The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, and Pakistan) to express large numbers. The terms lakh (100,000) and crore (10,000,000)^{[1]} are the most commonly used terms (even in English, such as in a local variety called 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 (10^{0}), ten (10^{1}), one hundred (10^{2}), one thousand (10^{3}), ten thousand (10^{4}). For higher powers of ten, the names no longer correspond. In the Indian system, 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 (10^{5 + 2n}): lakh (10^{5}), crore (10^{7}), arab (10^{9}), 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 (10^{3n}): million (10^{6}), billion (10^{9}), trillion (10^{12}), etc.
Written numbers differ in the placement of commas, grouping digits into powers of one hundred (10^{2}) in the Indian system (except for the first thousand), and into powers of one thousand (10^{3}) in the Western system. The Indian and most English systems both use the decimal point and the comma digit-separator, while some 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 and are unfamiliar to most.^{[]} 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 incorrectly 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.
150,000 rupees in India is referred to as "1.5 lakh rupees", which is written as 1,50,000 rupees; 30,000,000 (thirty million) rupees is referred to as "3 crore rupees", which is written as 3,00,00,000 rupees with commas at the thousand, lakh, and crore places.
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 thousand 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 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.
Hindustani | Marathi | Bengali | Odia | Tamil | Telugu | Kannada | Malayalam | Nepali | Indian notation | Power notation |
International notation^{[4]} | Short scale Western (long scale Western) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
South Asian English | ||||||||||||
/ (?k) |
(?k) |
(êk) |
(eka) |
(ou) |
? (oka?i) |
? (ondu) |
(onn) |
(?k) |
1 | 10^{0} | 1 | One |
One | ||||||||||||
/ (das) |
(dah?) |
(dô?) |
(dasa) |
(pattu) |
(padi) |
(hattu) |
(patt) |
(da?) |
10 | 10^{1} | 10 | Ten SI prefix: deca- |
Ten | ||||||||||||
/ (sau) |
? (?ambhar) |
(êk) |
(sahe) |
? (nu) |
/? (vanda/n?ru) |
? (n?ru) |
? (nu?) |
(saya) |
100 | 10^{2} | 100 | One hundred SI prefix: hecto- |
One hundred | ||||||||||||
/ ? (haz?r) |
? (?k haj?r) |
(h?z?r) |
? (haj?ra) (sahasra) |
(?yiram) |
(veyyi) |
(s?vira) |
(?yira?) |
? (?k haj?r) |
1,000 | 10^{3} | 1,000 | One thousand SI prefix: kilo- |
One thousand | ||||||||||||
/ ? (das haz?r) |
? (dah? haj?r) |
(dô? h?z?r) ? (?jut) |
? (dasa haj?ra) ? (ayuta) |
? (patt?yiram) (?yutam) |
? (padi v?lu) |
(hattu s?vira) |
(patin?yira?) |
? (da? haj?r) |
10,000 | 10^{4} | 10,000 | Ten thousand |
Ten thousand | ||||||||||||
/ ? (l?kh) |
(?k l?kh) |
? (lôkkh?) (l?kh) |
? (lakhya) |
? (ila?cam) ? (niyutam) |
? (lak?a) |
? (lak?a) |
(lak?a?) |
(?k l?kh) |
1,00,000 | 10^{5} | 100,000 | One hundred thousand |
