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The former Weights and Measures office in Seven Sisters, London.

A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity.[1] Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.

For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 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 this day. Disparate 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 is often a subject of governmental regulation, to ensure fairness and transparency. The Bureau international des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI). Metrology is the science for developing national and internationally accepted units of weights and measures.

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 developed long ago for commercial purposes.

Science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving (see, for example, dimensional analysis).

In the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement.

History

A unit of measurement is a standardised 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 weights and measures 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.

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…."[1]. The Magna Carta helped lay the foundations of freedom codified in English Law and subsequently American Law.

Many systems were based on the use of parts of the body and the natural surroundings as measuring instruments. Our present knowledge of early weights and measures comes from many sources.

Systems of units

This derivation of the Vitruvian Man by Leonardo da Vinci, depicts nine historical units of measurement: the yard, the span, the cubit, the Flemish ell, the English ell, the French ell, the fathom, the hand, and the foot. The Vitruvian Man was drawn to scale, so the units depicted are displayed with their proper historical ratios.

Prior to the near 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 according to the proportions described by Marcus Vitruvius Pollio. As a result, units of measure could vary not only from location to location, but from person to person.

Metric systems

A number of metric systems of units have evolved since the adoption of the original metric system in France in 1791. The current international standard metric system is the International system of units. An important feature of modern systems is standardization. Each unit has a universally recognized size.

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 despite Congress having legally authorized metric measure on 28 July 1866.[2] Some steps towards US metrication have been made, particularly the redefinition of basic US units to derive exactly from SI units, so that in the US the inch is now defined as 0.0254 m (exactly), and the avoirdupois pound is now defined as 453.59237 g (exactly)[3]

Natural systems

While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called natural units. Similar to natural units, atomic units (au) are a convenient system of units of measurement used in atomic physics.

Also a great number of unusual and non-standard units may be encountered. These may include the Solar mass, the Megaton (1,000,000 tons of TNT), and the Hiroshima atom bomb.

Legal control of weights and measures

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.

Base and derived units

Different systems of units are based on different choices of a set of fundamental units. The most widely used system of units is the International System of Units, or SI. There are seven SI base units. All other SI units can be derived from these base units.

For most quantities a unit is absolutely 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. Other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.

The base units of SI are actually not the smallest set possible. Smaller sets have been defined. For example, there are unit sets in which the electric and magnetic field have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon.

Calculations with units

Units as dimensions

Any value of a physical quantity is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity Z is expressed as the product of a unit [Z] and a numerical factor:

$Z = n \times [Z] = n [Z].$

The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. The conventions 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.

A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be one metre long only at a certain temperature.

Guidelines

• Treat units algebraically. Only add like terms. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metres 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 one kg·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 (newtons per metre) or kg/s2 (kilograms per second squared). Whether these designations are equivalent is disputed amongst metrologists.[4]

Expressing a physical value in terms of another unit

Conversion of units involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities.

Starting with:

$Z = n_i \times [Z]_i$

just replace the original unit [Z]i with its meaning in terms of the desired unit [Z]j, e.g. if $[Z]_i = c_{ij} \times [Z]_j$, then:

$Z = n_i \times (c_{ij} \times [Z]_j) = (n_i \times c_{ij}) \times [Z]_j$

Now ni and cij are both numerical values, so just calculate their product.

Or, which is just mathematically the same thing, multiply Z by unity, the product is still Z:

$Z = n_i \times [Z]_i \times ( c_{ij} \times [Z]_j/[Z]_i )$

For example, you have an expression for a physical value Z involving the unit feet per second ([Z]i) and you want it in terms of the unit miles per hour ([Z]j):

