The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties where numbers from 11 to 14 are "1–4 on ten", 16–19 are "1–4 on fifteen" (though 18 is more commonly "two nines"); numbers from 21 to 39 are "1–19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.

There is also a decimal counting system, where numbers are "x ten y" unit(s), e.g. thirty-five (35) in decimal is (three ten five) while in vigesimal it is (fifteen – itself "five-ten" – on twenty).

Cardinal numbers Number Vigesimal system Decimal system 0 1 2 (m), (f) 3 (m), (f) 4 (m), (f) 5 6 7 8 9 10 , 11 ("one on ten") 12 , 13 14 15 , 16 ("one on fifteen") 17 18 ("two nines"/"three on fifteen") 19 20 21 ("one on twenty") 22 23 24 25 etc. 30 ("ten on twenty") 31 32 40 ("two twenty") 41 ("two twenty and one") 50 hanner cant/("half a hundred"/"ten and forty") 51 60 ("three twenty") 61 70 ("ten and three twenty") 71 ("one on ten and three twenty") 80 ("four twenty") 81 90 ("ten and four twenty") 91 ("one on ten and four twenty") 100 200 300 400 500 600 700 800 900 1000 2000 1,000,000 1,000,000,000 1,000,000,000,000

Ordinal numbers Despite a decimal system being used for cardinal numbers, there are no common ordinal numbers based on a decimal system, although "-fed" can be used as a suffix on the decimal numbers (e.g. "un deg unfed" for 11th), it is not generally accepted formally. NumberOrdinal 0feddimfed 1afcyntaf/unfed 2ailail 3yddtrydydd (m), trydedd (f) 4yddpedwerydd (m), pedwaredd (f) 5edpumed 6edchweched 7fedseithfed 8fedwythfed 9fednawfed 10feddegfed 11egunfed ar ddeg 12feddeuddegfed/ail ar ddeg 13egtrydydd ar ddeg (m), trydedd ar ddeg (f) 14egpedwerydd ar ddeg (m), pedwaredd ar ddeg (f) 15fedpymthegfed 16egunfed ar bymtheg 17egail ar bymtheg 18feddeunawfed 19egpedwerydd ar bymtheg (m), pedwaredd ar bymtheg (f) 20fedungeinfed 21ainunfed ar hugain 22ainail ar hugain 23aintrydydd ar hugain (m), trydedd ar hugain (f) 24ainpedwerydd ar hugain (m), pedwaredd ar hugain (f) 25ainpumed ar hugain 30aindegfed ar hugain 31ainunfed ar ddeg ar hugain 32aindeuddegfed ar hugain40feddeugainfed50fedhannercanfed/degfed ar ddeugain60fedtrigainfed70feddegfed ar trigain80fedpedwar ugeinfed (m), pedair ugeinfed (f)90feddegfed a phedwar ugain (m), degfed a phedair ugain (f)100fedcanfed200feddau ganfed1,000fedmilfed2,000feddwy filfed10,000feddeng milfed100,000fedcan milfed1,000,000fedmiliynfed1,000,000,000fedbiliynfed

Variation in form There is some syntactically and phonologically triggered variation in the form of numerals. There are, for example, masculine and feminine forms of the numbers "two" ( and ), "three" ( and ) and "four" ( and ), which must agree with the grammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (, and ) also have reduced forms (, , ) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (, , ) have the alternative forms , , used before nasals (which may be the result of mutation) and, occasionally, vowels; these forms are becoming less common. Numerals change as expected according to normal rules of consonant mutation; some also trigger mutation in some following words (see below for details).

Use of the decimal system The decimal system is widely used, but is rather uncommon for dates and ages. Larger numbers, however, tend to be expressed in this system e.g. 1,965 . In referring to years, on the other hand, the number of thousands is stated, followed by the individual digits, e.g. 1965 . This system appears to have broken down for years after 2000, e.g. whereas 1905 is , 2005 is .

The Welsh decimal counting system was devised by 19th-century Patagonian Welsh businessmen in Argentina for accountancy purposes. It was recommended to teachers for use in the first Welsh language schools in Patagonia by Richard Jones Berwyn in a book published in 1878. The system was later adopted in Wales in the late 1940s with the beginning of Welsh-medium education.

Use with nouns and mutations The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where ("of") with the plural noun follows the number. Except where using this plural form, the noun is placed directly after the number but before any parts of the number that are added using ("on") in the traditional system.

Nouns are also mutated following many numbers. triggers the soft mutation () of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. and both trigger the soft mutation (ll and rh included). (but not ) and trigger the aspirate mutation. Several higher numbers (, , , , , and ) trigger the nasal mutation when used with ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with , the soft mutation is used as is normal after .

The numbers "deg" (ten), "cant" (hundred), and "biliwn" (billion) are masculine, and "mil" (thousand) and "miliwn" (million) are feminine, and the forms of the numbers above must therefore correspond with these (e.g. "dau ddeg", "dau gant", "dau filiwn", and "dwy fil", "dwy filiwn"), this also distinguishes between "(2) biliwn" and "(2) miliwn" which both mutate to "filiwn".

The following example illustrates several of these points:

English Thirty-six dogs Traditionalsystem Decimalsystem

Notes