# Indian numbering system

The Indian numbering system is used in India, Pakistan and Bangladesh to express large numbers, which differs from the International System of Units. Commonly used quantities include lakh (one hundred thousand) and crore (ten million) – written as 1,00,000 and 1,00,00,000 respectively in some locales. For example: 150,000 rupees is "1.5 lakh rupees" which can be written as "1,50,000 rupees", and 30,000,000 (thirty million) rupees is referred to as "3 crore rupees" which can be written as "3,00,00,000 rupees".
There are names for numbers larger than crore, but they are less commonly used. These include arab (100 crore, 1 billion), kharab (100 arab, 100 billion), nil or sometimes transliterated as neel (100 kharab, 10 trillion), padma (100 nil, 1 quadrillion), shankh (100 padma, 100 quadrillion), and mahashankh (100 shankh, 10 quintillion). In common parlance (though inconsistent), the lakh and crore terminology repeats for larger numbers. Thus lakh crore is 1 trillion.
In the ancient Indian system, still in use in regional languages of India, there are words for (10$^{62}$). These names respectively starting at 1000 are sahasra, ayuta, laksha, niyuta, koti, arbhudha, abhja, karva, nikarva, mahapadma, shanmkhu, jaladhi, amtya, madhya, paraardha. In the Indian system, now prevalent in the northern parts, the next powers of ten are one lakh, ten lakh, one crore, ten crore, one arab (or one hundred crore), and so on.

## Multiples

The Indian system is decimal (base-10), same as in the International System of Units, and the first five orders of magnitude are named in a similar way: one (10$^0$), ten (10$^1$), one hundred (10$^2$), one thousand (10$^3$), and ten thousand (10$^4$). For higher powers of ten, naming diverges. The Indian system uses names for every second power of ten: lakh (10$^5$), crore (10$^7$), arab (10$^9$), kharab (10$^{11}$), etc. In the rest of the world, long and short scales, there are names for every third power of ten. The short scale uses million (10$^6$), billion (10$^9$), trillion (10$^{12}$), etc.

## Decimal formatting

The Indian system groups digits of a large decimal representation differently than the International System of Units. The Indian system does group the first three digits to the left of the decimal point. But thereafter, groups by two digits to align with the naming of quantities at multiples of 100.
| Indian | Rest of the world |
| 5,00,000 | 500,000 |
| 12,34,56,789 | 123,456,789 |
| 17,00,00,00,000 | 17,000,000,000 |
| 6,78,90,00,00,00,00,000 | 6,789,000,000,000,000 |
Like English and other locales, the Indian system uses a period as the decimal separator and the comma for grouping. While others use a comma for decimal separator and a thin space or point to group digits.

## Pronunciation in English

When speakers of indigenous Indian languages are speaking English, the pronunciations may be closer to their mother tongue; e.g. "lakh" and "crore" might be pronounced /lɑkʰ/, /kɑrɔːr/, respectively.
* lakh /lɑːkʰ/
* crore /kɹɔːɹ/ (or /kɹoʊɹ/ in American English)
* arab /ʌˈɾʌb/
* kharab /kʰʌˈɾʌb/