1. Find facts relating the original unit to the desired unit:
1 mile = 5280 feet and 1 hour = 3600 seconds
2. Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:
$1 = \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}\quad \mathrm{and}\quad 1 = \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}$
3. Last,multiply the original expression of the physical value by the fraction, called a conversion factor, to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are dimensionless and have a numerical value of one, multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.
$52.8\,\frac{\mathrm{ft}}{\mathrm{s}} = 52.8\,\frac{\mathrm{ft}}{\mathrm{s}} \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}} \frac{3600\,\mathrm{s}}{1\,\mathrm{h}} = \frac {52.8 \times 3600}{5280}\,\mathrm{mi/h} = 36\,\mathrm{mi/h}$

Or as an example using the metric system, you have a value of fuel economy in the unit litres per 100 kilometres and you want it in terms of the unit microlitres per metre:

$\mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}} = \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}} \mathrm{\frac{1000000\,\rm{\mu L}}{1\,\rm{L}}} \mathrm{\frac{1\,\rm{km}}{1000\,\rm{m}}} = \frac {9 \times 1000000}{100 \times 1000}\,\mathrm{\mu L/m} = 90\,\mathrm{\mu L/m}$

Real-world implications

One example of the importance of agreed units is the failure of the NASA Mars Climate Orbiter, which was accidentally destroyed on a mission to the planet 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). Enormous amounts of effort, time, and money were wasted.[5][6]

On April 15, 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.[7][8]

In 1983, a Boeing 767 (which came to be know 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.[9] This accident is apparently the result of confusion both due to the simultaneous use of metric & Imperial measures as well as mass & volume measures.

Notes

1. ^ "measurement unit", in  International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM) (8th ed.), Joint Committee for Guides in Metrology, 2008, pp. 6–7 .
2. ^   as amended by Public Law 110–69 dated August 9, 2007
3. ^
4. ^ Emerson, W.H. (2008), "On quantity calculus and units of measurement", Metrologia 45: 134–138
5. ^ "Unit Mixups". US Metric Association.
6. ^
7. ^ NTSB. "Korean Air Flight 6316". Press release.
8. ^ "Korean Air incident". Aviation Safety Net.
9. ^ "Jet's Fuel Ran Out After Metric Conversion Errors". New York Times. July 30, 1983. Retrieved 2007-08-21. "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."

Simple English

Measurement is a process to attach a numerical value to an observation. This is done to be able to compare or order two or more such observations. Units of Measurement provide standards to compare against. For example, the metre is the standard unit to measure length. Before 1982, it was defined as the distance between two markers on a certain rod. Now scientists define the metre as the distance light travels in a certain time, in vacuum.

Saying something has a length of 2 metres therefore means that it is exactly twice as long as that rod used to define the metre, or that light takes twice the time defined for a metre to travel that distance.

This also makes it easy to say that something that is 3 metres long is longer than something else, that is only 2 metres long.

Today, most units of measure fall into one of two systems. The older, imperial system uses the foot as a mesure of length, the pound as a mesure for weight and the second as a measure for time. There are other units as well. Most of the time 12 or 16 of the smaller unit make the bigger unit. This is difficult to remember, so there is another system that uses 10 of the smaller unit to make the bigger one. It is known as the SI system or metric system. It uses the metre for length, the kilogram for weight, and the second for time.

Number and Unit of measure

The property of the thing being measured is given as a number of units of measure. The number only has sense when the unit of measurement is also given.

For example, The Eiffel Tower in Paris, France is 300 meters tall.[1] That is, the distance from the top to the bottom of the Eiffel Tower is 300 meters. The property of the Eiffel Tower being measured is a distance. The number measured is 300. This number does not make sense without the unit of measure. The unit of measure is the meter.

Measurement Standards

Standards are used in measurements. That is, the unit of measurement used to measure a property is the same everywhere and does not change. This makes measurement easier and comparisons between measurements easier.[2]

Size of Units of Measurement

There are units of measurement of different sizes. There are small units of measurement to measure small things. There are big units of measurement to measure big things.

Science, medicine and engineering use smaller units of measurement to measure small things with less error. It is easier to measure large things using larger units of measurement. Large measurements like the width of a galaxy and small measurements like the mass of an atom use special units of measurement.

Systems of Units of Measurement

There are many different standards and units used all over the world.

