The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka) to express large numbers. The terms lakh or 1,00,000 (one hundred thousand, written as 100,000 in Pakistan, and outside the Indian subcontinent) and crore or 1,00,00,000[1] (ten million, written as 10,000,000 outside the subcontinent) are the most commonly used terms in Indian English to express large numbers in the system.
The Indian numbering system corresponds to the Western system for the zeroth through fourth powers of ten: one (100), ten (101), one hundred (102), one thousand (103), and ten thousand (104). For higher powers of ten, the names no longer correspond. In the ancient Indian system still in use in regional languages of India, there are words for (1062). 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 called one lakh, ten lakh, one crore, ten crore, one arab (or one hundred crore), and so on; there are new words for every second power of ten (105 + 2n): lakh (105), crore (107), arab (109), kharab (1011), etc.In the Western system, the next powers of ten are called one hundred thousand, one million, ten million, one hundred million, one billion (short scale)/one thousand million (long scale), and so on; in the short scale, there are new words for every third power of ten (103n): million (106), billion (109), trillion (1012), etc.
Written numbers differ in the placement of commas, grouping digits into powers of one hundred (102) in the Indian system (except for the first thousand), and into powers of one thousand (103) in the Western system. The Indian and most English systems both use the decimal point and the comma digit-separator, while other languages and countries using the Western numbering system use the decimal comma and the thin space or point to group digits.[2]
There are terms for numbers larger than 1 crore as well, but these are not commonly used. These include 1 arab (equal to 100 crore or 1 billion (short scale)), 1 kharab (equal to 100 arab or 100 billion (short scale)), 1 nil (sometimes transliterated as neel; equal to 100 kharab or 10 trillion), 1 padma (equal to 100 nil or 1 quadrillion), 1 shankh (equal to 100 padma or 100 quadrillion), and 1 mahashankh (equal to 100 shankh or 10 quintillion). In common parlance, the thousand, lakh, and crore terminology (though inconsistent) repeats for larger numbers: thus 1,000,000,000,000 (one trillion) becomes 1 lakh crore, written as 10,00,00,00,00,000.
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.
The Indian numbering system uses separators differently from the international norm. Instead of grouping digits by threes as in the international system, the Indian numbering system groups the rightmost three digits together (until the hundreds place), and thereafter groups by sets of two digits.[3] One trillion would thus be written as 10,00,00,00,00,000 or 10 kharab (or one lakh crore). This makes the number convenient to read using the system's terminology. For example:
| Indian system | Indian system (words) | International system | International system (words) | |
|---|---|---|---|---|
| 5,00,000 | Five lakh | 500,000 | Five hundred thousand | |
| 12,34,56,789 | Twelve crore, thirty-four lakh, fifty-six hazar, seven hundred, and eighty-nine | 123,456,789 | One hundred and twenty-three million, four hundred and fifty-six thousand, seven hundred and eighty-nine | |
| 17,00,00,00,000 | Seventeen arab | 17,000,000,000 | Seventeen billion (short scale) | |
| 6,78,90,00,00,00,00,000 | Six padma, seventy-eight nil, and ninety kharab | 6,789,000,000,000,000 | Six quadrillion, seven hundred and eighty-nine trillion |
This accords with the Indian numbering system, which has units for thousands, hundreds of thousands, tens of millions, etc.
The table below follows the short scale usage of one billion being one thousand million. In India, Bangladesh and Pakistan, following former British usage, the long scale was used, with one billion equivalent to one million million.