## Names of numbers

The table below includes the spelling and pronunciation of numbers in various Indian languages along with corresponding short scale names.
| Value | Short scale | Indian English | Hindustani Hindi / Urdu | Marathi | Bengali | Odia | Nepali | Tamil | Telugu | Kannada | Malayalam |
| 1 | one | one | एक / ایک (ēk) | एक (ēk) | এক (êk) | ଏକ (ekå) | एक (ēk) | ஒன்று (oṉṟu) | ఒకటి (okaṭi) | ಒಂದು (ಬಿಡಿ) (ondu) | ഒന്ന് (onn) |
| 10 | ten | ten | दस / دس (das) | दहा (dahā) | দশ (dôś) | ଦଶ (dåśå) | दश (daś) | பத்து (pattu) | పది (padi) | ಹತ್ತು (hattu) | പത്ത് (patt) |
| 10$^2$ | hundred | hundred | सौ / سو (sau) | शंभर (śambhar) | শত (śato) | ଶହେ (śåhe) | सय (saya) | நூறு (nūṟu) | వంద/నూరు (vanda/nūru) | ನೂರು (nūru) | നൂറ് (nuṟ) |
| 10$^3$ | thousand | thousand | हज़ार / ہزار (hazār) | एक हजार (ēk hajār) | হাজার (hāzār) | ହଜାର (håjārå) ସହସ୍ର (såhåsrå) | एक हजार (ēk hajār) | ஆயிரம் (āyiram) | వెయ్యి (veyyi) | ಸಾವಿರ (sāvira) | ആയിരം (āyiraṁ) |
| 10$^4$ | ten thousand | ten thousand | दस हज़ार / دس ہزار (das hazār) | दहा हजार (dahā hajār) | অযুত (ōjut) দশ হাজার (dôś hāzār) | ଦଶ ହଜାର (dåśå håjārå) ଅୟୁତ (åyutå) | दश हजार (daś hajār) | பத்தாயிரம் (pattāyiram) ஆயுதம் (āyutam) | పది వేలు (padi vēlu) | ಹತ್ತು ಸಾವಿರ (ಅಯುತ) (hattu sāvira) | പതിനായിരം (patināyiraṁ) |
| 10$^5$ | hundred thousand | lakh | लाख / لاکھ (lākh) | एक लाख (ēk lākh) | লক্ষ (lôkkhō) লাখ (lākh) | ଲକ୍ଷ (låkṣå) | एक लाख (ēk lākh) | இலட்சம் (ilaṭcam) நியுதம் (niyutam) | లక్ష (lakṣa) | ಲಕ್ಷ (lakṣa) | ലക്ഷം (lakṣaṁ) |
| 10$^6$ | million | ten lakh | दस लाख / دس لاکھ (das lākh) | दहा लाख (dahā lākh) | নিযুত (nijut) দশ লাখ (dôś lākh) | ଦଶ ଲକ୍ଷ (dåśå låkṣå) ନିୟୁତ (niyutå) | दश लाख (daś lākh) | பத்து இலட்சம் (pattu ilaṭcam) | పది లక్షలు (padi lakṣalu) | ಹತ್ತು ಲಕ್ಷ (ನಿಯುತ) (hattu lakṣa) | പത്തുലക്ഷം (pattulakṣaṁ) |
| 10$^7$ | ten million | crore | करोड़ / کروڑ (karōṛ) | एक कोटी (ēk kōṭī) | কোটি (kōṭi) | କୋଟି (koṭi) | एक करोड (ēk karoḍ) | கோடி (kōṭi) | కోటి (kōṭi) | ಕೋಟಿ (kōṭi) | കോടി (kōṭi) |
| 10$^8$ | hundred million | ten crore | दस करोड़ / دس کروڑ (das karōṛ) | दहा कोटी (dahā kōṭī) | অর্বুদ (ōrbud) দশ কোটি (dôś kōṭi) | ଦଶ କୋଟି (dåśå koṭi) ଅର୍ବୁଦ (årbudå) | दश करोड (daś karoḍ) | அற்புதம் (aṟputam) | పది కోట్లు (padi kōṭlu) | ಹತ್ತು ಕೋಟಿ (ಅರ್ಭುಧ) (hattu kōṭi) | പത്തുകോടി (pattukōṭi) |
| 10$^9$ | billion | arab / hundred crore | अरब / ارب (arab) सौ करोड़ / سو کروڑ (sau karōṛ) | एक अब्ज (ēk abja) | মহার্বুদ (môhārbud) একশ কোটি (êkśō kōṭi) | ଶହେ କୋଟି (śåhe koṭi) ବୃନ୍ଦ (brundå) | एक अर्ब (ēk arba) | நிகற்புதம் (nikaṟputam) | వంద కోట్లు (vanda kōṭlu) | ನೂರು ಕೋಟಿ (ಅಭ್ಜ) (nūru kōṭi) | നൂറുകോടി (nūṟukōṭi) |
| 10$^{10}$ | ten billion | ten arab / thousand crore | दस अरब / دس ارب (das arab) एक हज़ार करोड़ / ایک ہزار کروڑ (ēk hazār karōṛ) | एक खर्व (ek kharva) | খর্ব (khôrbō) হাজার কোটি (hāzār kōṭi) | ହଜାର କୋଟି (håjārå koṭi) ଖର୍ବ (khårbå) | दश अर्ब (daś arba) | கும்பம் (kumpam) | వెయ్యి కోట్లు (veyyi kōṭlu) | ಒಂದು ಸಾವಿರ ಕೋಟಿ (ಕರ್ವ) (ondu sāvira kōṭi) | ആയിരം കോടി (āyiraṁ kōṭi) |
| 10$^{11}$ | hundred billion | kharab / hundred arab / ten thousand crore | खरब / کھرب (kharab) | एक निखर्व (ek nikharva) | মহাখর্ব (môhākhôrbō) দশ হাজার কোটি (dôś hājār kōṭi) | ଦଶ ହଜାର କୋଟି (dåśå håjārå koṭi) ନିଖର୍ବ (nikhårbå) | एक खर्ब (ēk kharba) | கணம் (kaṇam) | పది వేల కోట్లు (padi vēla kōṭlu) | ಹತ್ತು ಸಾವಿರ ಕೋಟಿ (ನಿಕರ್ವ) (hattu sāvira kōṭi) | പതിനായിരം കോടി (patināyiraṁ kōṭi) |
