Long and short scales

The long and short scales are two ways people name big numbers. They work the same for small numbers like one, ten, or a hundred, but they change for really big numbers. Most of the world uses one of these two scales to talk about huge amounts.

Countries in Europe, places where people speak French, German, or Spanish, usually use the long scale. Places where people speak English, Arabic, or Hebrew, along with many countries in Europe and Brazil, use the short scale.

The big difference shows up when numbers get really large. In the short scale, a word like "billion" means a thousand million (10⁹). But in the long scale, "billion" means a million million (10¹²). This makes the word "billion" tricky because it means different things in different places. To avoid confusion, scientists use special names from the International System of Units, like giga, which always means 10⁹, no matter which scale is used.

Some other places, like in East Asia and South Asia, have their own special ways of naming big numbers. These include systems used in India, China, Japan, and Korea.

Naming

Both the long and short scales name numbers in steps of 1000. For smaller numbers, like those below 10⁹, both scales use the same names. However, for larger numbers, the two scales use the same names but give them different values.

For example, the word "billion" means different amounts depending on which scale you use. Some languages using the long scale add special names by changing the ending to "–iard". After "million" comes "milliard" (10⁹), and after "billion" comes "billiard" (10¹⁵).

Comparison

The following tables show the names and values of the two number systems, the long and short scales.

Note that sometimes a quantity is described using the smaller word, like "thousand billion" instead of the longer word "billiard".

The different sizes of the same name in the two scales can be described as:

Avoiding confusion

One way to avoid confusion between the two scales is to use numbers like 1,000,000,000,000 instead of words like "trillion" or "billion." This can get tricky with really big numbers.

Better methods for larger numbers include using scientific notation, like 1.2×10¹⁰, or using metric prefixes such as "giga" for 10⁹ and "tera" for 10¹². These help avoid mix-ups, even when talking about things like gigawatts or terawatts.

History

The way people name big numbers has changed over many years. In the 1200s, people started to talk about two different ways to name these big numbers. In 1975, a French mathematician first used the words "short scale" and "long scale" to describe these two systems.

The short scale became common in the United States after it was taught in schools in the early 1800s. Now, many English-speaking countries use it. For a long time, the United Kingdom used the long scale, but in 1974, it switched to the short scale, matching the United States.

Because of these two different ways, it's important to be careful when looking at old documents or comparing numbers between countries. Some countries have used both systems at different times.

In the past, some languages used the word "billion" to mean 10¹², which is now called "trillion" in American English. Other languages used "billion" to mean 10⁹, which matches the American use today.

The word "million" comes from old French and Italian words that mean "big thousand." Some European languages still use the word "milliard" for 10⁹, but this word is not used in American English.

