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 | *Hoi-no-/*Hoi-wo-/*Hoi-k(ʷ)o-; *sem- | *Hoi(H)nos ; sem-/sm̥- |
| two | *d(u)wo- | *du̯oh₁ |
| three | *trei- (full grade) / *tri- (zero grade) | *trei̯es |
| four | *kʷetwor- (o-grade) / *kʷetur- (zero grade) (see also the kʷetwóres rule) |
*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”) | *ǵʰesl- |
Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction (by Brugmann) for thousand is *tūsḱmtiə. See also Fortson 2004.
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 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.
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) | *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:
- “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 ” (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 aṣṭamá– “eighth” and Lithuanian deviñtas “ninth”.
Reflexes
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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 | *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. tuwa/i-, Lyc. kbi-, Mil. tba-, 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, Roman. doi, 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, Roman. trei,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, 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 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, 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 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. sëhs/sechs, Gaul. suex, Ir. sé/sé, Welsh chwech, Arm. vec῾/vec῾/vec῾, Toch. ṣäk/ṣkas, OPruss. usjai, Latv. seši, Lith. šešì, OCSšestĭ, Pol. sześć, Roman. șase, 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, Roman. șapte, 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, Roman. opt, Osc. uhto, ONátta, 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, Roman. nouă, 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, 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 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, Kurdish sih, si. |
| forty | *kʷetwr̥̄ḱomt- | Skr. catvāriṅśat, Gk. τεσσεράκοντα tessarákonta, Lat. quadrāgintā, Lith. keturias-de-šimt, Kurdish chil. |
| fifty | *penkʷēḱomt- | Skr. pañcāśat, Gk. πεντήκοντα pentêkonta, Lat. quinquāgintā, Ir. /caoga, Lith. penkias-de-šimt, Kurdish pe`nci, penca. |
| sixty | *s(w)eḱsḱomt- | Skr. ṣaṣṭih, Gk. ἐξήκοντα exêkonta, Lat. sexāgintā, Ir. /seasca, Lith. šešias-de-šimt, Russ. šest’desjat, Kurdish shest. |
| seventy | *septm̥̄ḱomt- | Skr. saptatih, Gk. heptákonta, Lat. septuāgintā, Ir. /seachtó, Lith. septynias-de-šimt, Russ. sem’desjat, Kurdish hefte`, hefta. |
| eighty | *h₃eḱtō(u)ḱomt- | Skr. aśītih, Gk. ὀγδοήκοντα ogdοêkonta, Lat. octāgintā, Ir. /ochtó, Lith. aštuonias-de-šimt, Russ. vosem’desjat, Kurdish heshte`, heshta. |
| ninety | *(h₁)newn̥̄ḱomt- | Skr. navatih, Gk. ἐνενήκοντα enenêkonta, Lat. nonāgintā, Ir. /nócha, Lith. devynias-de-šimt, Russ. devjanosto, Kurdish not, newet. |
| hundred | *ḱm̥tom | 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 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. tūkstantis, Latv. tūkstots, OCStysǫšti, Pol. tysiąc, Russ. tys’ača | |
| *wel-tyo- | 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 | *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) |
|---|---|---|
| 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, Pol. pierwszy, Russ. pervyj, Toch. parwät/parwe |
| *pr̥h₃-mó- | 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. prōtos, 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. deúteros, Russ. vtoroj |
| third | *tri-t(y)ó- | Ved. tr̥tīya-, Gk. trítos, Lat. tertius,Alb. (i) tretë, Lith. trečias < *tretias, Russ. tretij |
| fourth | *kʷetwr̥-tó- | Gk. tétartos, Eng. feorþa/fourth, OCS četvirĭtŭ,Alb. (i) katërt, Lat. quartus, Lith. ketvirtas, Russ. chetv’ortyj |
| fifth | *penkʷ-tó- | Av. puxδa-, Gk. pémptos,Lat. quīntus, Alb. (i) pestë, Lith. penktas, Russ. p’atyj |
| sixth | *sweḱs-tó- | Gk. héktos, Lat. sextus,Alb.(i) gjashtë, Lith. šeštas, Russ. šestoj |
| seventh | *septm̥-(m/t)ó- | Gk. hébdomos, Lat. septimus, OCS sedmŭ,Lith. septintas, sekmas, Russ. sed’moj |
| eighth | *h₃eḱtōw-ó- | Gk. ógdo(w)os, Lat. octāvus,Russ. vos’moj, Lith. aštuntas, ašmas |
| ninth | *(h₁)newn̥-(n/t)ó- | Lat. nōnus,Gk. énatos, Russ. dev’atyj, Lith. devintas |
| tenth | *deḱm̥-(m/t)ó- | Ved. daśamá-, Av. dasəma-, Lat. decimus,Gk. dékatos, Lith. dešimtas, Russ. desjatyj |