A unit of measurement, or unit of measure, is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.[1] Any other quantity of that kind can be expressed as a multiple of the unit of measurement.[2]
For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10metres" (or 10m), what is actually meant is 10 times the definite predetermined length called "metre".
The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.
In trade, weights and measures are often a subject of governmental regulation, to ensure fairness and transparency. The International Bureau of Weights and Measures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI).
Metrology is the science of developing nationally and internationally accepted units of measurement.
In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures historically developed for commercial purposes.[3]
Science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life. The judicious selection of the units of measurement can aid researchers in problem solving (see, for example, dimensional analysis).
A unit of measurement is a standardized quantity of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials.
The earliest known uniform systems of measurement seem to have all been created sometime in the 4th and 3rd millennia BC among the ancient peoples of Mesopotamia, Egypt and the Indus Valley, and perhaps also Elam in Persia as well.
Weights and measures are mentioned in the Bible (Leviticus 19:35–36). It is a commandment to be honest and have fair measures.
In the Magna Carta of 1215 (The Great Charter) with the seal of King John, put before him by the Barons of England, King John agreed in Clause 35 "There shall be one measure of wine throughout our whole realm, and one measure of ale and one measure of corn—namely, the London quart;—and one width of dyed and russet and hauberk cloths—namely, two ells below the selvage..."
As of the 21st century, multiple unit systems are used all over the world such as the United States Customary System, the Imperial System, and the International System. However, the United States is the only industrialized country that has not yet at least mostly converted to the metric system. The systematic effort to develop a universally acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. This system was the precursor to the metric system which was quickly developed in France but did not take on universal acceptance until 1875 when The Metric Convention Treaty was signed by 17 nations. After this treaty was signed, a General Conference of Weights and Measures (CGPM) was established. The CGPM produced the current SI, which was adopted in 1954 at the 10th Conference of Weights and Measures. Currently, the United States is a dual-system society which uses both the SI and the US Customary system.[4][5]
The use of a single unit of measurement for some quantity has obvious drawbacks. For example, it is impractical to use the same unit for the distance between two cities and the length of a needle. Thus, historically they would develop independently. One way to make large numbers or small fractions easier to read, is to use unit prefixes.
At some point in time though, the need to relate the two units might arise, and consequently the need to choose one unit as defining the other or vice versa. For example, an inch could be defined in terms of a barleycorn. A system of measurement is a collection of units of measurement and rules relating them to each other.
As science progressed, a need arose to relate the measurement systems of different quantities, like length and weight and volume. The effort of attempting to relate different traditional systems between each other exposed many inconsistencies, and brought about the development of new units and systems.
Historically many of the systems of measurement which had been in use were to some extent based on the dimensions of the human body. Such units, which may be called anthropic units, include the cubit, based on the length of the forearm; the pace, based on the length of a stride; and the foot and hand. As a result, units of measure could vary not only from location to location but from person to person. Units not based on the human body could be based on agriculture, as is the case with the furlong and the acre, both based on the amount of land able to be worked by a team of oxen.
An example of metrication in 1860 when Tuscany became part of modern Italy (ex. one "libbra" = 339.54 grams)
Both the imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire. US customary units are still the main system of measurement used in the United States outside of science, medicine, many sectors of industry, and some of government and military, and despite Congress having legally authorised metric measure on 28 July 1866.[8] Some steps towards US metrication have been made, particularly the redefinition of basic US and imperial units to derive exactly from SI units. Since the international yard and pound agreement of 1959 the US and imperial inch is now defined as exactly 0.0254m, and the US and imperial avoirdupois pound is now defined as exactly 0.45359237kg.[9]
While the above systems of units are based on arbitrary unit values, formalised as standards, natural units in physics are based on physical principle or are selected to make physical equations easier to work with. For example, atomic units (au) were designed to simplify the wave equation in atomic physics.[10]
To reduce the incidence of retail fraud, many national statutes have standard definitions of weights and measures that may be used (hence "statute measure"), and these are verified by legal officers.[citation needed]
In informal settings, a quantity may be described as multiples of that of a familiar entity, which can be easier to contextualize than a value in a formal unit system. For instance, a publication may describe an area in a foreign country as a number of multiples of the area of a region local to the readership. The propensity for certain concepts to be used frequently can give rise to loosely defined "systems" of units.[11][12]
For most quantities a unit is necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.
But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the base units and the other units are derived units. Thus base units are the units of the quantities which are independent of other quantities and they are the units of length, mass, time, electric current, temperature, luminous intensity and the amount of substance. Derived units are the units of the quantities which are derived from the base quantities and some of the derived units are the units of speed, work, acceleration, energy, pressure etc.[6]
Different systems of units are based on different choices of a set of related units including fundamental and derived units.