Metric System

see SI

The metric system is a system of measurement used in most of the world. It is also called the International System of Units, or SI.

Units of measure in the metric system include:

• The unit of volume is the litre. It is used for measuring an amount of liquid. A millilitre (abbreviated as ml) is the amount of liquid that would fill up a cube that measures 1 centimetre on each side. One l litre of liquid would fill up a cube that is 10 cm on each side.
• The unit of mass is the kilogram. A kilogram (kg) weighs the same as a litre of water (at normal temperature, and pressure). 1 gram (g) is the weight of 1 millilitre of water at 0 degrees Celsius. The metric tonne is 1000 kilograms or a million grams.

Imperial Units

See US units of measurement

Imperial units were used in countries that were part of the British Empire, however they can be different in different countries. For example, the fluid ounce in Britain is smaller than the fluid ounce in the US, but the US gallon is smaller than the British gallon. The imperial units are now used mainly in the United States. While many countries have officially adopted SI, older system of units are still used. In the United States, the metric system has been legal for trade since 1866 but other measurements such as the gallon, inch, and the pound are still widely used.

Imperial units of measurement include:

• Length - inch(in), foot (ft), yard (yd), and mile
• 1 foot = 12 inches
• 1 yard = 3 feet (plural of foot) = 36 inches
• 1 mile = 1760 yards = 5280 feet
• Volume is based on fluid ounces (oz). It includes the ounce, cup (8oz), pint (16oz), quart (32oz) and gallon (128oz).
• Weight and mass are measured in ounces (oz)and pounds (lb). There are 16 ounces in one pound.

The ounces for weight and volume are different. Even when measuring water, the number of ounces of weight is not the same as the number of fluid ounces.

Converting Between Systems

Metric to US
• 1 meter = 1.09 yards = 39.37 inches.
• 1 liter = 33.3 fluid ounces = 1.76 pints = .26 US gallons.
• 1 kilogram = 35.32 ounces = 2.2 pounds
US to metric
• Length
• 1 inch = 2.54 centimetres
• 1 foot = 30.48 centimetres
• 1 yard = .914 metres
• 1 mile = 1.61 kilometres
• Volume
• 1 fluid ounce = 29.6 millilitres
• 1 pint = 473.1 millilitres
• 1 gallon = 3.79 litres
• 1 cup = 16 ounces
• Mass
• 1 ounce = 28.35 grams
• 1 pound = .45 kilograms

Other Units of Measure

Time

The unit of time is the second. The minute (60 seconds) and hour (60 minutes or 3600 seconds) are larger units. A day is usually said to be 24 hours, but is actually a small bit longer. This difference is corrected at the end of every year. A week (7 days) and month are also standard units.

Money

A unit of measurement that applies to money is called a unit of account. This is normally a currency issued by a country. For instance, the United States use dollars. Each dollar is 100 cents. The United Kingdom uses pounds. Each pound is 100 pennies or pence. Other countries in Europe use the Euro which is 100 cent for the Euro they are not called "cents")

Notes

1. A person can also say "The Eiffel Tower's height is 300 meters."
2. An example of unit of measurement standards:
David is making a house. David wants a window in his house. David makes a hole in the wall of his house for a window. David measures the hole using the length of his arm as a unit of measurement. The hole is one arm tall and two arms wide.

Abbie makes windows. Abbie measures her windows using her arm as a unit of measurement. Some of Abbie's windows are two arms wide and one arm tall.

David buys a window from Abbie that Abbie says is two arms wide and one arm tall. If David's arms are a different length than Abbie's arms, then the window will be the wrong size.

For David to get the right size window, he has to tell the people with the windows what size the hole is. The easy way to do this is for David and Abbie to use the same unit of measurement standard. If David and Abbie both use the meter, they will both know the size of the hole and the size of the windows.

Michael wants to use the same window in his house ten years later. Michael makes a hole in his house wall. If the unit of measurement changed in ten years, then Michael would have to remeasure the window. The easiest way to do this is if the unit of measurement did not change in ten years.