Unit of measurement

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Exact copy, made in 1884, of the international prototype kilogram registered at the International Bureau of Pesas and Measures, in Sèvres, France, which defines mass unity in the SI, the modern metric system

A unit of measurement is a quantity of a certain physical magnitude, defined and adopted by convention or by law. Any value of a physical quantity can be expressed as a multiple of the unit of measurement.

A unit of measure takes its value from a pattern or from a composition of other previously defined units. The first units are known as basic or base (fundamental) units, while the second are called derived units.

A set of units of measurement in which no quantity has more than one associated unit is called a system of units.

All units denote scalar quantities. In the case of vector magnitudes, it is interpreted that each of the components is expressed in the indicated unit.

History

Units of measurement were among the first tools invented by humans. Primitive societies needed rudimentary measures for many tasks: building houses, making clothes, or preparing food and raw materials.

The oldest known systems of weights and measures appear to have been created between the fourth and third millennium BC, among the ancient peoples of Mesopotamia, Egypt, and the Indus Valley, and perhaps also in Elam and Persia. Weights and measures are also mentioned in the Bible (Lev. 19, 35-36) as a mandate that requires honesty and fair measures.

Many systems of measurement were based on the use of parts of the human body and the natural surroundings as measuring instruments.

Traditional measurement systems

Traditional systems base their distance measurement units on the dimensions of the human body. The inch represents the length of the distal phalanx of a thumb, from which it gets its name. The foot originally represented the length of a human foot, although this unit was transformed over time into the equivalent of 12 inches in the Anglo-Saxon system. The yard, on the other hand, represents the length from the tip of the nose to the tip of the middle finger. One fathom corresponded to the distance from tip to tip of the middle fingers with the arms extended. Other units were the span (the length of the palm of the hand) and the cubit (approximately the length of the forearm). For greater distances, there was the mile, a unit of measurement created in ancient Rome that was originally equivalent to 2000 steps a legion. Based on the mile, the Romans defined the furlong in such a way that eight furlongs corresponded to one mile. Likewise, the league in ancient Rome was equal to approximately one and a half miles.

Pound-based measures of weight were used in most European countries. This unit, whose name comes from the Latin libra pondo, was divided into twelve ounces (from the Latin uncia, meaning 'twelfth part'). However, in some Countries during the Middle Ages used pounds that were divided into 16 ounces. Another traditional unit of weight was the grain, which in the current English system equals 64.79891 mg. From this unit, the pound was defined as 5,760 grains in some cases or as 7,000 grains in other cases. Likewise, in jewelry a unit called a metric grain is used, which is equivalent to 0.25 carats or 50 mg. In the Iberian Peninsula, a quintal was equivalent to 100 pounds (which would currently be about 46 kg); a quintal was called an arroba (from Arabic ar rub', 'fourth part').

The movements of the Sun and the Moon determined the traditional units of time. The apparent movement of the Sun from its sunrise on the horizon to the next, its sunset to the next, or its successive passages along a meridian, depending on the culture, defined the day. The Babylonians divided time between sunrise and sunset. Sun in twelve parts that we now know as hours. With the invention of mechanical clocks it was possible to divide the night as well, so that today a full day is made up of 24 hours. An hour was divided into 60 minutes and these, in turn, were divided into 60 seconds (however, the current second has a modern definition independent of the definition of the day). From the Jewish religion, the Christian and Muslim nations inherited the definition of week: a period of seven days. On the other hand, the movement of the Sun observed with respect to distant stars defined the year. Since the period of the Earth's revolution is not an integer number of days, there was a need to introduce the leap year into the Julian calendar and the Gregorian calendar. From the year, larger units of time were defined, such as the century (hundred years) and the millennium (thousand years). The period of translation of the Moon around the Earth defined the concept of the month. Since this period does not correspond to a whole number of days, different cultures had different definitions of a month. In the current Western calendar, months can be 28, 29, 30, or 31 days long, depending on the case.

International System of Units (SI)

The International System of Units is the current form of the Decimal Metric System and establishes the units that must be used internationally. It was created by the International Committee of Weights and Measures based in France in 1960. It establishes 7 fundamental magnitudes, with the standards to measure them:

Length
Masa
Time
Electrical intensity
Temperature
Bright intensity
Amount of substance

It also establishes many derived magnitudes, which do not need a pattern, since they are composed of fundamental magnitudes.

See also: Basic units of the International System and Units derived from the International System.

Measurement standard

A pattern of measurements is the isolated and known fact that serves as the foundation for creating a unit of measuring magnitudes. Many units have standards, but in the SI only base units have standards of measurement. The patterns never vary their value, although they have evolved because the previous ones established were variable and other different ones were established, considered invariable.

An example of a standard of measurement would be: "Standard of the second: One second is the duration of 9,192,631,770 oscillations of the radiation emitted in the transition between the two hyperfine levels of the ground state of the isotope 133 of cesium atom (¹³³Cs), at a temperature of 0 K».

Of all the standards of the International System, there is only the material sample of one: the kilogram, preserved in the International Office of Weights and Measures. Several copies have been made of this pattern for different countries.

