Units and Measurements


For physics and chemistry, as experimental sciences, measurement is a fundamental operation. His descriptions of the physical world refer to measurable quantities or properties. Units, as reference quantities for comparison purposes, are part of the measurement results. Each experimental data is accompanied by its error or, at least, its figures are written in such a way that they reflect the precision of the corresponding measurement.

Experimental sciences are those that, due to their characteristics and, particularly due to the type of problems they deal with, can submit their affirmations or statements to the judgment of experimentation. In a scientific sense, experimentation refers to controlled observation; In other words, to experiment is to reproduce the phenomenon under study in the laboratory with the possibility of varying the observation conditions at will and precisely.

Physics and chemistry are examples of experimental sciences. The history of both disciplines shows that experimentation has played a dual role in their development. Frequently, scientific experiments can only be understood within the framework of a theory that guides and directs the researcher on what to look for and on what hypotheses must be experimentally contrasted. But, sometimes, the results of the experiments generate information that serves as the basis for a later theoretical elaboration. This dual role of experimentation as judge and guide of scientific work is supported by the performance of measurements that facilitate a description of phenomena in terms of quantity. Measurement then constitutes a key operation in the experimental sciences.

Magnitudes and measures

The great English physicist Lord Kelvin considered that our knowledge can only be accepted as satisfactory if we are able to express it in numbers. Even though Kelvin’s statement taken at face value would disqualify valuable forms of knowledge, it highlights the importance of quantitative knowledge. The operation that allows a property or physical attribute to be expressed in numerical form is precisely the measure.

Magnitude, quantity and unit

The notion of magnitude is inevitably related to that of measure. Quantities are called certain properties or observable aspects of a physical system that can be expressed in numerical form. In other terms, magnitudes are measurable properties or attributes .

Length, mass, volume, force, speed, amount of substance are examples of physical quantities. Beauty, however, is not a magnitude, among other reasons because it is not possible to develop a scale, much less an apparatus that allows determining how many times a person or an object is more beautiful than another. Sincerity or kindness are not either. These are qualitative aspects because they indicate quality and not quantity.

In the language of physics, the notion of quantity refers to the value that a given quantity takes in a concrete body or system; the length of this table, the mass of that coin, the volume of that pen, are examples of quantities. A reference quantity is called a unit and the physical system that embodies the quantity considered as a unit is called a standard.

Measurement as Comparison

The measurement of a physical magnitude supposes, ultimately, the comparison of the object that embodies said property with another of the same nature that is taken as a reference and that constitutes the pattern.

The measurement of lengths was carried out in ancient times using a rod as a pattern, that is, determining how many times the length of the object to be measured contained the pattern. The rod, as the predecessor of the tailor’s meter, has gone down in history as a unit of measurement equivalent to 835.9 mm. This type of immediate comparison of objects corresponds to the so-called direct measurements.

Frequently, the comparison is made between attributes that, even when they are related to what is to be measured, are of a different nature. Such is the case of thermal measurements, in which temperatures are determined by comparing lengths on the graduated scale of a thermometer. This other class of measures is called indirect.

Types of magnitudes

A basic classification can be established between the different measurable properties. An important group of them are perfectly determined when their quantity is expressed by means of a number followed by the corresponding unit. These types of magnitudes are called scalar magnitudes. Length, volume, mass, temperature, energy, are just a few examples. However, there are others that require specification of, in addition to the above elements, a direction or line of action and a sense for their complete definition: they are called vectorial or directed magnitudes. Force is a clear example of vectorial magnitude, since its effects when acting on a body will depend not only on its quantity, but also on the line along which its action is exerted.

Just as real numbers are used to represent scalar quantities, vector quantities require the use of other mathematical elements different from numbers, with a greater capacity for description. These mathematical elements that can represent intensity, direction and direction are called vectors. The magnitudes that are handled in daily life are, in general, scalars. The clerk of a grocery store, the merchant or even the accountant, manage masses, prices, volumes, etc., and for this reason it is enough for them to know how to operate well with numbers. However, the physicist, and to the corresponding extent the physics student, having to handle vector magnitudes, must also operate with vectors.

unit systems

In the physical sciences, both laws and definitions mathematically relate to each other groups, usually large, of magnitudes. For this reason, it is possible to select a reduced but complete set of them in such a way that any other magnitude can be expressed as a function of said set. Those few related quantities are called fundamental quantities, while the rest that can be expressed in terms of the fundamental quantities are called derived quantities.