One lakh (sometimes transliterated as lac) | ||||||||||||
/ ? (das l?kh) |
(dah? l?kh) |
(dô? l?kh) (nijut) |
? (da?a lakhya) (niyuta) |
? (pattu ila?cam) |
(padi lak?alu) |
? (hattu lak?a) |
? (pattulak?a?) |
(da? l?kh) |
10,00,000 | 10^{6} | 1,000,000 | One million SI prefix: mega- |
Ten lakh | ||||||||||||
/ ? (kar) |
? (?k k) |
? (ki) |
? (ko?i) |
? (ki) |
? (ki) |
? (ki) |
? (ki) |
? (?k karo?) |
1,00,00,000 | 10^{7} | 10,000,000 | Ten million |
One crore | ||||||||||||
/ ? (das kar) |
? (dah? k) |
? (dô? ki) (?rbud) |
? (dasa ko?i) (arbuda) |
(a?putam) |
(padi klu) |
? (hattu ki) |
(pattuki) |
? (da? karo?) |
10,00,00,000 | 10^{8} | 100,000,000 | One hundred million |
Ten crore | ||||||||||||
/ (arab) / ? (sau kar) |
? (?k abja) |
? (êk ki) (môh?rbud) |
? (eka sahe ko?i) (brunda) |
? (nika?putam) |
(vanda klu) |
? ? (n?ru ki) |
(nuki) |
? (?k arba) |
1,00,00,00,000 | 10^{9} | 1,000,000,000 | One billion (one milliard) SI prefix: giga- |
One arab / one hundred crore | ||||||||||||
/ (das arab) / ? ? (?k haz?r kar) |
? (ek kharva) |
? (h?z?r ki) ? (khôrb?) |
? ? (haj?ra ko?i) ? (kharba) |
? (kumpam) |
(veyyi klu) |
? ? (ondu s?vira ki) |
? (?yira? ki) |
? (da? arba) |
10,00,00,00,000 | 10^{10} | 10,000,000,000 | Ten billion (ten milliard) |
Ten arab / one thousand crore | ||||||||||||
/ ? (kharab) |
(ek nikharva) |
? (dô? h?j?r ki) ? (môh?khôrb?) |
? ? (dasa haj?ra ko?i) (nikharba) |
? (ka?am) |
(padi v?la klu) |
? (hattu s?vira ki) |
? (patin?yira? ki) |
? (?k kharba) |
1,00,00,00,00,000 | 10^{11} | 100,000,000,000 | One hundred billion (one hundred milliard) |
One kharab / one hundred arab / ten thousand crore | ||||||||||||
/ ? (das kharab) / ? ? (?k l?kh kar) |
? (?k padma) |
? (l?kh ki) ? (?ô?kh?) |
? ? (lakhya ko?i) ? (sa?kha) |
(ka?pam) |
? (lak?a klu) |
? ? ? (ondu lak?a ki) |
? (oru lak?a? ki) |
? (da? kharba) |
10,00,00,00,00,000 | 10^{12} | 1,000,000,000,000 | One trillion (one billion) SI prefix: tera- |
Ten kharab / one thousand arab / one lakh crore | ||||||||||||
/ (n?l) |
? (ek mah?padma) |
? (dô? l?kh ki) ? (pôdd?) ? (môhô?kh?) |
? ? (dasa lakhya ko?i) ? (padma) |
(nika?pam) |
(padi lak?ala klu) |
? ? (hattu lak?a ki) |
? ? (pattulak?a? ki) |
(n?l) |
1,00,00,00,00,00,000 | 10^{13} | 10,000,000,000,000 | Ten trillion (ten billion) |
One nil / one hundred kharab / ten thousand arab / ten lakh crore | ||||||||||||
/ (das n?l) / ? ? (?k kar kar) |
? (?k ?a?kh?) |
? (êk l?kh ki) ? (?ôtôki lôkk?) ? (môh?pôdd?) |
? ? (sahe lakhya ko?i) ? (s?gara) |
(patumam) |
? (ki klu) |
? ? ? (ondu ki ki) |
? ? (nu? lak?a? ki) |
(da? n?l) |
10,00,00,00,00,00,000 | 10^{14} | 100,000,000,000,000 | One hundred trillion (one hundred billion) |
Ten nil / one crore crore | ||||||||||||
? / (padma) |
? ? (eka jaladhi ?a?kh?) |
? (h?z?r l?kh ki) |
? ? ? (haj?ra lakhya ko?i) (antya) |
(ca?kam) |
(padi kla klu) |
? ? (hattu ki ki) |
? (?yira? lak?a? ki) |
? (padma) |
100,00,00,00,00,00,000 | 10^{15} | 1,000,000,000,000,000 | One quadrillion (one billiard) SI prefix: peta- |
