# Physical quantity

A **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. Read also: Quantity value. They can be of two types: scalar or vector.

A **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 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 quantity | Symbol for quantity | Symbol for dimension | SI unit | SI unit symbol |
---|---|---|---|---|

length | \(l\) | L | metre | m |

mass | \(m\) | M | kilogram | kg |

time | \(t\) | T | second | s |

electric current | \(I\) | I | ampere | A |

thermodynamic temperature | \(T\) | \(\Theta\) | kelvin | K |

amount of substance | \(n\) | N | mole | mol |

luminous intensity | \(I_{\textrm{v}}\) | J | candela | cd |

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

Name | Symbol | Quantity | Equivalents | SI base unit Equivalents |
---|---|---|---|---|

hertz | Hz | frequency | 1/s | s^{−1} |

radian | rad | angle | m/m | 1 |

steradian | sr | solid angle | m^{2}/m^{2} | 1 |

newton | N | force, weight | kg·m/s^{2} | kg·m·s^{−2} |

pascal | Pa | pressure, stress | N/m^{2} | kg·m^{−1}·s^{−2} |

joule | J | energy, work, heat | N·m C·V W·s | kg·m^{2}·s^{−2} |

watt | W | power, radiant flux | J/s V·A | kg·m^{2}·s^{−3} |

coulomb | C | electric charge or quantity of electricity | s·A F·V | s·A |

volt | V | voltage, electrical potential difference, electromotive force | W/A J/C | kg·m^{2}·s^{−3}·A^{−1} |

farad | F | electrical capacitance | C/V s/Ω | kg^{−1}·m^{−2}·s^{4}·A^{2} |

ohm | Ω | electrical resistance, impedance, reactance | 1/S V/A | kg·m^{2}·s^{−3}·A^{−2} |

siemens | S | electrical conductance | 1/Ω A/V | kg^{−1}·m^{−2}·s^{3}·A^{2} |

weber | Wb | magnetic flux | J/A T·m ^{2} | kg·m^{2}·s^{−2}·A^{−1} |

tesla | T | magnetic field strength, magnetic flux density | V·s/m^{2}Wb/m ^{2}N/(A·m) | kg·s^{−2}·A^{−1} |

henry | H | electrical inductance | V·s/A Ω·s Wb/A | kg·m^{2}·s^{−2}·A^{−2} |

degree Celsius | °C | temperature relative to 273.15 K | K | K |

lumen | lm | luminous flux | cd·sr | cd |

lux | lx | illuminance | lm/m^{2} | m^{−2}·cd |

becquerel | Bq | radioactivity (decays per unit time) | 1/s | s^{−1} |

gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}·s^{−2} |

sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}·s^{−2} |

katal | kat | catalytic activity | mol/s | s^{−1}·mol |