When that reduced and complete set of fundamental quantities has been chosen and their corresponding units have been correctly defined, then a system of units is available. The definition of units within a system follows different criteria. Thus the unit must be constant as corresponds to its equivalent reference quantity function for the different measurements, but it must also be relatively easily reproducible in a laboratory.

Thus, for example, the definition of ampere as a unit of current intensity has evolved on the basis of this criterion. Due to the fact that forces are known to be measured quite precisely and easily, the ampere is currently defined from an electromagnetic phenomenon in which forces appear between conductors whose magnitude depends on the current intensity.

The International System of Units (SI)

The definition conditions of a system of units would allow the establishment of a considerable variety of them. Thus, it is possible to choose sets of different fundamental magnitudes or even, even accepting the same set, choose and define different units from one system to another. From a formal point of view, each scientist or each country could operate with their own system of units, however, and although such a situation has occurred with some frequency in the past (remember the Anglo-Saxon countries with their miles, feet, pounds, degrees Fahrenheit, etc.), there is a general tendency to adopt the same system of units in order to facilitate cooperation and communication in the scientific and technical fields.

In this line of action, the XI General Conference on Weights and Measures held in Paris in 1960, took the resolution to adopt the previously called Practical System of Units, as the International System, which is precisely how it is known from then. The International System of Units (abbreviated SI) distinguishes and establishes, in addition to the basic magnitudes and the derived magnitudes, a third type formed by those that are not yet included in any of the previous two, they are called supplementary magnitudes.

The SI takes length, mass, time, intensity of electric current, absolute temperature, luminous intensity and amount of substance as fundamental magnitudes, and fixes the corresponding units for each of them. To these seven fundamental magnitudes must be added two supplementary ones associated with angular measures, the plane angle and the solid angle. The definition of the different fundamental units has evolved over time at the same rate as the physical sciences themselves. Thus, the second was initially defined as 1/86,400 the length of the mean solar day, that is, averaged over a year.

A normal day has approximately 24 h, that is, 24 h·60 min = 1,440 min and 1,440 min·60 s = 86,400 s; however, this is only approximate, since the length of the day varies throughout the year by a few seconds, hence the average length of the solar day is taken as a reference. But because the Earth’s period of rotation can and does vary, the atom has been turned to a fixed period of time to which to refer the definition of its fundamental unit.

The international system

Throughout history, man has been using various types of unit systems. These are closely related to the historical condition of the peoples who created them, adapted them or imposed them on other cultures. Its permanence and extension over time has also logically been linked to the destiny of these peoples and the appearance of other more coherent and generalized systems. The Anglo-Saxon system of measurement – miles, feet, pounds, degrees Fahrenheit – still in force in certain geographical areas, is, however, an obvious example of a unit system in recession. Other systems are the cegesimal – centimeter, gram, second -, the terrestrial or technical -meter-kilogram, force-second-, the Giorgi or MKS – meter, kilogram, second- and the decimal metric system, very widespread in science,

The SI is the practical system of measurement units adopted by the XI General Conference on Weights and Measures held in October 1960 in Paris. It works on seven fundamental magnitudes (length, mass, time, electric current intensity, absolute temperature, luminous intensity and amount of substance) from which its corresponding fundamental units are determined (meter, kilogram, second, ampere, kelvin, candela and mole). ). The derivatives of these seven units are defined (coulomb, joule, newton, pascal, volt, ohm, etc.), as well as other supplementary units of the latter.

fundamental units

Unit of Length: The meter ( m ) is the length traveled by light in a vacuum during a period of time of 1/299,792,458 s.

Unit of Mass: The kilogram ( kg ) is the mass of the international prototype of platinum iridium that is kept in the Office of Weights and Measures in Paris.

Unit of Time: The second ( s ) is the duration of 9,192,631,770 periods of radiation corresponding to the transition between two fundamental levels of the Cesium 133 atom.

