prefix after the article an: an t-ochtú, an t-aonú.
• In the genitive singular, the most common pattern is to lenite the ordinal number while the noun remains in the nominative: hata an cheathrú fear (the hat of the fourth man).
• The shorthand for ordinals is a trailing ú: 1ú, 2ú, 3ú.

Fractions

Fractions (na codáin) are nouns in Irish.

Simple Fractions (Numerator = 1)

• Special forms:
  • leath - half
  • trian - third
  • ceathrú - quarter
• Regular forms (5th to 10th): These are identical to the ordinal numbers.
  • cúigiú - a fifth
  • séú - a sixth
• Forms for 11th to 19th: These are formed by adding -ú to déag.
  • aondéagú - an eleventh
  • dódhéagú - a twelfth
• Alternative with cuid (part): Any fraction can be expressed using the ordinal number + cuid.
  • an ceathrú cuid den úll - a quarter of the apple (lit. “the fourth part of the apple”)

Complex Fractions (Numerator > 1)

There are several ways to form complex fractions:

• Cardinal number + fraction: dhá thrian (2/3), sé fichiú (6/20).
• Using de (of): a haon déag de dhódhéaguithe - 11/12 (lit. “eleven of the twelfths”).
• Using ar (on): a haon ar a haon déag - 1/11 (lit. “one on eleven”).

Decimal Fractions

The decimal point is ponc. Digits are read out individually using substantival numbers.

• 0.5: náid ponc a cúig
• 5.6: a cúig ponc a sé

Mixed Numbers

Mixed numbers combine a whole number and a fraction.

• For “half”, the phrase go leith (with half) is used.
  • úll go leith - one and a half apples
  • dhá ghloine go leith - two and a half glasses
• For “third”, go dtrian (with third) is used.
  • seacht n-uaire go dtrian - seven and a third hours
• Other fractions are connected with is (and).
  • úll is ceathrú - one and a quarter apples

Derived Forms

Numbers as Prefixes

Numbers can be used as prefixes, usually causing lenition.

• aon-: aontheangach (monolingual)
• dá-/dé-: dátheangach (bilingual)
• trí-: trídhathach (tricolour)
• céad-: céadcheap (to invent, lit. “first-think”)

Adjectives and Adverbs from Numbers

• Multiplicatives (adverbs):
  • Using uair (time): trí huaire (three times)
  • Using faoi: faoi dhó (twice), faoi thrí (three times)
• Adverbs from Ordinals (firstly, secondly…):
  • ar an gcéad dul síos - firstly
  • sa dara háit - secondly (lit. “in the second place”)
  • sa tríú cás - thirdly (lit. “in the third case”)