# 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 "big hundred"[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 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 *-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 significant variation 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, Lithuanian 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-[10] Alb. njã > një (dialectal nji/njo), Lith. vienas, Latv. viens, Gaul. oinos, Gm. ein/eins, Eng. ān/one, Gk. οἶος oîos, Av. aēuua, Ir. óin/aon, Kashmiri akh, Lat. ūnus, Roman. unu, Osc. uinus, OCS edinŭ, ON einn, OPruss. aīns, Osset. iu/ieu, Pers. aiva-/yek, Kamviri ev, Pol. jeden, Russ. odin, Ved. aika, Umbr. uns, Goth. ains, Welsh un, Kurdish (Kurmanji) yek/êk
*sem-[11] Arm. mi/mek/meg, Alb. gjithë, Lith. sa, sav-as, Eng. sum/some, Gm. saman/zusammen, Gk. εἷς heîs, 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
two *du(w)o-[12] Hitt. dā-, Luv. tuwa/i-, Lyc. kbi-, Mil. tba-, Ved. dvā(u), Av. duua, Pers. duva/do, Osset. dyuuæ/duuæ, Kashmiri zū', Kamviri dü, Gk. δύο dúo, Lat. duō, Osc. dus, Umbr. tuf, Roman. doi, 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 (Kurmanji) du
three *trei-[13] Hitt. teriyaš (gen. pl.), Lyc. trei, Ved. tráyas, Av. θrāiiō, Pers. çi/se, Osset. ærtæ/ærtæ, Kashmiri tre, Kamviri tre, Gk. τρεῖς treîs, Lat. trēs, Osc. trís, Umbr. trif, Roman. trei, 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. Kurdish (Kurmanji)
four *kʷetwor-[14] Lyc. teteri, Ved. catvāras, Av. caθuuārō, Pers. /čahār, Osset. cyppar/cuppar, Kashmiri tsor, Kamviri što, Gk. τέτταρες téttares, Lat. quattuor, Osc. petora, Roman. patru, 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 (Kurmanji) çar
five *pénkʷe[15] Luv. panta, Ved. pañca, Av. panca, Pers. panča/panj, Osset. fondz/fondz, Kashmiri pā.~tsh Kamviri puč, Gk. πέντε pénte, Lat. quīnque, Roman. cinci, 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 (Kurmanji) pênc
six *s(w)eḱs[16] Ved. ṣáṣ, Av. xšuuaš, Pers. /šeš, Osset. æxsæz/æxsæz, Kashmiri śe, Kamviri ṣu, Gk. ἕξ héx, Lat. sex, Osc. sehs, Umbr. sehs, ON sex, Goth. saíhs, Eng. siex/six, Gm. sëhs/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, Roman. șase, Russ. šest', Alb. gjashtë/gjasht(ë);xhasht, Kurdish (Kurmanji) şeş
seven *septm̥[17] Hitt. šipta-, Ved. saptá, Av. hapta, Pers. hafta/haft, Osset. avd/avd, Kashmiri sath, Kamviri sut, Gk. ἑπτά heptá, Lat. septem, Osc. seften, Roman. șapte, 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 (Kurmanji) heft
eight *h₃eḱtō[18] Lyc. aitãta-,[19] Ved. aṣṭā(u), Av. ašta, Pers. ašta/hašt, Osset. ast/ast, Kashmiri ā.ṭh, Kamviri uṣṭ, Gk. ὀκτώ oktṓ, Lat. octō, Roman. opt, 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 (Kurmanji) heşt