Following ISO 80000-1,[13] any value or magnitude of a physical quantity is expressed as a comparison to a unit of that quantity. The value of a physical quantity Z is expressed as the product of a numerical value {Z} (a pure number) and a unit [Z]:
For example, let be "2 metres"; then, is the numerical value and is the unit. Conversely, the numerical value expressed in an arbitrary unit can be obtained as:
The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas. The convention used to express quantities is referred to as quantity calculus. In formulas the unit [Z] can be treated as if it were a specific magnitude of a kind of physical dimension: see Dimensional analysis for more on this treatment.
Units can only be added or subtracted if they are the same type; however units can always be multiplied or divided, as George Gamow used to explain. Let be "2 metres" and "3 seconds", then
.
There are certain rules that apply to units:
Only like terms may be added. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied or divided, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metre per second (m/s). See dimensional analysis. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m2/s2). Put simply, units obey the laws of indices. (See Exponentiation.)
Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to 1kg⋅m/s2. Thus a quantity may have several unit designations, for example: the unit for surface tension can be referred to as either N/m (newton per metre) or kg/s2 (kilogram per second squared).
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.
Unit conversion is often easier within a metric system such as the SI than in others, due to the system's coherence and its metric prefixes that act as power-of-10 multipliers.
Real-world implications
One example of the importance of agreed units is the failure of the NASAMars Climate Orbiter, which was accidentally destroyed on a mission to Mars in September 1999 instead of entering orbit due to miscommunications about the value of forces: different computer programs used different units of measurement (newton versus pound force). Considerable amounts of effort, time, and money were wasted.[14][15]
On 15 April 1999, Korean Air cargo flight 6316 from Shanghai to Seoul was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty-seven were injured.[16][17]
In 1983, a Boeing 767 (which thanks to its pilot's gliding skills landed safely and became known as the Gimli Glider) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements.[18] This accident was the result of both confusion due to the simultaneous use of metric and Imperial measures and confusion of mass and volume measures.
When planning his journey across the Atlantic Ocean in the 1480s, Columbus mistakenly assumed that the mile referred to in the Arabic estimate of 56⅔ miles for the size of a degree was the same as the actually much shorter Italian mile of 1,480 metres. His estimate for the size of the degree and for the circumference of the Earth was therefore about 25% too small.[19]:1:17
↑ Witkin, Richard (30 July 1983). "Jet's Fuel Ran Out After Metric Conversion Errors". The New York Times. Retrieved 21 August 2007. Air Canada said yesterday that its Boeing 767 jet ran out of fuel in mid-flight last week because of two mistakes in figuring the fuel supply of the airline's first aircraft to use metric measurements. After both engines lost their power, the pilots made what is now thought to be the first successful emergency dead stick landing of a commercial jetliner.
↑ Nunn, George Emra. "The geographical conceptions of Columbus: a critical consideration of four problems". No. 14. New York: American Geographical Society, 1924.1–217-18
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.
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.
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.
A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=nkg, where n is the numerical value and kg is the unit symbol. Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.
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 an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.
United States customary units form a system of measurement units commonly used in the United States and most U.S. territories, since being standardized and adopted in 1832. The United States customary system developed from English units that were in use in the British Empire before the U.S. became an independent country. The United Kingdom's system of measures was overhauled in 1824 to create the imperial system, which was officially adopted in 1826, changing the definitions of some of its units. Consequently, while many U.S. units are essentially similar to their imperial counterparts, there are noticeable differences between the systems.
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.
Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960.
Chinese units of measurement, known in Chinese as the shìzhì, are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal (base-10) since the Shang, several Chinese measures use hexadecimal (base-16). Local applications have varied, but the Chinese dynasties usually proclaimed standard measurements and recorded their predecessor's systems in their histories.
A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric units, used in every country globally. In the United States the U.S. customary units are also in use. British Imperial units are still used for some purposes in the United Kingdom and some other countries. The metric system is sub-divided into SI and non-SI units.
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or SI, the British imperial system, and the United States customary system.
Traditional Japanese units of measurement or the shakkanhō (尺貫法) is the traditional system of measurement used by the people of the Japanese archipelago. It is largely based on the Chinese system, which spread to Japan and the rest of the Sinosphere in antiquity. It has remained mostly unaltered since the adoption of the measures of the Tang dynasty in 701. Following the 1868 Meiji Restoration, Imperial Japan adopted the metric system and defined the traditional units in metric terms on the basis of a prototype metre and kilogram. The present values of most Korean and Taiwanese units of measurement derive from these values as well.
The foot–pound–second system is a system of units built on three fundamental units: the foot for length, the (avoirdupois) pound for either mass or force, and the second for time.
The vacuum magnetic permeability, also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0. Its purpose is to quantify the strength of the magnetic field emitted by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.
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 following outline is provided as an overview of and topical guide to the metric system:
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.
The imperial and US customary measurement systems are both derived from an earlier English system of measurement which in turn can be traced back to Ancient Roman units of measurement, and Carolingian and Saxon units of measure.
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