The seven patterns defined by the International System of Units are:

Second
Metro
Amperio
Mol
Kilogram
Kelvin
Candela

(time)

(length)

(electric current intensity)

(substance quantity)

(masa)

(temperature)

(Light intensity)

Cegesimal System

Main article: Cegesimal Unit System

Associated with the International System is the Cegesimal System (or CGS system) which is a system of mechanical units (that is, units that measure magnitudes used in mechanics: length, mass, time and their derivatives) based on three fundamental units which are submultiples of SI units: the centimeter, the gram, and the second. The CGS system is sometimes extended to non-mechanical quantities, such as those used in electromagnetism, by combining the use of Gaussian units (see below, natural units in electromagnetism).

Natural systems of units

In some disciplines it is convenient to define systems of units that allow us to simplify calculations and measurements. These systems define their units from magnitudes that occur frequently in nature. Among the disciplines where this occurs are astronomy, electromagnetism, particle physics and atomic physics.

In astronomy

In astronomy it is very common to find units defined from the physical magnitudes of certain objects. Different units of length are defined from astronomical distances:

Astronomical unit (UA)originally defined as the average distance from the Sun to Earth (currently fixed on 149 597 870 700 m).
Parasect (PC)defined as the distance to which an astronomical unit subsidizes an angle of 1 second arc.
Light year (AL)defined as the distance traveled by the light in the void for a year.

It is very common to use the physical magnitudes of the Sun to define units that would otherwise be extremely large:

Solar mass (M_Δ), approximately 1,9891 × 10³⁰kg.
Solar radioR_Δ), 6.96 × 10⁸m.
Solar brightness (L_Δ), 3,846 × 10²⁶W.
Solar Constant (I_Δ), irradiance due to the Sun at a distance of 1 au: 1361 W/m2.
Solar temperature (T_Δ)the temperature in the Sun's photosphere: 5778 K.

Other natural units used in astronomy, although less frequently, are the Earth's radius, the Earth's mass, the mass of Jupiter, etc.

In quantum and relativistic physics

In the different subdisciplines of physics that use relativistic and quantum models, such as atomic physics, nuclear physics, particle physics, etc., it is common to define unit systems where the different fundamental constants take the value of unit. The constants that are usually set equal to one are: the reduced Planck constant (ħ), the speed of light (c), the universal gravitational constant (G), the Boltzmann constant (k_B), the charge of the electron (e), the mass of the electron (m_e) and the mass of the proton (m_p). Other choices Common ones are to define certain quantities in terms of the fine structure constant (α):

{displaystyle hbar ={frac {1}{alpha }}{text{ o }}c={frac {1}{alpha }}}

Another unit commonly used as a unit of energy is the electronvolt (eV) defined as the amount of energy acquired by an electron when accelerated through a potential difference of one volt. That is, in SI units this is 1.602176462 × 10⁻¹⁹ J.

The following table summarizes common definitions for different unit systems.

Number and Symbol / Unit System	Planck (with gaussian units)	Stoney	Hartree	Rydberg	"Natural" (with Lorentz–Heaviside units)	"Natural" (with gaussian units)
Speed of light in the vacuum $c,$	$1,$	$1,$	${displaystyle {frac {1}{alpha }} }$	${displaystyle {frac {2}{alpha }} }$	$1,$	$1,$
Constant of Planck reduced ${displaystyle hbar ={frac {h}{2pi }}}$	$1,$	${displaystyle {frac {1}{alpha }} }$	$1,$	$1,$	$1,$	$1,$
Charge of the electron ${displaystyle e,}$	${displaystyle {sqrt {alpha }},}$	$1,$	$1,$	${displaystyle {sqrt {2}},}$	${displaystyle {sqrt {4pi alpha }}}$	${displaystyle {sqrt {alpha }}}$
Constant Josephson ${displaystyle K_{text{J}}={frac {e}{pi hbar }},}$	${displaystyle {frac {sqrt {alpha }}{pi }},}$	${displaystyle {frac {alpha }{pi }},}$	${displaystyle {frac {1}{pi }},}$	${displaystyle {frac {sqrt {2}}{pi }},}$	${displaystyle {sqrt {frac {4alpha }{pi }}},}$	${displaystyle {frac {sqrt {alpha }}{pi }},}$
Constant von Klitzing ${displaystyle R_{text{K}}={frac {2pi hbar }{e^{2}}},}$	${displaystyle {frac {2pi }{alpha }},}$	${displaystyle {frac {2pi }{alpha }},}$	${displaystyle 2pi ,}$	$pi ,$	${displaystyle {frac {1}{2alpha }}}$	${displaystyle {frac {2pi }{alpha }}}$
Constant universal gravitation $G,$	$1,$	$1,$	${displaystyle {frac {alpha _{text{G}}}{alpha }},}$	${displaystyle {frac {8alpha _{text{G}}}{alpha }},}$	${displaystyle {frac {alpha _{text{G}}}{{m_{text{e}}}^{2}}},}$	${displaystyle {frac {alpha _{text{G}}}{{m_{text{e}}}^{2}}},}$
Boltzmann Constant ${displaystyle k_{text{B}},}$	$1,$	$1,$	$1,$	$1,$	$1,$	$1,$
Mass of the electron ${displaystyle m_{text{e}},}$	${displaystyle {sqrt {alpha _{text{G}}}},}$	${displaystyle {sqrt {frac {alpha _{text{G}}}{alpha }}},}$	$1,$	${displaystyle {frac {1}{2}},}$	${displaystyle 511{text{ keV}}}$	${displaystyle 511{text{ keV}}}$

