Proto-Indo-European numerals explained

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)	Reconstruction (Beekes)
one
two
three	(full grade) / (zero grade)
four	(o-grade) / (zero grade) (see also the kʷetwóres rule)
five
six	originally perhaps
seven
eight	or,
nine
ten
twenty	originally perhaps
thirty	originally perhaps
forty	originally perhaps
fifty	originally perhaps
sixty	originally perhaps
seventy	originally perhaps
eighty	originally perhaps
ninety	originally perhaps
hundred	originally perhaps
thousand	(originally "big hundred")

Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction (by Brugmann) for thousand is . See also Fortson 2004.

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

Lehmann believes that the numbers greater than ten were constructed separately in the dialect groups and that originally meant "a large number" rather than specifically "one hundred."

Gender of numerals

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

Numerals as prefixes

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

Number	Prefix (Fortson)
one- (together, same)
two-
three-
four-	or

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 (related to some adverbs meaning "forth, forward, front" and to the particle "forth", thus originally meaning "foremost" or similar) plus various suffixes like (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, modern Icelandic annar).
• "third" to "sixth" were formed from the cardinals plus the suffix : "third" etc.
• "seventh" to "tenth" were formed by adding the thematic vowel to the cardinal: "eighth" etc.

The cardinals ending in a syllabic nasal (seven, nine, ten) inserted a second nasal before the thematic vowel, resulting in the suffixes and . These and the suffix spread to neighbouring ordinals, seen for example in Vedic Indic languages: aṣṭa'''má'''- "eighth" and Lithuanian Lithuanian: deviñ'''ta'''s "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
one	^[1]	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
	^[2]	Rodopi, 2019. pp. 203–218. doi: https://doi.org/10.1163/9789004409354_015	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	^[3]	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	^[4]	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) sê
four	^[5]	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	^[6]	Luv. pa^nta, 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	^[7]	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	^[8]	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	^[9]	Lyc. aitãta-,^[10] 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	^[11]	Lyc. ñuñtãta-,^[12] 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	^[13]	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		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		Skr. triṅśat, Gk. τριάκοντα triákonta, Lat. trīgintā, Ir. trícho/tríocha, Lith. tris-de-šimt, Kurdish (Kurmanji) sih, sî
forty		Skr. catvāriṅśat, Gk. τεσσαράκοντα tessarákonta, Lat. quadrāgintā, Ir. cethorcho/ceathracha, Lith. keturias-de-šimt, Kurdish (Kurmanji) çil
fifty		Skr. pañcāśat, Gk. πεντήκοντα pentḗkonta, Lat. quinquāgintā, Ir. coíca/caoga, Lith. penkias-de-šimt, Kurdish (Kurmanji) pênceh, pêncî
sixty		Skr. ṣaṣṭih, Gk. ἑξήκοντα hexḗkonta, Lat. sexāgintā, Ir. sesca/seasca, Lith. šešias-de-šimt, Russ. šest'desjat, Kurdish (Kurmanji) şêst
seventy		Skr. saptatih, Gk. ἑβδομήκοντα hebdomḗkonta, Lat. septuāgintā, Ir. sechtmoga/seachtó, Lith. septynias-de-šimt, Russ. sem'desjat, Kurdish (Kurmanji) heftê
eighty		Skr. aśītih, Gk. ὀγδοήκοντα ogdoḗkonta, Lat. octōgintā, Ir. ochtmoga/ochtó, Lith. aštuonias-de-šimt, Russ. vosem'desjat, Kurdish (Kurmanji) heştê
ninety		Skr. navatih, Gk. ἐνενήκοντα enenḗkonta, Lat. nōnāgintā, Ir. nócha/nócha, Lith. devynias-de-šimt, Russ. devjanosto, Kurdish (Kurmanji) not, newet
hundred	^[14]	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		Skr. sahasram, Av. hazarəm, Pers. /hazār, Gk. χίλιοι khílioi, Lat. mīlle, Kurdish (Kurmanji) hezar
		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
	^[15]	Toch. wälts/yaltse; OCS velьjь/velikъ

In the following languages, reflexes separated by slashes mean:

• Albanian: Tosk Albanian / Gheg Albanian
• Armenian: Classical Armenian / Eastern Armenian / Western Armenian
• English: Old English / Modern English
• German: Old High German / New High German
• Irish: Old Irish / Modern Irish
• Ossetic: Iron / Digor
• Persian: Old Persian / Modern Persian
• Tocharian: Tocharian A / Tocharian B

Reflexes of the feminine numbers

Number	Reconstruction	Reflexes
three		Ved. tisrás, Av. tišrō, Gaul. tidres, Ir. teoir/?
four		Ved. cátasras, Av. cataŋrō, Lith. keturios, Ir. cetheoir/?