Date	Event
13th century	The word million was not used in any language before the 13th century. The monk and polymath Maximus Planudes (c. 1260–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states. Over the next two centuries, the term became widely accepted and was adopted by other Italian states, France and other European countries.
Late 14th century	The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written c. 1360–1387 in Middle English), with Coueyte not his goodes For millions of moneye Translation: Covet not his goods for millions of money
1475	French mathematician Jehan Adam, writing in Middle French, recorded the words bymillion and trimillion as meaning 1012 and 1018 respectively in a manuscript Traicté en arismetique pour la practique par gectouers, now held in the Bibliothèque Sainte-Geneviève in Paris. ... item noctes que le premier greton dembas vault ung, le second vault dix, le trois vault cent, le quart vult [sic] mille, le Ve vault dix M, le VIe vault cent M, le VIIe vault Milion, Le VIIIe vault dix Million, Le IXe vault cent Millions, Le Xe vault Mil Millions, Le XIe vault dix mil Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault cent mil [sic] bymillions, Le XVIe vault mil bymillions, Le XVIIe vault dix Mil bymillions, Le XVIIIe vault cent mil bymillions, Le XIXe vault trimillion, Le XXe vault dix trimillions ... Translation: ... Likewise, note that the first counter from the bottom is worth one, the 2nd is worth ten, the 3rd is worth one hundred, the 4th is worth one thousand, the 5th is worth ten thousand, the 6th is worth one hundred thousand, the 7th is worth a million, the 8th is worth ten millions, the 9th is worth one hundred millions, the 10th is worth one thousand millions, the 11th is worth ten thousand millions, the 12th is worth one hundred thousand million, the 13th is worth a bymillion, the 14th is worth ten bymillions, the 15th is worth one [hundred] bymillions, the 16th is worth one thousand bymillions, the 17th is worth ten thousand bymillions, the 18th is worth hundred thousand bymillions, the 19th is worth a trimillion, the 20th is worth ten trimillions ...
1484	French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien, used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, ... 1054. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique. Chuquet's original article was rediscovered in the 1870s and then published for the first time in 1880. ...[preder s'] Item l'on doit savoir que ung million vault mille milliers de unitez, et ung byllion vault mille milliers de millions, et [ung] tryllion vault mille milliers de byllions, et ung quadrillion vault mille milliers de tryllions et ainsi des aultres : Et de ce en est pose ung exemple nombre divise et punctoye ainsi que devant est dit, tout lequel nombre monte 745324 tryllions 804300 byllions 700023 millions 654321. Exemple : 745324'8043000'700023'654321 ... [sic] Translation: ...likewise, one should know that a million is worth a thousand thousand units, and a byllion is worth a thousand thousand millions, and tryllion is worth a thousand thousand byllions, and a quadrillion is worth a thousand thousand tryllions, and so on for the others. And an example of this follows, a number divided up and punctuated as previously described, the whole number being 745324 tryllions, 804300 byllions 700023 millions 654321. Example: 745324'8043000'700023'654321 ... [sic] The extract from Chuquet's manuscript, the transcription and translation provided here all contain an original mistake: one too many zeros in the 804300 portion of the fully written out example: 745324'8043000 '700023'654321 ...
1516	French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "ten myriad myriad" or 109 in his book De Asse et partibus eius Libri quinque. .. hoc est decem myriadum myriadas:quod vno verbo nostrates abaci studiosi Milliartum appellant:quasi millionum millionem Translation: .. this is ten myriad myriads, which in one word our students of numbers call Milliart, as if a million millions
1549	The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart) to mean 1012, attributing the term to the earlier usage by Guillaume Budé
17th century	With the increased usage of large numbers, the traditional punctuation of large numbers into six-digit groups evolved into three-digit group punctuation. In some places, the large number names were then applied to the smaller numbers, following the new punctuation scheme. Thus, in France and Italy, some scientists then began using billion to mean 109, trillion to mean 1012, etc. This usage formed the origins of the later short scale. The majority of scientists either continued to say thousand million or changed the meaning of the Pelletier term, milliard, from "million of millions" down to "thousand million". This meaning of milliard has been occasionally used in England, but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping the original long scale billion from Adam, Chuquet and Pelletier.
1676	The first published use of milliard as 109 occurred in the Netherlands. .. milliart/ofte duysent millioenen.. Translation: ..milliart / also thousand millions..
1729	The short-scale meaning of the term billion had already been brought to the British American colonies. The first American appearance of the short scale value of billion as 109 was published in the Greenwood Book of 1729, written anonymously by Prof. Isaac Greenwood of Harvard College.
Late 18th century	As early as 1762 (and through at least the early 20th century), the dictionary of the Académie française defined billion as a term of arithmetic meaning a thousand millions.
Early 19th century	France widely converted to the short scale, and was followed by the U.S., which began teaching it in schools. Many French encyclopedias of the 19th century either omitted the long scale system or called it "désormais obsolète", a now obsolete system. Nevertheless, by the mid 20th century France would officially convert back to the long scale.
1926	H. W. Fowler's A Dictionary of Modern English Usage noted It should be remembered that "billion" does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform. Although American English usage did not change, within the next 50 years, French usage changed from short scale to long, and British English usage changed from long scale to short.
1948	The 9th General Conference on Weights and Measures received requests to establish an International System of Units. One such request was accompanied by a draft French Government discussion paper, which included a suggestion of universal use of the long scale, inviting the short-scale countries to return or convert. This paper was widely distributed as the basis for further discussion. The matter of the International System of Units was eventually resolved at the 11th General Conference in 1960. The question of long scale versus short scale was not resolved and does not appear in the list of any conference resolutions.
1960	The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes. SI is therefore independent of the number scale being used. SI also notes the language-dependence of some larger-number names and advises against using ambiguous terms such as billion, trillion, etc. The National Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.
1961	The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).
1974	British prime minister Harold Wilson explained in a written answer to the House of Commons that UK government statistics would from then on use the short scale, reported in Hansard for 20 December 1974: Mr. Maxwell-Hyslop asked the Prime Minister whether he would make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million. The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning. The BBC and other UK mass media quickly followed the government's lead within the UK. During the last quarter of the 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either also followed this lead or independently switched to the short scale use. However, in most of these countries, some limited long scale use persists and the official status of the short scale use is not clear.
1975	French mathematician Geneviève Guitel introduced the terms long scale (French: échelle longue) and short scale (French: échelle courte) to refer to the two numbering systems.
1994	The Italian Government confirmed their official usage of the long scale.