| Indian English | Hindustani | Marathi | Bengali | Odia | Tamil | Telugu | Kannada | Malayalam | Nepali | Indian notation | Power notation | International notation[4] | Short scale Western (long scale Western) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| One | Hindi: एक / Urdu: {{nq|ایک | Marathi: एक | Bengali: এক | Oriya: ଏକ | Tamil: ஒன்று | Telugu: ఒకటి | Kannada: ಒಂದು (ಬಿಡಿ) | Malayalam: ഒന്ന് | Nepali: एक | 1 | 100 | 1 | One |
| Ten | Hindi: दस / Urdu: {{nq|دس | Marathi: दहा | Bengali: দশ | Oriya: ଦଶ | Tamil: பத்து | Telugu: పది | Kannada: ಹತ್ತು | Malayalam: പത്ത് | Nepali: दश | 10 | 101 | 10 | Ten SI prefix |
| One hundred | Hindi: सौ / Urdu: {{nq|سو | Marathi: शंभर | Bengali: শত | Oriya: ଶହେ | Tamil: நூறு | Telugu: వంద/నూరు | Kannada: ನೂರು | Malayalam: നൂറ് | Nepali: सय | 100 | 102 | 100 | One hundred SI prefix: hecto- |
| One thousand | हज़ार / Urdu: {{nq|ہزار | Marathi: एक हजार | Bengali: হাজার | Oriya: ହଜାର Oriya: ସହସ୍ର | Tamil: ஆயிரம் | Telugu: వెయ్యి | Kannada: ಸಾವಿರ | Malayalam: ആയിരം | Nepali: एक हजार | 1,000 | 103 | 1,000 | One thousand SI prefix: kilo- |
| Ten thousand | Hindi: दस हज़ार / Urdu: {{nq|دس ہزار | Marathi: दहा हजार | Bengali: অযুত Bengali: দশ হাজার | Oriya: ଦଶ ହଜାର Oriya: ଅୟୁତ | Tamil: பத்தாயிரம் Tamil: ஆயுதம் | Telugu: పది వేలు | Kannada: ಹತ್ತು ಸಾವಿರ (ಅಯುತ) | Malayalam: പതിനായിരം | Nepali: दश हजार | 10,000 | 104 | 10,000 | Ten thousand |
| One lakh | Hindi: लाख / Urdu: {{nq|لاکھ | Marathi: एक लाख | Bengali: লক্ষ Bengali: লাখ | Oriya: ଲକ୍ଷ | Tamil: இலட்சம் Tamil: நியுதம் | Telugu: లక్ష | Kannada: ಲಕ್ಷ | Malayalam: ലക്ഷം | Nepali: एक लाख | 1,00,000 | 105 | 100,000 | One hundred thousand |
| Ten lakh | Hindi: दस लाख / Urdu: {{nq|دس لاکھ | Marathi: दहा लाख | Bengali: নিযুত Bengali: দশ লাখ | Oriya: ଦଶ ଲକ୍ଷ Oriya: ନିୟୁତ | Tamil: பத்து இலட்சம் | Telugu: పది లక్షలు | Kannada: ಹತ್ತು ಲಕ್ಷ (ನಿಯುತ) | Malayalam: പത്തുലക്ഷം | Nepali: दश लाख | 10,00,000 | 106 | 1,000,000 | One million SI prefix: mega- |
| One crore | Hindi: करोड़ / Urdu: {{nq|کروڑ | Marathi: एक कोटी | Bengali: কোটি | Oriya: କୋଟି | Tamil: கோடி | Telugu: కోటి | Kannada: ಕೋಟಿ | Malayalam: കോടി | Nepali: एक करोड | 1,00,00,000 | 107 | 10,000,000 | Ten million |
| Ten crore | Hindi: दस करोड़ / Urdu: {{nq|دس کروڑ | Marathi: दहा कोटी | Bengali: অর্বুদ Bengali: দশ কোটি | Oriya: ଦଶ କୋଟି Oriya: ଅର୍ବୁଦ | Tamil: அற்புதம் | Telugu: పది కోట్లు | Kannada: ಹತ್ತು ಕೋಟಿ (ಅರ್ಭುಧ) | Malayalam: പത്തുകോടി | Nepali: दश करोड | 10,00,00,000 | 108 | 100,000,000 | One hundred million |
| One / one hundred crore | Hindi: अरब / Urdu: {{nq|ارب Hindi: सौ करोड़ / Urdu: {{nq|سو کروڑ | Marathi: एक अब्ज | Bengali: মহার্বুদ Bengali: একশ কোটি | Oriya: ଶହେ କୋଟି Oriya: ବୃନ୍ଦ | Tamil: நிகற்புதம் | Telugu: వంద కోట్లు | Kannada: ನೂರು ಕೋಟಿ (ಅಭ್ಜ) | Malayalam: നൂറുകോടി | Nepali: एक अर्ब | 1,00,00,00,000 | 109 | 1,000,000,000 | One billion (one milliard) SI prefix: giga- |
