System of measurement

The French Revolution gave rise to the metric system, and this has spread around the world, replacing most customary units of measure. In most systems, length (distance), mass, and time are base quantities.

Later science developments showed that either electric charge or electric current could be added to extend the set of base quantities by which many other metrological units could be easily defined. (However, electrical units are not necessary for such a set. Gaussian units, for example, have only length, mass, and time as base quantities, and the ampere is defined in terms of other units.) Other quantities, such as power and speed, are derived from the base set: for example, speed is distance per unit time. Historically a wide range of units was used for the same type of quantity: in different contexts, length was measured in inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, stadia, leagues, with conversion factors which were not powers of ten. Such arrangements were satisfactory in their own contexts.

The preference for a more universal and consistent system (based on more rational base units) only gradually spread with the growth of science. Changing a measurement system has substantial financial and cultural costs which must be offset against the advantages to be obtained from using a more rational system. However pressure built up, including from scientists and engineers for conversion to a more rational, and also internationally consistent, basis of measurement.

In antiquity, systems of measurement were defined locally: the different units might be defined independently according to the length of a king's thumb or the size of his foot, the length of stride, the length of arm, or maybe the weight of water in a keg of specific size, perhaps itself defined in hands and knuckles. The unifying characteristic is that there was some definition based on some standard. Eventually cubits and strides gave way to "customary units" to meet the needs of merchants and scientists.

In the metric system and other recent systems, a single basic unit is used for each base quantity. Often secondary units (multiples and submultiples) are derived from the basic units by multiplying by powers of ten, i.e. by simply moving the decimal point. Thus the basic metric unit of length is the metre; a distance of 1 m is 1,000 millimetres, or 0.001 kilometres.

A baby bottle that measures in three measurement systems—metric, imperial (UK), and US customary.

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795. During this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, and then to English speaking countries.

Multiples and submultiples of metric units are related by powers of ten and their names 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 base units, the metre for length and the gram for mass. The other units of length and mass, and all units of area, volume, and derived units such as density were derived from these two base units.

Mesures usuelles (French for customary measurements) were a system of measurement introduced as a compromise between the metric system and traditional measurements. It was used in France from 1812 to 1839.

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 (mks). In some engineering fields, like computer-aided design, millimetre–gram–second (mmgs) is also used.

The current international standard for the metric system is the International System of Units (Système international d'unités or SI). It is a system in which all units can be expressed in terms of seven units. The units that serves as the SI base units are the metre, kilogram, second, ampere, kelvin, mole, and candela.

Both imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the former British Empire and the British Commonwealth, but in all these countries they have been largely supplanted by the metric system. They are still used for some applications in the United Kingdom but have been mostly replaced by the metric system in commercial, scientific, and industrial applications. US customary units, however, are still the main system of measurement in the United States. While some steps towards metrication have been made (mainly in the late 1960s and early 1970s), the customary units have a strong hold due to the vast industrial infrastructure and commercial development.

While imperial and US customary systems are closely related, there are a number of differences between them. Units of length and area (the inch, foot, yard, mile, etc.) have been identical since the adoption of the International Yard and Pound Agreement; however, America and, formerly, India retained older definitions for surveying purposes. This gave rise to the US survey foot for instance. The Avoirdupois 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 US and the hundredweights and tons are short: 100 lb and 2000 lb respectively.

Where these systems most notably differ is in their units of volume. A US fluid ounce (fl oz), about 29.6 millilitres (ml), is slightly larger than the imperial fluid ounce (about 28.4 ml). However, as there are 16 US fl oz to a US pint and 20 imp fl oz per imperial pint, the imperial pint is about 20% larger. The same is true of quarts, gallons, etc.; six US gallons are a little less than five imperial gallons.

The Avoirdupois system served as the general system of mass and weight. In addition to this there are the Troy and the Apothecaries' systems. Troy weight was customarily used for precious metals, black powder and gemstones. The troy ounce is the only unit of the system in current use; it is used for precious metals. Although the troy ounce is larger than its Avoirdupois equivalent, the pound is smaller. The obsolete troy pound was divided into 12 ounces, rather than the 16 ounces per pound of the Avoirdupois system. The Apothecaries' system was traditionally used in pharmacology, but has now been replaced by the metric system; it shared the same pound and ounce as the troy system but with different further subdivisions.

Natural units are physical units of measurement defined in terms of universal physical constants in such a manner that selected physical constants take on the numerical value of one when expressed in terms of those units. Natural units are so named because their definition relies on only properties of nature and not on any human construct. Various systems of natural units are possible.

Some other examples are as follows:

• Geometric unit systems are useful in relativistic physics. In these systems the base physical units are chosen so that the speed of light and the gravitational constant are set equal to unity.
• Planck units are a form of geometric units obtained by also setting the reduced Planck constant to unity. They are based only on properties of free space rather than any object or particle.
• Stoney units are a form of geometric units obtained by also setting the Coulomb constant and the elementary charge to unity.
• "Schrödinger" units are similar to Planck units and also set the elementary charge to unity, but allow the speed of light to float.
• Hartree atomic units are a system of units used in atomic physics, particularly for describing the properties of electrons. The atomic units have been chosen such that several constants relating to the electron are all equal to one: the electron mass, the elementary charge, the Coulomb constant and the reduced Planck constant. The unit of energy in this system is the total energy of the electron in the Bohr atom and called the Hartree energy. The unit of length is the Bohr radius.
• Electronic units are similar to Stoney units but set the electron mass to unity and allow the gravitational constant to float. They are also similar to atomic units but set the speed of light to unity and allow the Planck constant to float.
• Quantum electrodynamical units are similar to the electronic system of units except that the proton mass is normalised rather than the electron mass.

Non-standard measurement units also found in books, newspapers etc., include:

A unit of measurement that applies to money is called a unit of account in economics and unit of measure in accounting.[3] This is normally a currency issued by a country or a fraction thereof; for instance, the US dollar and US cent (​¹⁄₁₀₀ of a dollar), or the euro and euro cent.

ISO 4217 is the international standard describing three letter codes (also known as the currency code) to define the names of currencies established by the International Organization for Standardization (ISO).

Throughout history, many official systems of measurement have been used. While no longer in official use, some of these customary systems are occasionally used in day-to-day life, for instance in cooking.

• Tavernor, Robert (2007), Smoot's Ear: The Measure of Humanity, ISBN 0-300-12492-9

• CLDR - Unicode localization of currency, date, time, numbers
• A Dictionary of Units of Measurement
• Old units of measure
• Measures from Antiquity and the Bible Antiquity and the Bible at the Wayback Machine (archived May 10, 2008)
• Reasonover's Land Measures A Reference to Spanish and French land measures (and their English equivalents with conversion tables) used in North America
• The Unified Code for Units of Measure