| 10$^{12}$ | trillion | ten kharab / one thousand arab / one lakh crore | दस खरब / دس کھرب (das kharab) एक लाख करोड़ / ایک لاکھ کروڑ (ēk lākh karōṛ) | एक पद्म (ēk padma) | শঙ্খ (śôṅkhō) লাখ কোটি (lākh kōṭi) | ଲକ୍ଷ କୋଟି (låkṣå koṭi) ଶଙ୍ଖ (śåṅkhå) | दश खर्ब (daś kharba) | கற்பம் (kaṟpam) | లక్ష కోట్లు (lakṣa kōṭlu) | ಒಂದು ಲಕ್ಷ ಕೋಟಿ (ಮಹಾಪದ್ಮ) (ondu lakṣa kōṭi) | ഒരു ലക്ഷം കോടി (oru lakṣaṁ kōṭi) |
| 10$^{13}$ | ten trillion | nil / hundred kharab / ten thousand arab / ten lakh crore | नील / نیل (nīl) | एक महापद्म (ek mahāpadma) | মহাশঙ্খ (môhāśôṅkhō) দশ লাখ কোটি (dôś lākh kōṭi) | ଦଶ ଲକ୍ଷ କୋଟି (dåśå låkṣå koṭi) ପଦ୍ମ (pådmå) | नील (nīl) | நிகற்பம் (nikaṟpam) | పది లక్షల కోట్లు (padi lakṣala kōṭlu) | ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ (ಶಂಖು) (hattu lakṣa kōṭi) | പത്തുലക്ഷം കോടി (pattulakṣaṁ kōṭi) |
| 10$^{14}$ | hundred trillion | ten nil / crore crore | दस नील / دس نیل (das nīl) एक करोड़ करोड़ / ایک کروڑ کروڑ (ēk karōṛ karōṛ) | एक शंखू (ēk śaṅkhū) | পদ্ম (pôddō) একশ লাখ কোটি (êkśō lākh kōṭi) শতলক্ষ কোটি (śôtôkōṭi lôkkō)f | ଶହେ ଲକ୍ଷ କୋଟି (śåhe låkṣå koṭi) ସାଗର (sāgårå) | दश नील (daś nīl) | பதுமம் (patumam) | కోటి కోట్లు (kōṭi kōṭlu) | ಒಂದು ಕೋಟಿ ಕೋಟಿ (ಜಲಧಿ) (ondu kōṭi kōṭi) | നൂറ് ലക്ഷം കോടി (nuṟ lakṣaṁ kōṭi) |
| 10$^{15}$ | quadrillion | padma / hundred nil / ten crore crore | पद्म / پدم (padma) | एक जलधि शंखू (eka jaladhi śaṅkhū) | মহাপদ্ম (môhāpôddō) হাজার লাখ কোটি (hāzār lākh kōṭi) | ହଜାର ଲକ୍ଷ କୋଟି (håjārå låkṣå koṭi) ଅନ୍ତ୍ୟ (åntyå) | पद्म (padma) | சங்கம் (caṅkam) | పది కోట్ల కోట్లు (padi kōṭla kōṭlu) | ಹತ್ತು ಕೋಟಿ ಕೋಟಿ (ಅಂತ್ಯ) (hattu kōṭi kōṭi) | ആയിരം ലക്ഷം കോടി (āyiraṁ lakṣaṁ kōṭi) |
| 10$^{16}$ | ten quadrillion | ten padma / hundred crore crore | दस पद्म / دس پدم (das padma) | एक अंत्य (eka antya) | বঙ্গ (bongo)দশ হাজার লাখ কোটি (dôś hāzār lākh kōṭi) | ଦଶ ହଜାର ଲକ୍ଷ କୋଟି (dåśå håjārå låkṣå koṭi) ମଧ୍ୟ (mådhyå) | दश पद्म (daś padma) | வெள்ளம் (veḷḷam) சமுத்திரம் (camuttiram) | వంద కోట్ల కోట్లు (vanda kōṭla kōṭlu) | ನೂರು ಕೋಟಿ ಕೋಟಿ (ಮಧ್ಯ) (nūru kōṭi kōṭi) | പതിനായിരം ലക്ഷം കോടി (patināyiraṁ lakṣaṁ kōṭi) |
| 10$^{17}$ | hundred quadrillion | shankh / hundred padma / thousand crore crore / lakh lakh crore | शंख / شنکھ (śaṅkh) | एक परार्ध (eka parārdha) | মহাবঙ্গ (mohabongo)শত হাজার লাখ কোটি (śoto hāzār lākh kōṭi) | ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (śåhe håjārå låkṣå koṭi) ପରାର୍ଦ୍ଧ (pårārddhå) | शंख (śaṅkha) | அந்நியம் (anniyam) | వెయ్యి కోట్ల కోట్లు (veyyi kōṭla kōṭlu) | ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (ಪರಾರ್ಧ) (ondu sāvira kōṭi kōṭi) | ലക്ഷം ലക്ഷം കോടി (lakṣaṁ lakṣaṁ kōṭi) |
| 10$^{18}$ | quintillion | ten shankh / ten thousand crore crore | दस शंख / دس شنکھ (das śaṅkh) गुलशन / گلشن (gulśan) | एक महापरार्ध (eka mahāparārdha) | গুলশান (gulśān) দশ শত হাজার লাখ কোটি (doś śoto hāzār lākh kōṭi) | ଦଶ ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (dåśå śåhe håjārå låkṣå koṭi) ଦଶ ପରାର୍ଦ୍ଧ (dåśå pårārddhå) | दश शंख (daś śaṅkha) | அர்த்தம் (arttam) | పది వేల కోట్ల కోట్లు (padi vēla kōṭla kōṭlu) | ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (hattu sāvira kōṭi kōṭi) | പത്തുലക്ഷം ലക്ഷം കോടി (pattulakṣaṁ lakṣaṁ kōṭi) |

