Long and Short Scales

The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries and Arabic-speaking countries use the short scale. In all such countries, the number names are translated into the local language, but retain a name similarity due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from the long and short scales.

Long scale is the English translation of the French term échelle longue. It refers to a system of large-number names in which every new term greater than million is 1,000,000 times the previous term: billion means a million millions (1012), trillion means a million billions (1018), and so on.

Short scale is the English translation of the French term échelle courte. It refers to a system of large-number names in which every new term greater than million is 1,000 times the previous term: billion means a thousand millions (109), trillion means a thousand billions (1012), and so on.

For integers less than a thousand million (< 109), the two scales are identical. At and above a thousand million (≥ 109), the two scales diverge by using the same words for different number values. These "false friends" can be a source of misunderstanding.

For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that the two systems were often referred to as British and American in the English language. In 1974, the government of the UK switched to the short scale, a change that is reflected in its mass media and official usage. Although some residual usage of the long scale continues in the UK, the phrases British usage and American usage are no longer accurate characterisations. Usage of the two systems can be a subject of controversy. Differences in opinion as to which system should be used can evoke resentment between adherents, while national differences of any kind can acquire jingoistic overtones.

The first recorded use of the terms échelle courte and échelle longue was by the French mathematician Geneviève Guitel in 1975.