In Electromagnetism

In electromagnetism it is possible to define a system of natural units from the law of Coulomb, which allows to calculate the force exercised between two electrical loads $q_1$ and $q_{2}$ based on distance $r$ which separates such burdens:

{displaystyle |mathbf {F} |=K{frac {q_{1}q_{2}}{r^{2}}}.}

$K$ is a constant whose value depends on the system of chosen units (in the SI, it has an approximate value of 9 × 10⁹N m2 C⁻²). In this system of natural units—known as the gaussian unit system—the value of such constant equals unity is chosen. In this way, two electrical loads of 1 statC (statcoulomb, the electrical load unit defined in this unit of units) of separate magnitude a distance of 1 cm feel a force of 1 dyn magnitude. From this can be defined other units such as the statamperio (1 statC/s), etc. The units of the Gaussian system are often considered as part of the CGS system.

Conversion tables

SI units have not been adopted worldwide. Anglo-Saxon countries use many SI units, but they still use units specific to their culture, such as the foot, pound, mile, etc. In the United States, the SI is not used on a daily basis outside of science and medicine..

Nautical miles and leagues are still used in navigation. Units such as: PSI, BTU, gallons per minute, grains per gallon, barrels of oil, etc. are still used in industries around the world. That is why conversion tables are still necessary, which convert the value of one unit to the value of another unit of the same magnitude. Example: With a conversion table, 5 p is converted to its corresponding value in meters, which would be 1.524& #39; m.

Conversion errors

Inaccuracies are made when converting units, because sometimes the converted value does not exactly equal the original unit, because the value of the conversion factor may be inaccurate.

Example: 5 lbs is approximately 2.268 kg, because the conversion factor indicates that 1 lb is worth approximately 0.4536 kg. However, 5 lb equals 2.26796185 kg, because the conversion factor has been defined in such a way that 1 lb equals exactly 0.45359237 kg.

However, the conversion of units is frequently used since, in general, it is enough to have approximate values.

Types of measurement units

Depending on the physical magnitudes that need to be measured, different types of measurement units are used. Among these we can mention the following types:

Capacity units
Density units
Energy units
Force units
Units of length
Mass units
Specific weight units
Power units
Surface units
Temperature units
Time units
Speed units
Viscosity units
Volume units
Electrical units

Symbols

Many units have an associated symbol, usually made up of one or more letters from the Latin or Greek alphabet (for example, "m" stands for "meter"). This symbol is located to the right of a factor that expresses how many times that quantity is represented (for example, "5 m" means "five meters").

It is common to refer to a multiple or submultiple of a unit, which is indicated by placing a prefix before the symbol that identifies it (for example, "km", symbol for "kilometer", is equivalent to "1000 meters").

Following another example, a specific measure of the magnitude «time» could be expressed by the unit «second», together with its submultiple «milli» and its number of units (12). In abbreviated form: t = 12 ms (the symbols for magnitudes are usually expressed in italics, while those for units are usually expressed in round type).

See also: Orthographic rules for symbols

Unit conversion factors

Some conversion factors between common unit systems and the International System are:

Time
- 1 h = 60 min = 3600 s
- 1 min = 60 s
- 1 day = 24 h = 1440 min

Length
- 1 m = 100 cm = 39.4 in = 3.28 ft
- 1 ft = 12 in = 0.305 m
- 1 km = 1000 m = 0.621 mi
- 1 mi = 5280 ft = 1609 m
- 1 yard = 0.915 m

Masa
- 1 kg = 1000 g = 0.0685 slug
- 1 slug = 14,6 kg = 32,2 Lbmasa
- 1 oz = 0.0283 kg
- 1 English ton = 907 kg
- 1 metric ton = 1000 kg

Area
- 1 m2 = 10000 cm2 = 10,76 ft2
- 1 cm2 = 0.155 in2
- 1 ft2 = 144 in2 = 9.29*10-2 m2,

Volume
- 1 m3 = 1000 L = 1 000 000 cm3 = 35.3 ft3
- 1 ft3 = 2.83*10-2 m3 = 28.3 L
- 1 gallon = 3,785 l

Force
- 1 newton = 0.225 Lbfuerza = 100000dinas
- 1Force = 4.42 N = 32.2 Poundal

Pressure
- 1 pascal = 1 N/m2 = 2.09×10^-2 lb/ft2 = 1.45×10^-4 lb/in2
- 1 atm = 1,013×10⁵ Pa = 14,7 lb/in2 (PSI) = 760 mm Hg

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