# Proto-Indo-European numerals

The numerals and derived numbers of the Proto-Indo-European language (PIE) 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:

Number Reconstruction (Sihler)[1] Reconstruction (Beekes)[2]
one *Hoi-no-/*Hoi-wo-/*Hoi-k(ʷ)o-; *sem- *Hoi(H)nos ; sem-/sm̥-
two *d(u)wo- *du̯oh₁
*kʷétu̯ōr
five *penkʷe *penkʷe
six *s(w)eḱs; originally perhaps *weḱs *(s)u̯éks
seven *septm̥ *séptm̥
eight *oḱtō, *oḱtou or *h₃eḱtō, *h₃eḱtou *h₃eḱteh₃
nine *(h₁)newn̥ *(h₁)néun
ten *deḱm̥(t) *déḱm̥t
twenty *wīḱm̥t-; originally perhaps *widḱomt- *du̯idḱm̥ti
thirty *trīḱomt-; originally perhaps *tridḱomt- *trih₂dḱomth₂
forty *kʷetwr̥̄ḱomt-; originally perhaps *kʷetwr̥dḱomt- *kʷeturdḱomth₂
fifty *penkʷēḱomt-; originally perhaps *penkʷedḱomt- *penkʷedḱomth₂
sixty *s(w)eḱsḱomt-; originally perhaps *weḱsdḱomt- *u̯eksdḱomth₂
seventy *septm̥̄ḱomt-; originally perhaps *septm̥dḱomt- *septm̥dḱomth₂
eighty *oḱtō(u)ḱomt-; originally perhaps *h₃eḱto(u)dḱomt- *h₃eḱth₃dḱomth₂
ninety *(h₁)newn̥̄ḱomt-; originally perhaps *h₁newn̥dḱomt- *h₁neundḱomth₂
hundred *ḱm̥tom; originally perhaps *dḱm̥tom *dḱm̥tóm
thousand *ǵʰeslo-; *tusdḱomti (originally "a massive number"[citation needed]) *ǵʰesl-

Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction (by Brugmann) for thousand is *tūsḱmtiə.[3][4] See also Fortson 2004.[5]

The elements *-dḱomt- (in the numerals "twenty" to "ninety") and *dḱm̥t- (in "hundred") are reconstructed on the assumption that these numerals are derivatives of *deḱm̥(t) "ten".

Lehmann[6] believes that the numbers greater than ten were constructed separately in the dialects 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 *-s(o)r-, reconstructed as *t(r)i-sr- and *kʷetwr̥-sr-, respectively.[5]

## Numerals as prefixes

Special forms of the numerals were used as prefixes, usually to form bahuvrihis (like five-fingered in English):

Number Prefix (Fortson)[7]
one- (together, same) *sm̥-
two- *dwi-
three- *tri-
four- *kʷ(e)tru- or *kʷetwr̥-

## Ordinal numbers

The ordinal numbers are difficult to reconstruct due to their variety in the daughter languages. The following reconstructions are tentative:[8]

• "first" is formed with *pr̥h₃- (related to some adverbs meaning "forth, forward, front" and to the particle *prō "forth", thus originally meaning "foremost" or similar) plus various suffixes like *-mo-, *-wo- (cf. Latin primus, Russian perv-).
• "second": The daughter languages use a wide range of expressions, often unrelated to the word for "two" (including Latin and English), so that no PIE form can be reconstructed. A number of languages use the form derived from *h₂enteros meaning "the other [of two]" (cf. OCS vĭtorŭ, Lithuanuan añtras, Old Icelandic annarr)
• "third" to "sixth" were formed from the cardinals plus the suffix *-t(ó)-: *tr̥-t(ó)- / *tri-t(ó)- "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 (seven, nine, ten) inserted a second nasal before the thematic vowel, resulting in the suffixes *-mó- and *-nó-. These and the suffix *-t(ó)- spread to neighbouring ordinals, seen for example in Vedic aṣṭa- "eighth" and Lithuanian deviñtas "ninth".