## Historic numbering systems
### Numbering systems in Hindu epics

There are various systems of numeration found in various ancient epic literature of India (itihasas). The following table gives one such system used in the Valmiki Ramayana.
| Name | Indian decimal | Value | Short scale |
| एक (ēka) | 0,00,001 | 1 | one |
| दश (daśa) | 0,00,010 | 10 | ten |
| शत (śata) | 0,00,100 | 10$^2$ | hundred |
| सहस्र (sahasra) | 0,01,000 | 10$^3$ | thousand |
| लक्ष (lakṣa) | 1,00,000 | 10$^5$ | hundred thousand |
| कोटि (kōṭi) | 1,00,00,000 | 10$^7$ | ten million |
| शङ्कु (śaṅku) | 1,00,000 koṭi | 10$^{12}$ | trillion |
| महाशङ्कु (mahāśaṅku) | 1,00,000 śaṅku | 10$^{17}$ | hundred quadrillion |
| वृन्द (vr̥nda) | 1,00,000 mahāśaṅku | 10$^{22}$ | ten sextillion |
| महावृन्द (mahāvr̥nda) | 1,00,000 vr̥nda | 10$^{27}$ | octillion |
| पद्म (padma) | 1,00,000 mahāvr̥nda | 10$^{32}$ | hundred nonillion |
| महापद्म (mahāpadma) | 1,00,000 padma | 10$^{37}$ | ten undecillion |
| खर्व (kharva) | 1,00,000 mahāpadma | 10$^{42}$ | tredecillion |
| महाखर्व (mahākharva) | 1,00,000 kharva | 10$^{47}$ | hundred quattuordecillion |
| समुद्र (samudra) | 1,00,000 mahākharva | 10$^{52}$ | ten sexdecillion |
| ओघ (ogha) | 1,00,000 samudra | 10$^{57}$ | octodecillion |
| महौघ (mahaugha) | 1,00,000 ogha | 10$^{62}$ | hundred novemdecillion |