One padma / one hundred nil / ten crore crore | ||||||||||||
? / (das padma) |
(eka antya) |
? (dô? h?z?r l?kh ki) |
? ? ? (dasa haj?ra lakhya ko?i) ? (madhya) |
? (veam) ? (camuttiram) |
(vanda kla klu) |
? ? ? (n?ru ki ki) |
? (patin?yira? lak?a? ki) |
? (da? padma) |
10,00,00,00,00,00,00,000 | 10^{16} | 10,000,000,000,000,000 | Ten quadrillion (ten billiard) |
Ten padma / one hundred crore crore | ||||||||||||
/ ? (?a?kh) |
(eka par?rdha) |
? (?oto h?z?r l?kh ki) |
? ? ? (sahe haj?ra lakhya ko?i) (par?rddha) |
(anniyam) |
(veyyi kla klu) |
? ? ? (ondu s?vira ki ki) |
? (lak?a? lak?a? ki) |
(?a?kha) |
100,00,00,00,00,00,00,000 | 10^{17} | 100,000,000,000,000,000 | One hundred quadrillion (one hundred billiard) |
One shankh / one hundred padma / one thousand crore crore / one lakh lakh crore | ||||||||||||
/ ? (das ?a?kh) / ? (gul?an) |
(eka mah?par?rdha) |
? (do? ?oto h?z?r l?kh ki) (guln) |
? ? ? (dasa sahe haj?ra lakhya ko?i) (da?a par?rddha) |
(arttam) |
(padi v?la kla klu) |
? ? (hattu s?vira ki ki) |
? ? (pattulak?a? lak?a? ki) |
(da? ?a?kha) |
10,00,00,00,00,00,00,00,000 | 10^{18} | 1,000,000,000,000,000,000 | One quintillion (one trillion) SI prefix: exa- |
Ten shankh / ten thousand crore crore |
There are various systems of numeration found in various ancient Vedic literary works of India. The following table gives one such system used in the Valmiki Ramayana.^{[5]}
Name | Indian notation | Power notation | Indian system | Short scale Western |
---|---|---|---|---|
(?ka) | 1 | 10^{0} | One | One |
(da?a) | 10 | 10^{1} | Ten | Ten |
(?ata) | 100 | 10^{2} | One hundred | One hundred |
(sahasra) | 1,000 | 10^{3} | One thousand | One thousand |
? (lak?a) | 1,00,000 | 10^{5} | One lakh | One hundred thousand |
? (ki) |
1,00,000 ?ata | 10^{7} | One crore | Ten million |
(?a?ku) | 1,00,000 ko?i | 10^{12} | Ten kharab or One lakh crore | One trillion |
(maha?ku) | 1,00,000 ?a?ku | 10^{17} | One shankh or One thousand crore crore | One hundred quadrillion |
(vrinda) | 1,00,000 maha?ku | 10^{22} | Ten sextillion (ten trilliard) | |
(mah?vrinda) | 1,00,000 vrinda | 10^{27} | One octillion | |
? (padma) | 1,00,000 mah?vrinda | 10^{32} | One hundred nonillion | |
? (mah?padma) | 1,00,000 padma | 10^{37} | Ten undecillion | |
? (kharva) | 1,00,000 mah?padma | 10^{42} | One tredecillion | |
? (mah?kharva) | 1,00,000 kharva | 10^{47} | One hundred quattuordecillion | |
(samudra) | 1,00,000 mah?kharva | 10^{52} | Ten sexdecillion | |
(ogha) | 1,00,000 samudra | 10^{57} | One octodecillion | |
? (mahaugha) | 1,00,000 ogha | 10^{62} | One hundred novemdecillion |
Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.^{[6]}
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.^{[7]}
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 English numbering system is preferred for higher denominations (i.e millions etc).
Most institutions and citizens in India use the Indian number system, although the Reserve Bank of India has been noted as a rare exception.^{[8]}