## Reflexes

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

### Reflexes of the cardinal numbers

Number Reconstruction (Sihler) Reflexes[5][9]
one *Hoi-no- Alb. njã > një (dialectal nji;njo), Lith. vienas, Latv. viens, Gaul. oinos, Gm. ein/eins, Eng. ān/one, Gk. oios, Av. aēuua, Ir. óin/aon, Kashmiri akh, Lat. ūnus, Kamviri ev, Osc. uinus, OCS edinŭ, ON einn, OPruss. aīns, Osset. iu/ieu, Pers. aiva-/yek, Pol. jeden, Roman. unu, Russ. odin, Ved. aika, Umbr. uns, Goth. ains, Welsh un
*sem- Arm. mi/mek/meg, Alb. gjithë, Lith. sa, sav-as, Eng. sum/some, Gm. saman/zusammen, Gk. εἷς heis, Hitt. san, Av. hakeret, Ir. samail/samhail, Lat. semel, Lyc. sñta, Kamviri sâ~, Pers. hama/hamin, Russ. odin, yedin, perviy Ved. sakŕ̥t, Toch. sas/ṣe, Welsh hafal, ON sami, Goth. sama, Kurdish yek, ek, hev- as prefix.
two *du(w)o- Hitt. dā-, Luv. tuwi-, Lyc. tuwa, Ved. dvā(u), Av. duua, Pers. duva/do, Osset. dyuuæ/duuæ, Kashmiri zū', Kamviri dü, Gk. δύω dúō, Lat. duō, Osc. dus, Umbr. tuf, ON tveir, Goth. twai, Eng. twā/two, Gm. zwêne/zwei, Gaul. vo, Ir. dá/dó, Welsh dau, Arm. erkow/yerku/yergu, Toch. wu/wi, OPruss. dwāi, Latv. divi, Lith. dù, OCS dŭva, Pol. dwa, Russ. dva, Alb. dy;di/dy;dў, Kurdish du.
three *trei- Hitt. teriyaš (gen. pl.), Lyc. trei, Ved. tráyas, Av. θrāiiō, Pers. çi/se, Osset. ærtæ/ærtæ, Kashmiri tre, Kamviri tre, Gk. τρεῖς treĩs, Lat. trēs, Osc. trís, Umbr. trif, ON þrír, Goth. þreis, Eng. þrēo/three, Gm. drī/drei, Gaul. treis, Ir. treí/trí, Welsh tri, Arm. erek῾/yerek῾/yerek῾, Toch. tre/trai, OPruss. tri, Latv. trīs, Lith. trỹs, OCS trije, Pol. trzy, Russ. tri, Alb. tre/tre. se`(thr>s).
four *kʷetwor- Lyc. teteri, Ved. catvāras, Av. caθuuārō, Pers. /čahār, Osset. cyppar/cuppar, Kashmiri tsor, Kamviri što, Gk. téttares, Lat. quattuor, Osc. petora, Umbr. petor, ON fjórir, Goth. fidwor, Eng. fēower/four, Gm. feor/vier, Gaul. petor, Ir. cethir/ceathair, Welsh pedwar, Arm. čork῾/čors/čors, Toch. śtwar/śtwer, OPruss. keturjāi, Latv. četri, Lith. keturì, OCS četyre, Pol. cztery, Russ. četyre, Alb. katër;katrë/katër, Kurdish char, chwar.
