Indian numbering system

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This article is about digit grouping of numbers in India. For the symbols used to write digits in India, see Indian numerals.

The Indian Numbering System is used in India as well as in Bangladesh, Nepal, Pakistan, and Sri Lanka. It is based on the Vedic numbering system in which numbers over 9,999 are written in two-digit groups (or a mix of two- and three-digit groups) rather than the three-digit groups used in most other parts of the world. In Pakistan, this system is used in Urdu and other regional language media, but not in English-language media.

The terms lakh (100,000 – that is to say 1,00,000 in the Indian system) and crore (10,000,000 – that is to say 1,00,00,000 in the Indian system) are used in Indian English to express large numbers. For example, in India 150,000 rupees becomes 1.5 lakh rupees, written as 1,50,000 or INR 1,50,000, while 30,000,000 (thirty million) rupees becomes 3 crore rupees, written as 3,00,00,000 with commas at the thousand, lakh, and crore levels, and 1,000,000,000 (one billion) rupees (one hundred crore rupees) is written 1,00,00,00,000.

A simplified conversion between the Arabic and Indian numbering systems is :

1 million (1,000,000) = 10 lakh

1 billion (1,000,000,000) = 100 crores

Use of separators

The Indian Numbering System uses separators differently from the Arabic system; in such numbers of at least one lakh (one hundred thousand), a comma divides every two rather than every three digits, thus:

Indian system Arabic system
5,05,000 505,000
12,12,12,123 121,212,123
7,00,00,00,000 7,000,000,000

This accords with the Indian Numbering System, which has units for thousand, hundred thousand, ten million, etc.

Names of numbers

The table below follows the short scale usage of billion being a thousand million. In India, following former British usage, the long scale was used, with one billion equivalent to one million million.

Hindi / Urdu (transliteration)
South Asian English
Indian figure Power
notation
International figure Short scale Arabic
(long scale Arabic)
एक / ایک (ek)
one
1 100 1 One
दस / دس (das)
ten
10 101 10 Ten
Scientific (SI prefix): deca-
सौ / سو (sau)
one hundred
100 102 100 One hundred
SI prefix: hecto-
सहस्र (sahasra) / हज़ार / ہزار (hazār)
one thousand
1,000 103 1,000 One thousand
SI prefix: kilo-
दस हज़ार / دس ہزار (das hazār)
ten thousand
10,000 104 10,000 Ten thousand
लाख / لاکھ (lākh)
one lakh (also lac)
1,00,000 105 100,000 One hundred thousand
अदन्त / ادنت (adant) / दस लाख / دس لاکھ (das lākh)
ten lakh
10,00,000 106 1,000,000 One million
SI prefix: mega-
करोड़ / کروڑ (karoṛ)
one crore
1,00,00,000 107 10,000,000 Ten million
दस करोड़ / دس کروڑ (das karoṛ)
ten crore
10,00,00,000 108 100,000,000 One hundred million
अरब / ارب (arab) / सौ करोड़ (sau karoṛ)
one arab / one hundred crore
1,00,00,00,000 109 1,000,000,000 One billion
(one milliard)
SI prefix: giga-
एक हज़ार करोड़ (ek hazār karoṛ) / دس ارب (das arab)
one thousand crore / ten arab
10,00,00,00,000 1010 10,000,000,000 Ten billion
(ten milliard)
खरब / کھرب (kharab)
ten thousand crore / one kharab / one hundred arab
1,00,00,00,00,000 1011 100,000,000,000 One hundred billion
(one hundred milliard)
एक लाख करोड़ (ek lākh karoṛ) / دس کھرب (das kharab)
one lakh crore / ten kharab / one thousand arab
10,00,00,00,00,000 1012 1,000,000,000,000 One trillion
(one billion)
SI prefix: tera-
नील / نیل (neel / nīl)
ten lakh crore / one neel / one hundred kharab / ten thousand arab
1,00,00,00,00,00,000 1013 10,000,000,000,000 Ten trillion
(ten billion)
एक करोड़ करोड़ (ek karoṛ karoṛ) / دس نیل (das nīl)
one crore crore / ten neel
10,00,00,00,00,00,000 1014 100,000,000,000,000 One hundred trillion
(one hundred billion)
पद्म / پدم (padm)
one padm / one hundred neel / ten crore crore
1,00,00,00,00,00,00,000 1015 1,000,000,000,000,000 One quadrillion
(one billiard)
SI prefix: peta-
दस पद्म / دس پدم (das padm)
ten padm / one hundred crore crore
10,00,00,00,00,00,00,000 1016 10,000,000,000,000,000 Ten quadrillion
(ten billiard)
शङ्ख / شنکھ (shankh / śaṅkh)
one shankh / one hundred padm / one thousand crore crore / one lakh lakh crore
1,00,00,00,00,00,00,00,000 1017 100,000,000,000,000,000 One hundred quadrillion
(one hundred billiard)
गुलशन / پدم (gulshan)
one गुलशन / ten shankh / ten thousand crore crore
10,00,00,00,00,00,00,00,000 1018 1,000,000,000,000,000,000 One quintillion
(one trillion)
SI prefix: exa-