Current usage

Most of the world uses one of two ways to name really big numbers. These are called the short scale and the long scale.

The short scale is mostly used in English-speaking countries like Australia, Canada, Ireland, the United Kingdom, and the United States. In these places, a billion means 1,000 million.

The long scale is used by most countries in Europe and other places where languages like French, German, and Spanish are spoken. In these places, a billion means a million million. Countries using the long scale include France, Germany, Spain, and Italy.

Some countries, like Canada, use either the short or long scale depending on the language spoken. For example, English-speaking Canadians use the short scale, while French-speaking Canadians use the long scale.

Country or territory	Short scale usage	Long scale usage
Canada	Canadian English (109 = billion, 1012 = trillion)	Canadian French (109 = milliard, 1012 = billion or mille milliards).
Mauritius  Seychelles  Vanuatu	English (109 = billion, 1012 = trillion)	French (109 = milliard, 1012 = billion)
Namibia  South Africa	South African English (109 = billion, 1012 = trillion)	Afrikaans (109 = miljard, 1012 = biljoen)
Puerto Rico	Economic and technical (109 = billón, 1012 = trillón)	Latin American export publications (109 = millardo or mil millones, 1012 = billón)

Country	Number system	Naming of large numbers
Bangladesh  India  Maldives  Nepal  Pakistan	Indian numbering system	Traditional system for everyday use, but short or long scale may also be in use
Bhutan	Dzongkha numerals	Traditional system
Cambodia	Khmer numerals	Traditional system
China  Republic of China  South Korea  North Korea  Japan	East Asian numbering system: Chinese numerals Korean numerals Japanese numerals	Traditional myriad system for the larger numbers; special words and symbols up to 1068
Greece	Calque of the short scale	Names of the short scale have not been loaned but calqued into Greek, based on the native Greek word for million, εκατομμύριο ekatommyrio ("hundred-myriad", i.e. 100 × 10,000): δισεκατομμύριο disekatommyrio "bi+hundred-myriad" = 109 (short scale billion) τρισεκατομμύριο trisekatommyrio "tri+hundred-myriad" = 1012 (short scale trillion) τετράκις εκατομμύριο tetrakis ekatommyrio "quadri+hundred-myriad" = 1015 (short scale quadrillion), and so on.
Laos	Lao numerals	Traditional system
Mongolia	Mongolian numerals	Traditional myriad system for the larger numbers; special words up to 1067
Sri Lanka	Sinhala numerals Tamil numerals	Traditional systems
Thailand	Thai numerals	Traditional system based on millions
Vietnam	Vietnamese numerals	Traditional system(s) based on thousands