five *pénkʷe Luv. panta, Ved. pañca, Av. panca, Pers. panča/panj, Osset. fondz/fondz, Kashmiri pā.~tsh Kamviri puč, Gk. πέντε pénte, Lat. quīnque, Osc. pompe, Umbr. pumpe, ON fimm, Goth. fimf, Eng. fīf/five, Gm. fimf/fünf, Gaul. pempe, Ir. cóic/cúig, Welsh pump, Arm. hing/hing/hink, Toch. päñ/piś, OPruss. pēnkjāi, Latv. pieci, Lith. penkì, OCS pętĭ, Pol. pięć, Russ. pjat', Alb. pesë/pes(ë);pês, Kurdish penc.
six *s(w)eḱs Ved. ṣáṣ, Av. xšuuaš, Pers. /šeš, Osset. æxsæz/æxsæz, Kashmiri śe, Kamviri ṣu, Gk. ἕξ héks, Lat. sex, Osc. sehs, Umbr. sehs, ON sex, Goth. saíhs, Eng. siex/six, Gm. sēhs/sechs, Gaul. suex, Ir. sé/sé, Welsh chwech, Arm. vec῾/vec῾/vec῾, Toch. ṣäk/ṣkas, OPruss. usjai, Latv. seši, Lith. šešì, OCS šestĭ, Pol. sześć, Russ. šest', Alb. gjashtë/gjasht(ë);xhasht, Kurdish shesh.
seven *septm̥ Hitt. šipta-, Ved. saptá, Av. hapta, Pers. hafta/haft, Osset. avd/avd, Kashmiri sath, Kamviri sut, Gk. ἑπτά heptá, Lat. septem, Osc. seften, ON sjau, Goth. sibun, Eng. seofon/seven, Gm. sibun/sieben, Gaul. sextan, Ir. secht/seacht, Welsh saith, Arm. ewt῾n/yot῾/yot῾ě, Toch. ṣpät/ṣukt, OPruss. septīnjai, Lith. septynì, Latv. septiņi, OCS sedmĭ, Pol. siedem, Russ. sem', Alb. shtatë/shtat(ë), Kurdish heft.
eight *h₃eḱtō Lyc. aitãta-, Ved. aṣṭā(u), Av. ašta, Pers. ašta/hašt, Osset. ast/ast, Kashmiri ā.ṭh, Kamviri uṣṭ, Gk. ὄκτω oktō, Lat. octō, Osc. uhto, ON átta, Goth. ahtau, Eng. eahta/eight, Gm. ahto/acht, Gaul. oxtū, Ir. ocht/ocht, Welsh wyth, Arm. owt῾/ut῾ě, Toch. okät/okt, OPruss. astōnjai, Latv. astoņi, Lith. aštuonì, OCS osmĭ, Pol. osiem, Russ. vosem', Alb. tëte/tet(ë), Kurdish hesht.
nine *(h₁)newn̥ Lyc. ñuñtãta-, Ved. nava, Av. nauua, Pers. nava/noh, Kashmiri nav, Kamviri nu, Gk. ἐννέ(ϝ)α enné(w)a, Lat. novem, Osc. nuven, Umbr. nuvim, ON níu, Goth. niun, Eng. nigon/nine, Gm. niun/neun, Gaul. navan, Ir. nói/naoi, Welsh naw, Arm. inn/inn/inně, TochA. ñu, OPruss. newīnjai, Latv. deviņi, Lith. devynì, OCS devętĭ, Pol. dziewięć, Russ. devjat', Alb. nëntë;nëndë/nând(ë);non(t), Kurdish neh, no.
ten *deḱm̥(t) Ved. dáśa, Av. dasa, Pers. daθa/dah, Osset. dæs/dæs, Kashmiri da.h, Kamviri duc, Gk. δέκα déka, Lat. decem, Osc. deken, Umbr. desem, ON tíu, Goth. taíhun, Eng. tīen/ten, Gm. zēhen/zehn, Gaul. decam, Ir. deich/deich, Welsh deg, Arm. tasn/tas/dasě, Toch. śäk/śak, OPruss. desīmtan, Latv. desmit, Lith. dẽšimt, OCS desętĭ, Pol. dziesięć, Russ. desjat', Alb. dhjetë/dhet(ë), Kurdish deh, de.