Electric Current Unit: The ampere ( A ) is the intensity of current, which, when maintained between two parallel, rectilinear conductors, infinite length, negligible circular cross-section and separated in a vacuum by a distance of one meter, will produce a force between these two conductors equal to 2 10 -7 N for each meter of length.

Thermodynamic Temperature Unit: The kelvin ( K ) is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Luminous Intensity Unit: the candela ( cd ) is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 10 12 hertz and that has an energetic intensity in this direction of 1/683 W per steradian (Mr).

Unit of Quantity of Substance: The mole is the quantity of matter contained in a system and that has as many elementary entities as there are atoms in 0.012 kilograms of carbon 12. When the mole is used, the elementary entities must be specified and they can be atoms, molecules, ions, electrons, other particles or groups of such particles.

The base units of the International System of Units are:

base magnitude Name Symbol
Electric current
Thermodynamic temperature
Amount of substance
Luminous intensity

Derived units

Certain derived units have been given special names and symbols. These units can also be used in combination with other base or derived units to express units of other quantities. These names and special symbols are a way of expressing frequently used units.

coulomb ( C ): Amount of electricity carried in one second by a current of one ampere.

joule ( J ): Work produced by a force of one newton when its point of application is displaced a distance of one meter in the direction of the force.

newton ( N ): It is the force that, applied to a body that has a mass of 1 kilogram, gives it an acceleration of 1 meter per second, every second.

pascal ( Pa ): Unit of pressure. It is the uniform pressure that, acting on a flat surface of 1 square meter, exerts a total force of 1 newton perpendicular to this surface.

volt ( V ): Unit of electrical tension, electrical potential, electromotive force. It is the difference in electrical potential that exists between two points of a conducting wire that carries a current of constant intensity of 1 ampere when the power dissipated between those points is equal to 1 watt.

watt ( W ): Power that gives rise to an energy production equal to 1 joule×second.

ohm ( Ω ): Unit of electrical resistance. It is the electrical resistance that exists between two points of a conductor when a constant potential difference of 1 volt applied between these two points produces, in said conductor, a current of intensity 1 ampere, when there is no electromotive force in the conductor.

weber ( Wb ): Unit of magnetic flux, flux of magnetic induction. It is the magnetic flux that, when crossing a circuit of a single turn, produces an electromotive force of 1 volt in it if said flux is annulled in 1 second by uniform decrease.

derived magnitude Name Symbol Expressed in terms of other SI units Expressed in terms of SI base units
flat angle radian rad m m -1 = 1
solid angle steradian Mr m² m -2 = 1
Frequency hertz/hertz Hz min -1 (RPM) -1
Force newton N m kg s -2
pressure, effort pascal Pa N/m² -1 kg s -2
energy, work, heat joule/joule J N m m² kg s -2
Power, energy flow watt/watt W J/s m² kg s -3
electric charge, amount of electricity coulomb/coulomb C s A
Electric potential difference, electromotive force volt/volt v w/o m² kg s -3 A -1
Capacitance farad F CV -2 kg -1 s 4 A²
Electric resistance ohm W GOES m² kg s -3 A -2
electrical conductance siemens yes AV -2 kg -1 s³ A²
Magnetic flux Weber wb V s m² kg s -2 A -1
Magnetic flux density Tesla T Wb/m² kg s -1 A -1
Inductance Henry H Wb/A m² kg s -2 A -2
celsius temperature Celsius °C K
Luminous flux lumen lm cd sr m² m² cd = cd
light radiation lux lx lm/m² m² m -4 cd = m -2 cd
Activity (ionizing radiation) becquerel bq -1
Absorbed dose, specific energy (transmitted) gray gy J/kg m² s -2
Equivalent dose sievert S.v. J/kg m² s -2