Reflexes of the numeral prefixes

Number	Reconstruction	Reflexes (with examples)
one- (together, same)		Ved. sa-kŕ̥t "once", Gk. ᾰ̔πλόος haplóos "one-fold, simple", Lat. sim-plex "one-fold"
two-		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-		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-		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		Ved. pūrviyá-, Lat. prīvus, OCS prĭvŭ, Pol. pierwszy, Russ. pervyj, Toch. parwät/parwe
		Goth. fruma, Lith. pìrmas, Latv. pirmais, Lat. prīmus, Osc. perum
	other forms	Eng. fyrst/first, 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		Skr. dvitīya, Gk. δεύτερος deúteros, Russ. vtoroj
third		Ved. tr̥tīya-, Gk. τρίτος trítos, Lat. tertius, Alb. (i) tretë, Lith. trečias < *tretias, Russ. tretij
fourth		Gk. τέταρτος tétartos, Eng. feorþa/fourth, OCS četvrĭtŭ, Alb. (i) katërt, Lat. quārtus, Lith. ketvirtas, Russ. chetv'ortyj
fifth		Av. puxδa-, Gk. πέμπτος pémptos, Lat. quīntus, Alb. (i) pestë, Lith. penktas, Russ. p'atyj
sixth		Gk. ἕκτος héktos, Lat. sextus, Alb.(i) gjashtë, Lith. šeštas, Russ. šestoj
seventh		Gk. ἕβδομος hébdomos, Lat. septimus, OCS sedmŭ, Lith. sẽkmas (then displaced by the neologism "septintas") Russ. sed'moj
eighth	s	Gk. ὄγδο(ϝ)ος ógdo(w)os, Lat. octāvus, Russ. vos'moj
	oḱtm-o-s?	Lith. ašmas (then displaced by the neologism "aštuntas")
ninth		Lat. nōnus, Gk. ἔνατος énatos, Pruss. newīnts; Russ. dev'atyj
tenth		Ved. daśamá-, Av. dasəma-, Lat. decimus, Gk. δέκατος dékatos, Lith. dešimtas, Russ. desjatyj

Further reading

• Bammesberg, Alfred (1995). "Latin quattuor and Its Prehistory". In: Journal of Indo-European Studies (JIES) 23 (1-2): 213–222.
• Beekes, Robert S. P. (1987). "The Word for 'Four' in Proto-Indo-European". In: Journal of Indo-European Studies (JIES) 15 (1/2): 215–219.
• Bomhard, Allan. "Some thoughts on the Proto-Indo-European cardinal numbers". In: In Hot Pursuit of Language in Prehistory: Essays in the four fields of anthropology. In honor of Harold Crane Fleming. Edited by John D. Bengtson. John Benjamins Publishing Company, 2008. pp. 213-221. 10.1075/z.145.18bom.

Notes and References

1. Blažek, Václav. "Indo-European "one" and "first"". In: Sborník prací Filosofické fakulty Brněnské university, A 47. Brno: MU, 1999. p. 7-27. A 47. .
2. de Vaan, Michiel. "Proto-Indo-European *sm and *si 'one'". In: The Precursors of Proto-Indo-European. Leiden, The Netherlands: Brill
3. Blažek, Václav. "Indo-European "two"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 1998. p. 5-25. A 46. .
4. Blažek, Václav. "Indo-European "three"". In: Lingua Posnaniensis, Polsko: neznámý, 1998, vol. 40, No 1, p. 33-45. .
5. Blažek, Václav. "Indo-European "four"." In: Indogermanische Forschungen, Berlin: Walter de Gruyter, 1998, vol. 103, No 1, p. 112-134. .
6. Blažek, Václav. "Indo-European "five"". In: Indogermanische Forschungen, Berlin-NY: Walter de Gruyter, 2000, vol. 105, No 1, p. 102-120. .
7. Blažek, Václav. "Indo-European "six"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 2000. p. 5-18. A 48. .
8. Blažek, Václav. "Indo-European 'Seven'". In: Journal of Indo-European Studies, Monograph Series 22 (1997): 9-29.
9. Blažek, Václav. "Indo-european "eight"". In: Historische Sprachforschung. SRN: neznám, 1998, vol. 111, No 1, p. 209-224. .
10. [Craig Melchert]
11. Blažek, Václav. "Indo-European "nine"". In: Historische Sprachforschung. Göttingen: Vanderhoeck & Ruprecht, 1999. vol. 112, No 2, p. 188-390. .
12. "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.
13. 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. .
14. Blažek, Václav. "Indo-European "hundred"". In: History of Language. Melbourne: Association for the History of Language, 1999, 5.2, No 2, p. 71-82. .
15. Douglas Q. Adams, A Dictionary of Tocharian B, 2nd ed., 2013, s.v. yaltse