nine *(h₁)newn̥[20] Lyc. ñuñtãta-,[21] Ved. nava, Av. nauua, Pers. nava/noh, Kashmiri nav, Kamviri nu, Gk. ἐννέ(ϝ)α enné(w)a, Lat. novem, Osc. nuven, Umbr. nuvim, Roman. nouă, 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 (Kurmanji) neh, no
ten *deḱm̥(t)[22] Ved. dáśa, Av. dasa, Pers. daθa/dah, Osset. dæs/dæs, Kashmiri da.h, Kamviri duc, Gk. δέκα déka, Lat. decem, Osc. deken, Umbr. desem, Roman. zece, ON tíu, Goth. taíhun, Eng. tīen/ten, Gm. zëhen/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 (Kurmanji) 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 (Kurmanji) bîst
thirty *trīḱomt- Skr. triṅśat, Gk. τριάκοντα triákonta, Lat. trīgintā, Ir. trícho/tríocha, Lith. tris-de-šimt[citation needed], Kurdish (Kurmanji) sih, sî
forty *kʷetwr̥̄ḱomt- Skr. catvāriṅśat, Gk. τεσσαράκοντα tessarákonta, Lat. quadrāgintā, Ir. cethorcho/ceathracha, Lith. keturias-de-šimt[citation needed], Kurdish (Kurmanji) çil
fifty *penkʷēḱomt- Skr. pañcāśat, Gk. πεντήκοντα pentḗkonta, Lat. quinquāgintā, Ir. coíca/caoga, Lith. penkias-de-šimt[citation needed], Kurdish (Kurmanji) pênceh, pêncî
sixty *s(w)eḱsḱomt- Skr. ṣaṣṭih, Gk. ἑξήκοντα hexḗkonta, Lat. sexāgintā, Ir. sesca/seasca, Lith. šešias-de-šimt, Russ. šest'desjat[citation needed], Kurdish (Kurmanji) şêst
seventy *septm̥̄ḱomt- Skr. saptatih, Gk. ἑβδομήκοντα hebdomḗkonta, Lat. septuāgintā, Ir. sechtmoga/seachtó, Lith. septynias-de-šimt, Russ. sem'desjat[citation needed], Kurdish (Kurmanji) heftê
eighty *h₃eḱtō(u)ḱomt- Skr. aśītih, Gk. ὀγδοήκοντα ogdoḗkonta, Lat. octōgintā, Ir. ochtmoga/ochtó, Lith. aštuonias-de-šimt, Russ. vosem'desjat[citation needed], Kurdish (Kurmanji) heştê
ninety *(h₁)newn̥̄ḱomt- Skr. navatih, Gk. ἐνενήκοντα enenḗkonta, Lat. nōnāgintā, Ir. nócha/nócha, Lith. devynias-de-šimt, Russ. devjanosto[citation needed], Kurdish (Kurmanji) not, newet
hundred *ḱm̥tom[23] Ved. śatám, Av. satəm, Roman. sută, 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 (Kurmanji) sed
thousand *(sm̥-)ǵʰéslo- Skr. sahasram, Av. hazarəm, Pers. /hazār, Gk. χίλιοι khílioi, Lat. mīlle, Kurdish (Kurmanji) hezar
*tusdḱomti ON þúsund, Goth. þūsundi, Eng. þūsend/thousand, Gm. þūsunt/tausend, TochA. tmāṃ, TochB. tmāne/tumane, Lith. tūkstantis, Latv. tūkstots, OCS tysǫšti, Pol. tysiąc, Russ. tys'ača
*wel-tyo-[24] 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][25]
one- (together, same) *sm̥- Ved. sa-kŕ̥t "once", Gk. ᾰ̔πλόος haplóos "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-, Lat. prīvus, 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. πρῶτος prôtos, Umbr. pert, ON fyrstr, Gm. furist/Fürst "prince, ruler"; fruo/früh "early", Ir. er/air, Welsh ar, OPruss. pariy, Alb. i parë