Vedic numbering systems

There are various systems of numeration found in various ancient Vedic literatures of India. The following table gives one such system used in the Valmiki Ramayana.[1]

Sanskrit (transliteration) Indian figure Power
notation
Hindu (Aryan) figure Short scale Arabic
एक (eka) 0,00,001 100 1 One
दश (daśa) 0,00,010 101 10 Ten
शत (śata) 0,00,100 102 100 One hundred
सह (sahasra) 0,01,000 103 1,000 One thousand
अयुत (ayuta) 0,10,000 104 10,000 Ten thousand
लक्ष (lakṣa) 1,00,000 105 1,00,000 One hundred thousand
नियुत (niyuta) 1,00,000 daśa 106 10,00,000 One million
कोटि (koṭi)
one crore
1,00,000 śata 107 1,00,00,000 Ten million
शङ्कु (śaṅku) 1,00,000 koṭi 1012 10,00,00,00,00,000 One trillion
महाशङ्कु (mahā-śaṅku) 1,00,000 śaṅku 1017 1,00,00,00,00,00,00,00,000 One hundred quadrillion
वृन्द (vṛnda) 1,00,000 mahā-śaṅku 1022 10,00,00,00,00,00,00,00,00,00,000 Ten sextillion
महावृन्द (mahā-vṛnda) 1,00,000 vṛnda 1027 1,00,00,00,00,00,00,00,00,00,00,00,00,000 One octillion
पद्म (padma) 1,00,000 mahā-vṛnda 1032 10,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 One hundred nonillion
महापद्म (mahā-padma) 1,00,000 padma 1037 1,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 Ten undecillion
खर्व (kharva) 1,00,000 mahā-padma 1042 10,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 One tredecillion
महाखर्व (mahā-kharva) 1,00,000 kharva 1047 1,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 One hundred quattuordecillion
समुद्र (samudra) 1,00,000 mahā-kharva 1052 10,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 Ten sexdecillion
ओघ (ogha) 1,00,000 samudra 1057 1,00,00,00,00,00,00,00,00,00,00.00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 One octodecillion
महौघ (mahaugha) 1,00,000 ogha 1062 10,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000 One hundred novemdecillion

Usage in different languages

Main articles: lakh and crore
• In Tamil, a lakh is called இலட்சம் latcham and a crore is called கோடி kodi.
• In Bengali, a lakh is called লক্ষ lokkho (ardha-tatsama), or laakh (tadbhava) and a crore is called কোটি koti.
• In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karod. A hundred crore is called અબજ abaj.
• In Kannada, a lakh is called ಲಕ್ಷ laksha and a crore is called ಕೋಟಿ koti.
• In Malayalam, a lakh is called ലക്ഷം laksham and a crore is called കോടി koti.
• In Marathi, a lakh is called लाख lākh and a crore is called कोटी koti, and an arab (109) is called अब्ज abja.
• In Nepali, a lakh is called लाख lākh and a crore is called करोड karod.
• In Odia, a lakh is called ଲକ୍ଷ lakhya and a crore is called କୋଟି koti.
• In Sinhalese, a lakh is called ලක්ෂ laksha and a crore is called කෝටි koti.
• In Telugu, a lakh is called లక్ష laksha and a crore is called కోటి koti.
• In Urdu, a lakh is called لاکھ lākh and a crore is called کروڑ karod.
• Lakh has entered the Swahili language as "laki" and is in common use.