The traditionalcounting system used in theWelsh language isvigesimal, i.e. based on twenties where numbers from 11 to 14 are "x on ten", 16–19 are "x on fifteen" (though 18 is more usually "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 teny" unit(s), e.g. thirty-five (35) in decimal istri deg pump (three ten five) while in vigesimal it ispymtheg ar hugain (fifteen – itself "five-ten" – on twenty).

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" (dau anddwy), "three" (tri andtair) and "four" (pedwar andpedair), which must agree with thegrammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (pump,chwech andcant) also have reduced forms (pum,chwe,can) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (deg,un deg dau/deuddeg,un deg pump/pymtheg) have the alternative formsdeng,deuddeng,pymtheng used before nasals (which may be the result of mutation) and, occasionally, vowels; these forms are becoming less common.^[1] Numerals change as expected according to normal rules ofconsonant mutation; some also trigger mutation in some following words (see below for details).^[2]

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. 1,965mil, naw cant chwe deg pump. In referring to years, on the other hand, the number of thousands is stated, followed by the individual digits, e.g. 1965mil naw chwe(ch) pump. This system appears to have broken down for years after 2000, e.g. whereas 1905 ismil naw dim pump, 2005 isdwy fil a phump.

The Welsh decimal counting system was devised by 19th-centuryPatagonian Welsh businessmen in Argentina for accountancy purposes. It was recommended to teachers for use in the first Welsh language schools in Patagonia byRichard Jones Berwyn in a book published in 1878. The system was later adopted in Wales in the late 1940s with the beginning ofWelsh-medium education.^[3]

The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, whereo ("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 usingar ("on") in the traditional system.

Nouns are also mutated following many numbers.Un triggers thesoft mutation (treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns.Dau anddwy both trigger the soft mutation (ll andrh included).Tri (but nottair) andchwe trigger the aspirate mutation. Several higher numbers (pum,saith,wyth,deng,deuddeng, andpymtheng) trigger the nasal mutation when used withblynedd ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form witho, the soft mutation is used as is normal aftero.

The following example illustrates several of these points:

• Welsh language
• Numerals

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