### Other numbering systems

The denominations by which land was measured in the Kumaon Kingdom were based on arable lands and thus followed an approximate system with local variations. The most common of these was a vigesimal (base-20) numbering system with the main denomination called a bisi (see Hindustani number bīs), which corresponded to the land required to sow 20 nalis of seed. Consequently, its actual land measure varied based on the quality of the soil. This system became the established norm in Kumaon by 1891.

## Usage in different languages

Below is a list of translations for the words lakh and crore in other languages spoken in the Indian subcontinent:
* In Assamese, a lakh is also called লক্ষ lokhyo, or লাখ lakh and a crore is called কৌটি বা কোটি kouti
* In Bengali, a lakh is natively (tadbhava) known as লাখ lākh, though some use the ardha-tatsama লক্ষ lokkho. A crore is called কোটি kōṭi
* In Burmese, crore is called ကုဋေ. Lakh is used in Burmese English.
* In Dhivehi, a lakh is called ލައްކަ la'kha and a crore is called ކްރޯރް kroaru
* In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karoḍ. A hundred crore is called અબજ abaj
* In Hindi, a lakh is called लाख lākh and a crore is called करोड karoḍ. A hundred crore is called अरब arab
* In Kannada, a lakh is called ಲಕ್ಷ lakṣha and a crore is called ಕೋಟಿ kōṭi
* In Khasi, a lakh is called lak and a crore is called klur or krur. A billion is called arab and hundred billion is called kharab.
* In Malayalam, a lakh is called ലക്ഷം laksham and a crore is called കോടി kodi.
* In Marathi, a lakh is called लाख/लक्ष lākh and a crore is called कोटी koṭi or करोड karoḍ, and an arab (10$^9$) is called अब्ज abja.
* In Nepali, a lakh is called लाख lākh and a crore is called करोड karoḍ.
* In Odia, a lakh is called ଲକ୍ଷ lôkhyô and a crore is called କୋଟି koṭi.
* In Punjabi, a lakh is called lakkh (Shahmukhi: لکھ, Gurmukhi: ਲੱਖ) and a crore is called karoṛ (Shahmukhi: کروڑ, Gurmukhi: ਕਰੋੜ).
* In Rohingya, a lakh is called lák and a crore is called kurul. A thousand crore is called kuthí.
* In Sinhala, a lakh is called ලක්ෂ lakṣa and a crore is called කෝටි kōṭi.
* In Tamil, a lakh is called இலட்சம் ilaṭcam and a crore is called கோடி kōṭi.
* In Telugu, a lakh is called లక్ష lakṣha and a crore is called కోటి kōṭi.
* In Urdu, a lakh is called لاکھ lākh and a crore is called کروڑ karoṛ. A billion is called arab (ارب), and one hundred billion/arab is called a kharab (کھرب).
* Lakh has entered the Swahili language as "laki" and is in common use.
Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.

## Current usage

The official usage of this system is limited to the nations of India, Pakistan and Bangladesh. It is universally employed within these countries, and is preferred to the International numbering system.
Sri Lanka and Nepal used this system in the past but has switched to the International numbering system in recent years. In the Maldives, the term lakh is widely used in official documents and local speech. However, the International System of Units is preferred for higher denominations (such as millions).
Most institutions and citizens in India use the Indian number system. The Reserve Bank of India was noted as a rare exception in 2015, whereas by 2024 the Indian system was used for amounts in rupees and the International system for foreign currencies throughout the Reserve Bank's website.