1 pica [computer ⅙ in] = 4.233333 10 -3 m

1 light year (1.y.) = 9.46073 10 15 m

1 chain (ch) = 22 yd = 66 ft = 792 in = 20.1168 m

1 mile (mi) = 1,760 yd = 5,280 ft = 63,360 in = 1,609.344 m

1 fathom = 2 yd = 6 ft = 72 in = 1.8288 m

1 point [1/72 in computer] = 3.527778 10 -4 m

1 rod (rd) = 5.5 yd = 16.5 ft = 198 in = 5.0292 m

1 µinch = 1 10 -6 in = 2.54 10 -8 m

1 mil (0.001 in) = 1 10 -3 in = 2.54 10 -5 m

1 astronomical unit (au) = 1.495979 10 11 m

1 angstrom (Å) = 1 10 -10 m

1 pica [printers] = 4.217518 10 -3 m

1 foot (ft) = 12 in = 0.3048 m

1 inch (in) = 0.0254m

1 fermi = 1 10 -15 m

1 point [printer] = 3.514598 10 -4 m

1 micron (µ) = 1 10 -6 m

1 parsec (pe) = 3.085678 10 16 m

1 yard (yd) = 3 ft = 36 in = 0.9144 m

1 nautical mile = 1,852 km = 1,852 m


1 carat, metric = 2 10 -4 kg

1 grain = 6.479891 10 -5 kg

1 slug (slug) = 14.5939 kg

1 pound (lb) = 16 oz = 0.4535924 kg

1 pound [troy] (lb) = 0.3732417 kg

1 ounce (oz) = 2.834952 10 -2 kg

1 troy ounce (oz) = 3.110348 10 -2 kg

1 ton, metric (t) = 1,000 kg

1 ton, assay (AT) = 2.916667 10 -2 kg

1 ton, short = 2,000 lb = 32,000 oz = 907.1847 kg

1 long ton = 2,240 lb = 35,840 oz = 1,016.047 kg

1 tonne [called “metric ton”] (t) = 1,000 kg

1 pennyweight (dwt) = 1.555174 10 -3 kg

1 hundred weight, short = 100 lb = 1,600 oz = 45.35924 kg

1 hundred weight, long = 112 lb = 1,792 oz = 50.80235 kg

1 kilogram-force second squared per meter (kgf s²/m) = 9.80665 kg


1 year = 365 d = 8,760 hrs = 525,600 min = 31,536,000 s

1 [sidereal] year = 3.155815 10 7 s

1 year [tropical] = 3.155693 10 7 s

1 day (d) = 24 hrs = 1,440 min = 86,400 s

1 day [sidereal] = 8,616.409 s

1 hour (h) = 60 min = 3,600 s

1 minute (min) = 60s

1 minute [sidereal] = 59.83617 s

1 [sidereal] second = 0.9972696 s

Electric current

1 ampere = 10 A

1 biot (Bi) = 10 A

1 EMU current (abampere) = 10 A

1 current ESU (statampere) = 3.335641 10 -10 A

1 gilbert (Gi) = 0.7957747 A

1 statampere = 3.335641 10 -10 A

thermodynamic temperature

T/K = T/°C + 273.15

T/°C = (T/°F – 32)/1.8

T/K = (T/°F + 459.67)/1.8

T/K = (T/R)/1.8

T/°C = T/K – 273.15

energy and work

1 British thermal unit IT (Btu) = 1.055056 10³ J

1 British thermal unit Th (Btu) = 1.054350 10³ J

1 British thermal unit [mean] (Btu) = 1.05587 10³ J

1 British thermal unit [39 °F] (Btu) = 1.05967 10³ J

1 British thermal unit [59 °F] (Btu) = 1.05480 10³ J

1 British thermal unit [60 °F] (Btu) = 1.05468 10³ J

IT calorie (cal) = 4.186 8 J

Th calorie (cal) = 4.184 J

1 [mean] calorie (cal) = 4.19002 J

1 calorie [15 °C] (cal) = 4.18580 J

1 calorie [20 °C] (cal) = 4.18190 J

1 electron volt (eV) = 1.602177 10 -19 J

1 erg (erg) = 1 10 -7 J

1 IT kilocalorie (cal) = 4.1868 10³ J

1 kilocalorie Th (cal) = 4.184 10³ J

1 kilocalorie [mean] (cal) = 4.19002 10³ J

1 kilowatt hour (kW h) = 3.6 10 6 J

1 poundal foot = 4.214011 10 -2 J

1 foot pound-force (ft lbf) = 1.355818 J

1 therm (EC) = 1.05506 10 8 J

1 therm (US) = 1.054804 10 8 J

1 ton of TNT = 4.184 10 9 J

1 watt×hour (W h) = 3,600 J

1 watt×second (W s) = 1 J

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