A system of measurement is a frame in which physical qualities (such as length, weight, temperature, etc.) can be quantified with numbers. Among many systems of measurement, the metric system refers to ones that standardise a set of base units and a nomenclature describing relatively large and small quantities using decimal-based multiplicative unit prefixes (such as kilo and milli). The International System of Units (SI) is a good example, and there are other widely accepted systems (less popular than SI) mainly used in specific fields, such as the Gaussian units for electromagnetism.
Though rules governing the metric system have changed over time, the modern definition in the International System of Units prescribes the metric prefixes and seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
An SI derived unit is a named combination of base units, such as the hertz (cycles per second), newton (kg⋅m/s2), and tesla (1 kg⋅s−2⋅A−1). In the case of degrees Celsius (°C), it is a shifted scale derived from the kelvin (273.15 K is equal to 0 °C while 1 K interval is same to the 1 °C interval).
The SI system derives from the older metre-kilogram-second (MKS) system of units, though the definitions of the base units have evolved over time. Today, all base units are defined by physical constants – not by prototypes in the form of physical objects, as they were in the past.
Other metric system variants include the centimetre–gram–second system of units, the metre–tonne–second system of units, and the gravitational metric system. Each has unaffiliated metric units, and some of these systems are still used in limited contexts. Particular non-SI units such as the litre remain widely used.
Adoption
The SI system has been adopted as the official system of weights and measures in almost all countries of the world.
A notable outlier is the United States (US). Although it uses the system in some contexts, the US has resisted full adoption, and continues to use different measurement systems.
Adopting the metric system is known as metrication.
Multiplicative prefixes
In the SI system and generally in older metric systems, multiples and fractions of a unit can be described via a prefix on a unit name that implies a decimal (base-10), multiplicative factor.
The prefix kilo, for example, implies a factor of 1000 (103), and the prefix milli implies a factor of 1/1000 (10−3). Thus, a kilometre is a thousand metres, and a milligram is one thousandth of a gram. These relations can be written symbolically as:
Base units
The decimalised system is based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body.
The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a base unit of measure. The definition of base units has increasingly been realised in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit derived from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second; the unit of length should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.
Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes, the CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian system; the metre–tonne–second (MTS) system; and the gravitational metric systems, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.
Attributes
Ease of learning and use The metric system is intended to be easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units.
It is a coherent system with derived units built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a common set of prefixes.
Extensibility The metric system is extensible since the governing body reviews, modifies and extends it needs arise. For example, the katal, a derived unit for catalytic activity equivalent to one mole per second (1 mol/s), was added in 1999.
Realisation
The base units used in a measurement system must be realisable. To that end, the definition of each SI base unit is accompanied by a mise en pratique (practical realisation) that describes at least one way that the unit can be measured. Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a mutual acceptance arrangement.
In 1791 the commission originally defined the metre based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard metre is now defined as exactly of the distance that light travels in a second. The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.
The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as de facto standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to the original, called the IPK. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of . The revision of the SI replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines the kilogram in terms of fundamental constants.
Base and derived unit structure
A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second. Density, or mass per unit volume, has the unit kilogram per cubic metre.
Decimal ratios A significant characteristic of the metric system is its use of decimal multiples powers of 10. For example, a length that is significantly longer or shorter than 1 metre can be represented in units that are a power of 10 or 1000 metres. This differs from many older systems in which the ratio of different units varied. For example, 12 inches is one foot, but the larger unit in the same system, the mile is not a power of 12 feet. It is 5,280 feet which is hard to remember for many.
In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega-, and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli-. However, 1935 extensions to the prefix system did not follow this convention: the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι (mýrioi), was used as a multiplier for .
When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below. 1 mm2 (square millimetre) = (1 mm)2 = (0.001 m)2 = 1 km2 (square kilometre) = (1 km)2 = (1000 m)2 = 1 mm3 (cubic millimetre) = (1 mm)3 = (0.001 m)3 = 1 km3 (cubic kilometre) = (1 km)3 = (1000 m)3 =
For the most part, the metric prefixes are used uniformly for SI units, but for large measures of seconds, the non-SI units of minute, hour and day are customary instead.
Coherence
Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors. For example, in a coherent system the units of force, energy, and power are chosen so that the equations force = mass × acceleration energy = force × distance energy = power × time hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, Einstein's mass–energy equation, , does not require extraneous constants when expressed in coherent units.
The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the joule.
Rationalisation Maxwell's equations of electromagnetism contained a factor of relating to steradians, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it.
Everyday notions The basic units of the metric system have always represented commonplace quantities or relationships in nature, even with modern refinements of definition and methodology. In cases where laboratory precision may not be required or available, or where approximations are good enough, the commonplace notions may suffice.
Time, length, volume and mass The second is readily determined from the Earth's rotation period. Unlike other units, time multiples are not decimal. A second is of a minute, which is of an hour, which is of a day, so a second is of a day.
The length of the equator is close to (more precisely ). In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre. A dining tabletop is typically about 0.75 metres high. A very tall human is about 2 metres tall.