Proto-Indo-European numerals


The numerals and derived numbers of the Proto-Indo-European language have been reconstructed by modern linguists based on similarities found across all Indo-European languages. The following article lists and discusses their hypothesized forms.

Cardinal numbers

The cardinal numbers are reconstructed as follows:
NumberReconstruction Reconstruction
oneHoi-no-/*Hoi-wo-/*Hoi-ko-; *sem-Hoinos ; sem-/sm̥-
twodwo-du̯oh₁
threetrei- ' / tri- 'trei̯es
fourkʷetwor- ' / kʷetur- '
kʷétu̯ōr
fivepenkʷepenkʷe
sixseḱs; originally perhaps weḱsu̯éks
sevenseptm̥séptm̥
eightoḱtṓw or h₃eḱtō, h₃eḱtowh₃eḱteh₃
ninenewn̥néun
ten*déḱm̥/deḱm̥déḱm̥t
twentywīḱm̥t-; originally perhaps widḱomt-du̯idḱm̥ti
thirtytrīḱomt-; originally perhaps tridḱomt-trih₂dḱomth₂
fortykʷetwr̥̄ḱomt-; originally perhaps kʷetwr̥dḱomt-kʷeturdḱomth₂
fiftypenkʷēḱomt-; originally perhaps penkʷedḱomt-penkʷedḱomth₂
sixtyseḱsḱomt-; originally perhaps weḱsdḱomt-u̯eksdḱomth₂
seventyseptm̥̄ḱomt-; originally perhaps septm̥dḱomt-septm̥dḱomth₂
eightyoḱtōḱomt-; originally perhaps h₃eḱtodḱomt-h₃eḱth₃dḱomth₂
ninetynewn̥̄ḱomt-; originally perhaps h₁newn̥dḱomt-h₁neundḱomth₂
hundredḱm̥tom; originally perhaps dḱm̥tomdḱm̥tóm
thousandǵʰeslo-; tusdḱomti ǵʰesl-

Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction for thousand is tūsḱmtiə. See also Fortson 2004.
The elements -dḱomt- and dḱm̥t- are reconstructed on the assumption that these numerals are derivatives of *deḱm̥ "ten".
Lehmann believes that the numbers greater than ten were constructed separately in the dialect groups and that ḱm̥tóm originally meant "a large number" rather than specifically "one hundred."

Gender of numerals

The numbers three and four had feminine forms with the suffix -sr-, reconstructed as ti-sr- and kʷetwr̥-sr-, respectively.

Numerals as prefixes

Special forms of the numerals were used as prefixes, usually to form bahuvrihis :
NumberPrefix
one- sm̥-
two-dwi-
three-tri-
four-kʷtru- or kʷetwr̥-

Ordinal numbers

The ordinal numbers are difficult to reconstruct due to their significant variation in the daughter languages. The following reconstructions are tentative:
  • "first" is formed with pr̥h₃- plus various suffixes like -mo-, -wo-.
  • "second": The daughter languages use a wide range of expressions, often unrelated to the word for "two", so that no PIE form can be reconstructed. A number of languages use the form derived from *h₂enteros meaning "the other ".
  • "third" to "sixth" were formed from the cardinals plus the suffix -t-: tr̥-t- / tri-t- "third" etc.
  • "seventh" to "tenth" were formed by adding the thematic vowel -ó- to the cardinal: oḱtow-ó- "eighth" etc.
The cardinals ending in a syllabic nasal inserted a second nasal before the thematic vowel, resulting in the suffixes -mó- and -nó-. These and the suffix -t- spread to neighbouring ordinals, seen for example in Vedic aṣṭamá- "eighth" and Lithuanian deviñtas "ninth".

Reflexes

, or descendants of the PIE reconstructed forms in its daughter languages, include the following.

Reflexes of the cardinal numbers

In the following languages, reflexes separated by slashes mean:

Reflexes of the numeral prefixes

Reflexes of the ordinal numbers