second *(d)wi-teró- Skr. dvitīya, Gk. δεύτερος deúteros, Russ. vtoroj[citation needed]
third *tri-t(y)ó- Ved. tr̥tīya-, Gk. τρίτος trítos, Lat. tertius,[8]

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

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

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

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

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

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

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

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

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

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

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

ninth *(h₁)newn̥-(n/t)ó- Lat. nōnus,[8]

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

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

Gk. δέκατος 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. ^ Blažek, Václav. "Indo-European "one" and "first"". In: Sborník prací Filosofické fakulty Brněnské university, A 47. Brno: MU, 1999. p. 7-27. A 47. ISBN 80-210-2098-9.
11. ^ de Vaan, Michiel. "Proto-Indo-European *sm and *si 'one'". In: The Precursors of Proto-Indo-European. Leiden, The Netherlands: Brill|Rodopi, 2019. pp. 203–218. doi: https://doi.org/10.1163/9789004409354_015
12. ^ Blažek, Václav. "Indo-European "two"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 1998. p. 5-25. A 46. ISBN 80-210-1796-1.
13. ^ Blažek, Václav. "Indo-European "three"". In: Lingua Posnaniensis, Polsko: neznámý, 1998, vol. 40, No 1, p. 33-45. ISSN 0079-4740.
14. ^ Blažek, Václav. "Indo-European "four"." In: Indogermanische Forschungen, Berlin: Walter de Gruyter, 1998, vol. 103, No 1, p. 112-134. ISSN 0019-7262.
15. ^ Blažek, Václav. "Indo-European "five"". In: Indogermanische Forschungen, Berlin-NY: Walter de Gruyter, 2000, vol. 105, No 1, p. 102-120. ISSN 0019-7262.
16. ^ Blažek, Václav. "Indo-European "six"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 2000. p. 5-18. A 48. ISBN 80-210-2350-3.
17. ^ Blažek, Václav. "Indo-European 'Seven'". In: Journal of Indo-European Studies, Monograph Series 22 (1997): 9-29.
18. ^ Blažek, Václav. "Indo-european "eight"". In: Historische Sprachforschung. SRN: neznám, 1998, vol. 111, No 1, p. 209-224. ISSN 0935-3518.
19. ^ Craig Melchert stated: "Meriggi, 'Fs Hirt' 266, suggests 'eighty' and 'ninety' respectively for aitãta and nuñtata ... 'Eight' and 'nine' are not only more reasonable contextually ... The remaining *aita- and *nuñta- may be derived from *ok̂tō and *néwn̥ ... " Melchert, H. Craig. "New Luvo-Lycian Isoglosses". In: Historische Sprachforschung. 102 Band. 1 Heft. Vandenhoeck & Ruprecht. 1989. pp. 24-25. ISSN 0935-3518
20. ^ Blažek, Václav. "Indo-European "nine"". In: Historische Sprachforschung. Göttingen: Vanderhoeck & Ruprecht, 1999. vol. 112, No 2, p. 188-390. ISSN 0935-3518.
21. ^ "This numeral ... is obviously derived from the word for "nine". (...) The etymological connection with PIE *newn ... is evident ...". Eichner, Heiner. "Anatolian". In: Gvozdanovic, Jadranka (ed.). Indo-European numerals. Trends in linguistics: Studies and monographs n. 57. Berlin; New York: Mouton de Gruyter. 1991. p. 87. ISBN 3-11-011322-8
22. ^ Blažek, Václav. "Indo-European "ten"". In: Bygone voices reconstructed. On language origins and their relationships: In honor of Aharon Dolgopolski. Ed. by Vitalij V. Shevoroshkin & Harald U. Sverdrup. Copenhagen: Underskoven Publishers ApS, 2009. pp. 113-123. ISBN 978-87-91947-33-9.
23. ^ Blažek, Václav. "Indo-European "hundred"". In: History of Language. Melbourne: Association for the History of Language, 1999, 5.2, No 2, p. 71-82. ISSN 1441-5542.
24. ^ Douglas Q. Adams, A Dictionary of Tocharian B, 2nd ed., 2013, ISBN 9401209367 s.v. yaltse
25. ^ Fortson (2004:120)