Physical quantity

physical quantity is defined as a physical property of a body or entity with which it is possible to describe phenomena that can be measured (quantified by measurement). A physical quantity can be expressed as the combination of a magnitude expressed by a number – usually a real number – and a unit of measurement. They can be of two types: scalar or vector.

scalar quantity is a quantity that is described solely, from a mathematical point of view, by a “scalar,” that is, by a real number associated with a unit of measurement (examples are the following: mass, energy, temperature, etc.). The definition of “scalar” derives from the possibility of reading the value on a graduated scale of a measuring instrument, as it does not need other elements to be identified.

On the other hand, it is more complex to define a physical quantity (such as velocity, acceleration, force, etc.) to associate its value with other information such as, for example, a direction or a verse or both; in this case, we are dealing with a vector quantity described by a vector. Unlike vector quantities, the scalar ones are therefore not sensitive to the size of the space, nor to the particular reference or coordinate system used.

Furthermore, each physical quantity corresponds to a unit of measurement that can be “fundamental” (base) if the physical quantity is one of the fundamental ones of the International System, or “derived” if it derives (or is formed) from the fundamental ones. So, the physical quantities can be classified into two types: base and derived.

Base physical quantities (SI base units)

By convention, the base physical quantities used in the International System of Units (SI) are seven, organized in a system of dimensions and assumed to be independent. Each of the seven base quantities used in the SI is regarded as having its dimension, which is symbolically represented by a single sans serif roman capital letter. The symbols used for the base quantities, and the symbols used to denote their dimension, are given as follows.

The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif type.

Base quantitySymbol for
Symbol for
SI unitSI unit symbol
electric currentIIampereA
thermodynamic temperatureTΘkelvinK
amount of substancenNmolemol
luminous intensityIvJcandelacd

The value of a quantity is generally expressed as the product of a number and a unit. The unit is a particular example of the quantity concerned which is used as a reference. Units should be chosen so that they are readily available to all, are constant throughout time and space, and are easy to realize with high accuracy. The number is the ratio of the value of the quantity to the unit. For a particular quantity, many different units may be used. All other quantities are called derived quantities, which may be written in terms of the base quantities by the equations of physics.

Derived physical quantities (SI derived units)

Derived units are products of powers of base units. They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation. Coherent derived units are products of powers of base units that include no numerical factor other than 1. The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.

The International System of Units (SI) assigns special names to 22 derived units from SI base units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

NameSymbolQuantityEquivalentsSI base unit equivalents
steradiansrsolid anglem2/m21
newtonNforce, weightkg·m/s2kg·m·s−2
pascalPapressure, stressN/m2kg·m−1·s−2
jouleJenergy, work, heatN·m
wattWpower, radiant fluxJ/s
coulombCelectric charge or
quantity of electricity
electrical potential difference,
electromotive force
faradFelectrical capacitanceC/V
ohmΩelectrical resistance,
impedance, reactance
siemensSelectrical conductance1/Ω
weberWbmagnetic fluxJ/A
teslaTmagnetic field strength,
magnetic flux density
henryHelectrical inductanceV·s/A
degree Celsius°Ctemperature relative to 273.15 KKK
lumenlmluminous fluxcd·srcd
(decays per unit time)
grayGyabsorbed dose
(of ionizing radiation)
sievertSvequivalent dose
(of ionizing radiation)
katalkatcatalytic activitymol/ss−1·mol

Definition of physical quantity value and true value

In metrology, the quantity value represents the number and the unit together expressing the magnitude of a physical quantity. Instead, the exact value of a variable is called the true value (corresponds to the correct measure without uncertainties). True value may be defined as the mean of the infinite number of measured values when the average deviation due to the various contributing factors tends to zero. In practice, the realization of the true value is not possible due to uncertainties (errors) of the measuring process and hence cannot be determined experimentally. Positive and negative deviations from the true value are not equal and will not cancel each other. One would never know whether the quantity being measured is the true value of the quantity or not. The sources of this uncertainty are many; for example:

  • impossibility of ensuring the absolute absence of measurement errors;
  • impossibility of having infinitely precise instrumentation;
  • impossibility of perfect control of the boundary conditions, which modify the measurand;
  • intrinsic instability present in practically all the measurands, linked to the nature of the measured quantity;
  • quantum effects on matter and energy.

Conventionally true value

The conventionally true value is the value of a quantity which, in particular cases, can be considered a true value. In general, for a given purpose, it is considered that the conventionally true value is close enough to the true value, that the difference can be considered as negligible. When the concept of conventionally true value is applied to a physical quantity that characterizes an object, and this can be considered stable, the true value is defined as the nominal value of the object. An example may be the nominal value of the sample weight.

Dimensionless physical quantity

dimensionless quantity is a physical quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the unit one (or 1), which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics.

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