| Ten / one thousand crore | Hindi: दस अरब / Urdu: {{nq|دس ارب Hindi: एक हज़ार करोड़ / Urdu: {{nq|ایک ہزار کروڑ | एक खर्व | Bengali: খর্ব Bengali: হাজার কোটি | Oriya: ହଜାର କୋଟି Oriya: ଖର୍ବ | Tamil: கும்பம் | Telugu: వెయ్యి కోట్లు | Kannada: ಒಂದು ಸಾವಿರ ಕೋಟಿ (ಕರ್ವ) | Malayalam: ആയിരം കോടി | Nepali: दश अर्ब | 10,00,00,00,000 | 1010 | 10,000,000,000 | Ten billion (ten milliard) |
| One kharab / one hundred / ten thousand crore | Hindi: खरब / Urdu: {{nq|کھرب | एक Marathi: निखर्व | Bengali: মহাখর্ব Bengali: দশ হাজার কোটি | Oriya: ଦଶ ହଜାର କୋଟି Oriya: ନିଖର୍ବ | Tamil: கணம் | Telugu: పది వేల కోట్లు | Kannada: ಹತ್ತು ಸಾವಿರ ಕೋಟಿ (ನಿಕರ್ವ) | Malayalam: പതിനായിരം കോടി | Nepali: एक खर्ब | 1,00,00,00,00,000 | 1011 | 100,000,000,000 | One hundred billion (one hundred milliard) |
| Ten kharab / one thousand / one lakh crore | Hindi: दस खरब / Urdu: {{nq|دس کھرب Hindi: एक लाख करोड़ / Urdu: {{nq|ایک لاکھ کروڑ | Marathi: एक पद्म | Bengali: শঙ্খ Bengali: লাখ কোটি | Oriya: ଲକ୍ଷ କୋଟି Oriya: ଶଙ୍ଖ | Tamil: கற்பம் | Telugu: లక్ష కోట్లు | Kannada: ಒಂದು ಲಕ್ಷ ಕೋಟಿ (ಮಹಾಪದ್ಮ) | Malayalam: ഒരു ലക്ഷം കോടി | Nepali: दश खर्ब | 10,00,00,00,00,000 | 1012 | 1,000,000,000,000 | One trillion (one billion) SI prefix: tera- |
| One nil / one hundred kharab / ten thousand / ten lakh crore | Hindi: नील / Urdu: {{nq|نیل | Marathi: एक महापद्म (ek mahāpadma) | Bengali: মহাশঙ্খ Bengali: দশ লাখ কোটি | Oriya: ଦଶ ଲକ୍ଷ କୋଟି Oriya: ପଦ୍ମ | Tamil: நிகற்பம் | Telugu: పది లక్షల కోట్లు | Kannada: ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ (ಶಂಖು) | Malayalam: പത്തുലക്ഷം കോടി | Nepali: नील | 1,00,00,00,00,00,000 | 1013 | 10,000,000,000,000 | Ten trillion (ten billion) |
| Ten nil / one crore crore | Hindi: दस नील / Urdu: {{nq|دس نیل Hindi: एक करोड़ करोड़ / Urdu: {{nq|ایک کروڑ کروڑ | Marathi: एक शंखू | Bengali: পদ্ম Bengali: একশ লাখ কোটি Bengali: শতলক্ষ কোটি f | Oriya: ଶହେ ଲକ୍ଷ କୋଟି Oriya: ସାଗର | Tamil: பதுமம் | Telugu: కోటి కోట్లు | Kannada: ಒಂದು ಕೋಟಿ ಕೋಟಿ (ಜಲಧಿ) | Malayalam: നൂറ് ലക്ഷം കോടി | Nepali: दश नील | 10,00,00,00,00,00,000 | 1014 | 100,000,000,000,000 | One hundred trillion (one hundred billion) |
| One padma / one hundred nil / ten crore crore | Hindi: पद्म / Urdu: {{nq|پدم | एक जलधि शंखू (eka jaladhi śaṅkhū) | Bengali: মহাপদ্ম Bengali: হাজার লাখ কোটি | Oriya: ହଜାର ଲକ୍ଷ କୋଟି Oriya: ଅନ୍ତ୍ୟ | Tamil: சங்கம் | Telugu: పది కోట్ల కోట్లు | Kannada: ಹತ್ತು ಕೋಟಿ ಕೋಟಿ (ಅಂತ್ಯ) | Malayalam: ആയിരം ലക്ഷം കോടി | Nepali: पद्म | 100,00,00,00,00,00,000 | 1015 | 1,000,000,000,000,000 | One quadrillion (one billiard) SI prefix: peta- |
| Ten padma / one hundred crore crore | Hindi: दस पद्म / Urdu: {{nq|دس پدم | एक अंत्य (eka antya) | বঙ্গ(bongo)Bengali: দশ হাজার লাখ কোটি | Oriya: ଦଶ ହଜାର ଲକ୍ଷ କୋଟି Oriya: ମଧ୍ୟ | Tamil: வெள்ளம் Tamil: சமுத்திரம் | Telugu: వంద కోట్ల కోట్లు | Kannada: ನೂರು ಕೋಟಿ ಕೋಟಿ (ಮಧ್ಯ) | Malayalam: പതിനായിരം ലക്ഷം കോടി | Nepali: दश पद्म | 10,00,00,00,00,00,00,000 | 1016 | 10,000,000,000,000,000 | Ten quadrillion (ten billiard) |
| One shankh / one hundred padma / one thousand crore crore / one lakh lakh crore | Hindi: शंख / Urdu: {{nq|شنکھ | एक परार्ध (eka parārdha) | মহাবঙ্গ(mohabongo)Bengali: শত হাজার লাখ কোটি | Oriya: ଶହେ ହଜାର ଲକ୍ଷ କୋଟି Oriya: ପରାର୍ଦ୍ଧ | Tamil: அந்நியம் | Telugu: వెయ్యి కోట్ల కోట్లు | Kannada: ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (ಪರಾರ್ಧ) | Malayalam: ലക്ഷം ലക്ഷം കോടി | Nepali: शंख | 100,00,00,00,00,00,00,000 | 1017 | 100,000,000,000,000,000 | One hundred quadrillion (one hundred billiard) |
