# Systems of measurement

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A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce. Scientifically, when later analyzed, some quantities are designated as fundamental units meaning all other needed units can be derived from them, whereas in the early and most historic eras, the units were designated by decree of the ruling entities and were not necessarily well inter-related or self-consistent.

## The metric system

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1791. During this evolution the use of these systems spread throughout the world, first to the non-English-speaking countries, and more recently to the English speaking countries.

Multiples and submultiples of metric units are related by powers of ten; the names for these are formed with prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units.

In the early metric system there were two fundamental or base units, the metre and the gram, for length and mass. The other units of length and mass, and all units of area, volume, and compound units such as density were derived from these two fundamental units.

Mesures usuelles (French for customary measurements) were a system of measurement introduced to act as compromise between the metric system and traditional measurements. It was used in France from 1812 to 1839. Similar proposals to metrify England's Imperial units were proposed but never officially adopted.

A number of variations on the metric system have been in use. These include gravitational systems, the centimetre-gram-second systems (cgs) useful in science, the metre-tonne-second system (mts) once used in the USSR and the metre-kilogram-second system of units (mks) most commonly used today.

The current international standard metric system is the International System of Units (Système international d'unités or SI). It is an mks system based on the metre, kilogram and second as well as the kelvin, ampere, candela, and mole.

The SI includes two classes of units which are defined and agreed internationally. The first of these classes are the seven SI base units for length, mass, time, temperature, electric current, luminous intensity and amount of substance. The second of these are the SI derived units. These derived units are defined in terms of the seven base units. All other quantities (e.g. work, force, power) are expressed in terms of SI derived units.

## Imperial and U.S. customary units

Both the Imperial units and U.S. customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire. They are still used to some extent but have now been mostly replaced by the metric system. U.S. customary units are the main system of measurement in the United States. However some steps towards metrication have been made. The metric system is preferred in certain fields such as science and medicine.

These two systems are closely related. There are, however, a number of differences between them. Units of length and area (the inch, foot, yard, mile etc.) are identical except for surveying purposes. Units of mass and weight differ for units larger than a pound (lb.). The Imperial system uses a stone of 14 lb., a long hundredweight of 112 lb. and a long ton of 2240 lb. The stone is not used in the U.S. and the hundredweights and tons are short being 100 lb. and 2000 lb. respectively.

Where these systems most notably differ is in their respective units of volume. A U.S. fluid ounce (fl. oz.) is slightly larger than its Imperial equivalent (the former being approximately 29.6 millilitres (ml) and the latter 28.4 ml). However, as there are 16 U.S. fl. oz. to a U.S. pint as opposed to the 20 Imperial fl. oz. per Imperial pint, these pints are quite different in volume. The same is true of quarts, gallons, etc. Six U.S. gallons are a little less than five Imperial gallons.

## Natural units

The above systems of units are based on arbitrary unit values, formalised as standards. Some unit values occur repeatedly in nature. Two systems of units based on these are called Planck units and Geometric units.

## Atomic units

Atomic units (au) are a convenient system of units of measurement used in atomic physics, particularly for describing the properties of electrons. The atomic units have been chosen such that the fundamental electron properties are all equal to one atomic unit.

## Non-standard units

Sometimes found in books etc., include:

• A ton of TNT, and its multiples the kiloton and the megaton and the gigaton. Often used in stating the power of very energetic events such as explosions and volcanic events and earthquakes and asteroid impacts. A gram of TNT as a unit of energy has been defined as 1000 thermochemical calories = roughly 4184 joules.
• The Hiroshima atom bomb. Its force is often used in the public media and popular books as a unit of energy. (Its yield was roughly 13 kilotons.)
• The weight of an elephant. It is often used as a unit of weight in popular books about very big animals such as dinosaurs. This unit needs to be defined, as the real weight of elephants varies much with age and sex and species.
• The (American) football field, which has a playing area 100 yards long. This is often used by the American public media for the sizes of large buildings or parks: easily walkable but non-trivial distances.

## Units of currency

A unit of measurement that applies to money is called a unit of account. This is normally a currency issued by a country or a fraction thereof; for instance, the U.S. dollar and U.S. cent (1/100 of a dollar), or the Euro and Eurocent.

## Historical Mediterranean and European systems of measurement

Prior to the global adoption of the metric system many different systems of measurement had been in use. Many of these were related to some extent or other. Often they were based on the dimensions of the human body.

In the History of measurement many of the units that we have records of, or at least the ones that have been used in Europe and around the Mediterranean are variations on older systems originating in the Ancient Near East and Egypt.