Metric units are units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. According to Schadow and McDonald, [1] metric units, in general, are those units "defined 'in the spirit' of the metric system, that emerged in late 18th century France and was rapidly adopted by scientists and engineers. Metric units are in general based on reproducible natural phenomena and are usually not part of a system of comparable units with different magnitudes, especially not if the ratios of these units are not powers of 10. Instead, metric units use multiplier prefixes that magnifies or diminishes the value of the unit by powers of ten." The most widely used examples are the units of the International System of Units (SI). By extension they include units of electromagnetism from the CGS and SI units systems, and other units for which use of SI prefixes has become the norm. Other unit systems using metric units include:
The first group of metric units are those that are at present defined as units within the International System of Units (SI). In its most restrictive interpretation, this is what may be meant when the term metric unit is used.
The unit one (1) is the unit of a quantity of dimension one. It is the neutral element of any system of units. [2]
In addition to the unit one, the SI defines 7 base units and associated symbols:
The SI also defines 22 derived units and associated symbols:
Furthermore, there are twenty-four metric prefixes that can be combined with any of these units except one (1) and kilogram (kg) to form further units of the SI. For mass, the same prefixes are applied to the gram (g) instead of the kilogram.
There are several metric systems, most of which have become disused or are still used in only niche disciplines. Systems are listed with named units that are associated with them.
The centimetre–gram–second system of units (CGS) is based on three base units: centimetre, gram and second. Its subsystems (CGS-ESU, CGS-EMU and CGS-Gaussian) have different defining equations for their systems of quantities for defining electromagnetic quantities and hence the associated units, with CGS-Gaussian units being selected from each of the other two subsystems.
The CGS-to-SI correspondence of electromagnetic units as given was exact prior to the 2019 redefinition of the SI base units, until which the magnetic constant μ0 was defined as 4π×10−7 N⋅A−2. As from the redefinition, μ0 has an inexactly known value when expressed in SI units, with the exactness of the electromagnetic unit correspondence given here being affected accordingly.
The ampere, often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb (C) moving past a point per second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.
The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism.
A centimetre or centimeter, with SI symbol cm, is a unit of length in the International System of Units (SI) equal to one hundredth of a metre, centi being the SI prefix for a factor of 1/100. Equivalently, there are 100 centimetres in 1 metre. The centimetre was the base unit of length in the now deprecated centimetre–gram–second (CGS) system of units.
The gauss, is a unit of measurement of magnetic induction, also known as magnetic flux density. The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second electromagnetic units (CGS-EMU) system. It was named after the German mathematician and physicist Carl Friedrich Gauss in 1936. One gauss is defined as one maxwell per square centimetre.
The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.
The metric system is a decimal-based system of measurement. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela.
The franklin (Fr), statcoulomb (statC), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. It is a derived unit given by
The pascal is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is an SI coherent derived unit defined as one newton per square metre (N/m2). It is also equivalent to 10 barye in the CGS system. Common multiple units of the pascal are the hectopascal, which is equal to one millibar, and the kilopascal, which is equal to one centibar.
The statvolt is a unit of voltage and electrical potential used in the CGS-ESU and gaussian systems of units. In terms of its relation to the SI units, one statvolt corresponds to ccgs 10−8 volt, i.e. to 299.792458 volts.
The maxwell is the CGS (centimetre–gram–second) unit of magnetic flux.
The metre–tonne–second (MTS) system of units was invented in France where it became the legal system between 1919 and 1961. It was adopted by the Soviet Union in 1933 and abolished there in 1955. It was a coherent metric system of units, much as SI and the centimetre–gram–second system (CGS), but with larger units for industrial use, whereas the CGS system was regarded as suitable for laboratory use only.
In physics, the weber is the unit of magnetic flux in the International System of Units (SI). The unit is derived from the relationship 1 Wb = 1 V⋅s (volt-second). A magnetic flux density of 1 Wb/m2 is one tesla.
The tesla is the unit of magnetic flux density in the International System of Units (SI).
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units.
The debye is a CGS unit of electric dipole moment named in honour of the physicist Peter J. W. Debye. It is defined as 10−18 statcoulomb-centimetres. Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb, which were separated by 1 ångström. This gave a convenient unit for molecular dipole moments.
The abampere (abA), also called the biot (Bi) after Jean-Baptiste Biot, is the derived electromagnetic unit of electric current in the emu-cgs system of units. One abampere corresponds to ten amperes in the SI system of units. An abampere of current in a circular path of one centimeter radius produces a magnetic field of 2π oersteds at the center of the circle.
The gravitational metric system is a non-standard system of units, which does not comply with the International System of Units (SI). It is built on the three base quantities length, time and force with base units metre, second and kilopond respectively. Internationally used abbreviations of the system are MKpS, MKfS or MKS . However, the abbreviation MKS is also used for the MKS system of units, which, like the SI, uses mass in kilogram as a base unit.
The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.
The statampere (statA) is the derived electromagnetic unit of electric current in the CGS-ESU and Gaussian systems of units.:278 One statampere corresponds to 10/ccgs ampere ≈ 3.33564×10−10 ampere in the SI system of units.
A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.