twenty *wīḱm̥t- Ved. viṁśatí-, Av. vīsaiti, Pers. /bēst, Kashmiri vuh, Kamviri vici, Doric ϝίκατι wíkati, Lat. vīgintī, Gaul. vocontio, Ir. fiche/fiche, M. Welsh ugein(t), Arm. k῾san/k῾san/k῾san, Toch. wiki/ikäṃ, Lith. dvi-de-šimt, Alb. njëzet/njizet, Kurdish bist.
thirty *trīḱomt- Skr. triṅśat, Gk. τριάκοντα triákonta, Lat. trīgintā, Ir. /tríocha, Lith. tris-de-šimt[citation needed], Kurdish sih, si.
forty *kʷetwr̥̄ḱomt- Skr. catvāriṅśat, Gk. τεσσεράκοντα tessarákonta, Lat. quadrāgintā, Lith. keturias-de-šimt[citation needed], Kurdish chil.
fifty *penkʷēḱomt- Skr. pañcāśat, Gk. πεντήκοντα pentêkonta, Lat. quinquāgintā, Ir. /caoga, Lith. penkias-de-šimt[citation needed], Kurdish pe`nci, penca.
sixty *s(w)eḱsḱomt- Skr. ṣaṣṭih, Gk. ἐξήκοντα exêkonta, Lat. sexāgintā, Ir. /seasca, Lith. šešias-de-šimt, Russ. šest'desjat[citation needed], Kurdish shest.
seventy *septm̥̄ḱomt- Skr. saptatih, Gk. heptákonta, Lat. septuāgintā, Ir. /seachtó, Lith. septynias-de-šimt, Russ. sem'desjat[citation needed], Kurdish hefte`, hefta.
eighty *h₃eḱtō(u)ḱomt- Skr. aśītih, Gk. ὀγδοήκοντα ogdοêkonta, Lat. octāgintā, Ir. /ochtó, Lith. aštuonias-de-šimt, Russ. vosem'desjat[citation needed], Kurdish heshte`, heshta.
ninety *(h₁)newn̥̄ḱomt- Skr. navatih, Gk. ἐνενήκοντα enenêkonta, Lat. nonāgintā, Ir. /nócha, Lith. devynias-de-šimt, Russ. devjanosto[citation needed], Kurdish not, newet.
hundred *ḱm̥tom Ved. śatám, Av. satəm, Pers. /sad, Osset. sædæ, Kashmiri śath, Gk. ἑκατόν hekatón, Lat. centum, ON hundrað, Goth. hund, Eng. hundred/hundred, Gm. hunt/hundert, Gaul. cantam, Ir. cét/céad, Welsh cant, Toch. känt/kante, Latv. simts, Lith. šim̃tas, OCS sŭto, Pol. sto, Russ. sto/sotnja, Kurdish sed.
thousand *(sm̥-)ǵʰéslo- Skr. sahasram, Av. hazarəm, Pers. /hazār, Gk. khilioi, Lat. mīlle, Kurdish hezar.
*tusdḱomti ON þúsund, Goth. þusundi, Eng. þusend/thousand, Gm. þūsunt/tausend, TochA. tmāṃ, TochB. tmāne/tumane, Lith. tūkst-ant-is, stūks-ant-is, Latv. tūkstots, OCS tysǫšti, Pol. tysiąc, Russ. tys'ača
*wel-tyo-[10] Toch. wälts/yaltse; OCS velьjь/velikъ

