# Welsh numerals

The traditional counting system used in the Welsh language is vigesimal, 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 ten y" unit(s), e.g. thirty-five (35) in decimal is tri deg pump (three ten five) while in vigesimal it is pymtheg ar hugain (fifteen – itself "five-ten" – on twenty).

## Numerals

| Number | Vigesimal system | Decimal system |
| 0 | sero/dim | sero/dim |
| 1 | un | un |
| 2 | dau (m), dwy (f) | dau (m), dwy (f) |
| 3 | tri (m), tair (f) | tri (m), tair (f) |
| 4 | pedwar (m), pedair (f) | pedwar (m), pedair (f) |
| 5 | pum(p) | pum(p) |
| 6 | chwe(ch) | chwe(ch) |
| 7 | saith | saith |
| 8 | wyth | wyth |
| 9 | naw | naw |
| 10 | deg/un deg, deng | deg/un deg, deng |
| 11 | un ar ddeg ("one on ten") | un deg un |
| 12 | deuddeg, deuddeng | un deg dau/dwy |
| 13 | tri/tair ar ddeg | un deg tri/tair |
| 14 | pedwar/pedair ar ddeg | un deg pedwar/pedair |
| 15 | pymtheg, pymtheng | un deg pump |
| 16 | un ar bymtheg ("one on fifteen") | un deg chwech |
| 17 | dau/dwy ar bymtheg | un deg saith |
| 18 | deunaw/tri/tair ar bymtheg ("two nines"/"three on fifteen") | un deg wyth |
| 19 | pedwar/pedair ar bymtheg | un deg naw |
| 20 | ugain | dau ddeg |
| 21 | un ar hugain ("one on twenty") | dau ddeg un |
| 22 | dau/dwy ar hugain | dau ddeg dau/dwy |
| 23 | tri/tair ar hugain | dau ddeg tri/tair |
| 24 | pedwar/pedair ar hugain | dau ddeg pedwar/pedair |
| 25 | pump ar hugain | dau ddeg pump |
| 26 | chwech ar hugain | dau ddeg chwech |
| 27 | saith ar hugain | dau ddeg saith |
| 28 | wyth ar hugain | dau ddeg wyth |
| 29 | naw ar hugain | dau ddeg naw |
| 30 | deg ar hugain ("ten on twenty") | tri deg |
| 31 | un ar ddeg ar hugain | tri deg un |
| 32 | deuddeg ar hugain | tri deg dau/dwy |
| etc. |||
| 40 | deugain ("two twenty") | pedwar deg |
| 41 | deugain ac un ("two twenty and one") | pedwar deg un |
| 50 | deg a deugain | pum deg hanner cant ("half a hundred") |
| 51 | un ar ddeg a deugain | pum deg un hanner cant ac un |
| 60 | trigain ("three twenty") | chwe deg |
| 61 | trigain ac un | chwe deg un |
| 70 | deg a thrigain ("ten and three twenty") | saith deg |
| 71 | un ar ddeg a thrigain ("one on ten and three twenty") | saith deg un |
| 80 | pedwar ugain ("four twenty") | wyth deg |
| 81 | pedwar ugain ac un | wyth deg un |
| 90 | deg a phedwar ugain ("ten and four twenty") | naw deg |
| 91 | un ar ddeg a phedwar ugain ("one on ten and four twenty") | naw deg un |
| 100 | can(t) | can(t) |
| 200 | dau gant | dau gant |
| 300 | tri chant | tri chant |
| 400 | pedwar cant | pedwar cant |
| 500 | pum cant | pum cant |
| 600 | chwe chant | chwe chant |
| 700 | saith cant | saith cant |
| 800 | wyth cant | wyth cant |
| 900 | naw cant | naw cant |
| 1000 | mil | mil |
| 2000 | dau fil/dwy fil | dau fil/dwy fil |
| 1,000,000 | miliwn | miliwn |
| 1,000,000,000 | biliwn | biliwn |
| 1,000,000,000,000 | triliwn | triliwn |

## 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" (dau and dwy), "three" (tri and tair) and "four" (pedwar and pedair), which must agree with the grammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (pump, chwech and cant) 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 forms deng, deuddeng, pymtheng 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 mil, 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. 1965 mil naw chwe(ch) pump. This system appears to have broken down for years after 2000, e.g. whereas 1905 is mil naw dim pump, 2005 is dwy fil a phump.
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

The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where o ("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 ar ("on") in the traditional system.
Nouns are also mutated following many numbers. Un triggers the soft mutation (treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. Dau and dwy both trigger the soft mutation (ll and rh included). Tri (but not tair) and chwe trigger the aspirate mutation. Several higher numbers (pum, saith, wyth, deng, deuddeng, and pymtheng) trigger the nasal mutation when used with blynedd ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with o, the soft mutation is used as is normal after o.
The following example illustrates several of these points:
| English | Thirty-six dogs |
| Traditional system | UnOnecidogaronbymthegfifteenaronhugaintwentyUn ci ar bymtheg ar hugainOne dog on fifteen on twenty |
| Traditional system | UnOnearonbymthegfifteenaronhugaintwentyoofgŵndogsUn ar bymtheg ar hugain o gŵnOne on fifteen on twenty of dogs |
| Decimal system | TriThreedegtenchwesixchidogTri deg chwe chiThree ten six dog |
| Decimal system | TriThreedegtenchwechsixoofgŵndogsTri deg chwech o gŵnThree ten six of dogs |