Long and short scales

What it is

The names of large numbers are a Latin number plus -illion: billion (two), trillion (three), quadrillion (four). What differs is how much one step is worth.

• The short scale, used in English: each new name is a thousand times the one before. A billion is a thousand million (10⁹), a trillion a thousand billion (10¹²).
• The long scale, used in most of continental Europe: each new name is a million times the one before. There a billion is a million million (10¹²) and a trillion a million billion (10¹⁸). The steps in between take -illiard: a milliard is a thousand million (10⁹).

The same word, different numbers:

• 1,000,000,000 (10⁹): one billion in English; un milliard in French, eine Milliarde in German, en miljard in Swedish.
• 1,000,000,000,000 (10¹²): one trillion in English; un billion in French, eine Billion in German, un billón in Spanish, en biljon in Swedish.

Up to a million the two scales agree. They part at 10⁹, and the gap widens as the numbers grow — every name is in the table of large numbers.

The rule behind them: the name with Latin number n is 10³ⁿ⁺³ on the short scale and 10⁶ⁿ on the long one. Billion, n = 2, is 10⁹ in English and 10¹² in German.

How it came about. The French mathematician Nicolas Chuquet used the names with bi-, tri- and so on for powers of a million in 1484 — the long scale in its first form. Jacques Peletier filled the gaps with milliard for a thousand million in his arithmetic of 1549. Later French and Italian reckoners let each name stand for a thousand times the one before, and that short scale is the one that took hold in the United States.

Britain long kept the long scale. On 20 December 1974 Prime Minister Harold Wilson was asked in the House of Commons whether ministers would use billion only in its British sense of a million million. He answered no: the word was now used internationally to mean a thousand million, and it would be confusing for British ministers to use it in any other sense. British English has followed the short scale since, broadly.

Roughly how it stands today:

• Short scale: English in the United States, the United Kingdom, Canada, Australia and the other English-speaking countries, and Portuguese in Brazil. Russian and Turkish use the short scale but keep a milliard word for 10⁹.
• Long scale: French, German, Dutch, Spanish, Italian, the Scandinavian languages and most other languages of continental Europe, and Spanish in Latin America.
• Neither: Chinese, Japanese and Korean count in groups of four digits, and in India lakh (10⁵) and crore (10⁷) are used as well.

Why it matters

Whenever a number crosses a language. A German report of 36 Billionen Euro is 36 trillion euros, not 36 billion, and a translation that keeps the word makes the number a thousand times too small.

The safe course is digits or powers of ten, which read the same everywhere: 10⁹ is 10⁹ in Berlin and in Boston. That is also why science uses SI prefixes — giga (10⁹) and tera (10¹²) mean one thing in every language. Numbers to words writes a number out in English or Swedish and uses each language’s own scale.

Underneath both scales is place value: the digits are grouped in threes, and the short scale gives each group of three a new name, the long scale every second one.

Common misconceptions

• “A German Billion is a billion.” It is a trillion. The German for a billion is Milliarde.
• “British English has always counted like American English.” British usage was the long scale, and a billion there meant a million million, until the government changed in 1974. In older British texts a billion can still be 10¹².
• “The scales only differ by a name.” The difference grows with every step: a long-scale trillion is 10¹⁸, a million times a short-scale one.

Common questions