In the following languages, reflexes separated by slashes mean:

### Reflexes of the feminine numbers

Number Reconstruction Reflexes[5]
three *t(r)i-sr- Ved. tisrás, Av. tišrō, Gaul. tidres, Ir. teoir/?
four *kʷetwr̥-sr- Ved. cátasras, Av. cataŋrō, Lith. keturios, Ir. cetheoir/?

### Reflexes of the numeral prefixes

Number Reconstruction Reflexes (with examples)[7][11]
one- (together, same) *sm̥- Ved. sa-kŕ̥t "once", Gk. há-ploos "one-fold, simple", Lat. sim-plex "one-fold"
two- *dwi- Ved. dvi-pád- "two-footed", Gk. dí-pod- "two-footed", Archaic Lat. dui-dent "a sacrificial animal with two teeth", Lith. dvi-kojis "two-footed"
three- *tri- Ved. tri-pád- "three-footed", Gk. trí-pod- "three-footed (table)", Lat. tri-ped- "three-footed", Lith. tri-kojis "three-footed", Gaul. tri-garanus "having three cranes", Alb. tri-dhjetë "thirty" (three ten)
four- *kʷ(e)tru- Ved. cátuṣ-pád- "four-footed", Av. caθru-gaoša- "four-eared", Gk. tetrá-pod- "four-footed", Lat. quadru-ped- "four-footed", Lith. ketur-kojis "four-footed"

### Reflexes of the ordinal numbers

Number Reconstruction Reflexes
first *pr̥h₃-wó- Ved. pūrviyá-, OCS prĭvŭ,[8] Pol. pierwszy, Russ. pervyj, Toch. parwät/parwe
*pr̥h₃-mó- Goth. fruma, Lith. pìrmas,[8] Latv. pirmais, Lat. prīmus, Osc. perum
other forms Eng. fyrst/first,[8]

Hitt. para, Lyc. pri, Av. pairi, vienet-as, paoiriia, Osset. fyccag, farast/farast, Kamviri pürük, Gk. prōtos, Umbr. pert, ON fyrstr, Gm. furist/Fürst "prince, ruler"; fruo/früh "early", Ir. er/air, Welsh ar, OPruss. pariy, Alb. i parë

second *dwo-teró-[citation needed] Skr. dvitīya, Gk. deúteros, Russ. vtoroj[citation needed]
third *tri-tó- Ved. tr̥tīya-, Gk. trítos, Lat. tertius,[8]

Alb. (i) tretë, Lith. trečias < *tretias, Russ. tretij[citation needed]

fourth *kʷetwr̥-tó- Gk. tétartos, Eng. feorþa/fourth, OCS četvirĭtŭ,[8]

Alb. (i) katërt, Lat. quartus, Lith. ketvirtas, Russ. chetv'ortyj[citation needed]

fifth *penkʷ-tó- Av. puxδa-, Gk. pémptos,[8]

Lat. quintus, Alb. (i) pestë, Lith. penktas, Russ. p'atyj[citation needed]

sixth *sweḱs-tó- Gk. héktos, Lat. sextus,[8]

Alb.(i) gjashtë, Lith. šeštas, Russ. šestoj[citation needed]

seventh *septm̥-(m)ó- Gk. hébdomos, Lat. septimus, OCS sedmŭ,[8]

Lith. septintas, sekmas, Russ. sed'moj[citation needed]

eighth *h₃eḱtōw-ó- Gk. ógdo(w)os, Lat. octāvus,[8]

Russ. vos'moj, Lith. aštuntas, ašmas[citation needed]

ninth *(h₁)newn̥-(n)ó- Lat. nonus,[8]

Gk. énatos, Russ. dev'atyj, Lith. devintas[citation needed]

tenth *deḱm̥-(m)ó- Ved. daśamá-, Av. dasəma-, Lat. decimus,[8]

Gk. dékatos, Lith. dešimtas, Russ. desjatyj[citation needed]

## Notes

1. ^ Sihler (1995:402–24)
2. ^ Beekes (1995:212–16)
3. ^ Brugmann (1892:48)
4. ^ Meillet:372)
5. ^ a b c d Fortson (2004:131)
6. ^ Lehmann (1993:252–255)
7. ^ a b Fortson (2004:131–132)
8. Fortson (2004:132)
9. ^ Gvozdanovic (1991)
10. ^ Douglas Q. Adams, A Dictionary of Tocharian B, 2nd ed., 2013, ISBN 9401209367 s.v. yaltse
11. ^ Fortson (2004:120)