| Ten shankh / ten thousand crore crore | Hindi: दस शंख / Urdu: {{nq|دس شنکھ Hindi: गुलशन / Urdu: {{nq|گلشن | एक महापरार्ध (eka mahāparārdha) | Bengali: গুলশান Bengali: দশ শত হাজার লাখ কোটি | Oriya: ଦଶ ଶହେ ହଜାର ଲକ୍ଷ କୋଟି Oriya: ଦଶ ପରାର୍ଦ୍ଧ | Tamil: அர்த்தம் | Telugu: పది వేల కోట్ల కోట్లు | Kannada: ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ | Malayalam: പത്തുലക്ഷം ലക്ഷം കോടി | Nepali: दश शंख | 10,00,00,00,00,00,00,00,000 | 1018 | 1,000,000,000,000,000,000 | One quintillion (one trillion) SI prefix: exa- |
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.[5]
| Name | Indian notation | Power notation | Indian system | Short scale Western | |
|---|---|---|---|---|---|
| Sanskrit: एक () | 1 | 100 | One | One | |
| Sanskrit: दश () | 10 | 101 | Ten | Ten | |
| Sanskrit: शत () | 100 | 102 | One hundred | One hundred | |
| Sanskrit: सहस्र () | 1,000 | 103 | One thousand | One thousand | |
| Sanskrit: लक्ष () | 1,00,000 | 105 | One lakh | One hundred thousand | |
| Sanskrit: कोटि () | 1,00,00,000 | 107 | One crore | Ten million | |
| Sanskrit: शङ्कु () | 1,00,000 | 1012 | Ten kharab or One lakh crore | One trillion | |
| Sanskrit: महाशङ्कु () | 1,00,000 | 1017 | One shankh or One thousand crore crore | One hundred quadrillion | |
| Sanskrit: वृन्द () | 1,00,000 | 1022 | Ten sextillion | ||
| Sanskrit: महावृन्द () | 1,00,000 | 1027 | One octillion | ||
| Sanskrit: पद्म () | 1,00,000 | 1032 | One hundred nonillion | ||
| Sanskrit: महापद्म () | 1,00,000 | 1037 | Ten undecillion | ||
| Sanskrit: खर्व () | 1,00,000 | 1042 | One tredecillion | ||
| Sanskrit: महाखर्व () | 1,00,000 | 1047 | One hundred quattuordecillion | ||
| Sanskrit: समुद्र () | 1,00,000 | 1052 | Ten sexdecillion | ||
| Sanskrit: ओघ () | 1,00,000 | 1057 | One octodecillion | ||
| Sanskrit: महौघ () | 1,00,000 | 1062 | One hundred novemdecillion |
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.[6] This system became the established norm in Kumaon by 1891.[7]
See main article: crore. Below is a list of translations for the words lakh and crore in other languages spoken in the Indian subcontinent:
Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.[8]
The usage of this system is limited to the nations of India, Pakistan, Bangladesh, and Myanmar. It is universally employed within these countries, and is preferred to the English numbering system.[9]
Sri Lanka used this system in the past but has switched to the English numbering system in recent years.
In the Maldives, the term lakh is widely used in official documents and local speech. However, the Westernised Hindu-Arabic numeral system 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,[10] whereas by 2024 the Indian system was used for amounts in rupees and the Western system for foreign currencies throughout the Reserve Bank's website.[11]