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Physical Quantities

Physical quantities are properties of objects or phenomena that can be measured and expressed numerically with a value and a unit. Examples of physical quantities include length, mass, time, temperature, force, and energy.

They are classified into:

Fundamental quantities: Defined independently, such as time $\mathrm{(s)}$ , length $\mathrm{(m)}$ , or mass $\mathrm{(kg)}$ .
Derived quantities: Obtained from fundamental ones through mathematical relationships, such as speed $\mathrm{(m/s)}$ or acceleration $\mathrm{(m/s^{2})}$ .

The study and use of physical quantities make it possible to describe, compare, and predict natural phenomena in a precise, quantitative way.

Base units

Quantity	Name	Symbol
time	second	$\mathrm{s}$
length	metre	$\mathrm{m}$
mass	kilogram	$\mathrm{kg}$
electric current	ampere	$\mathrm{A}$
temperature	kelvin	$\mathrm{K}$
amount of substance	mole	$\mathrm{mol}$
luminous intensity	candela	$\mathrm{cd}$

Derived units

Special name units

Quantity	Name	Symbol	Equivalents	SI Equivalents
frequency	hertz	$\mathrm{Hz}$	$\mathrm{ 1 / s }$	$\mathrm{ s^{-1}}$
angle	radian	$\mathrm{rad}$	$\mathrm{m / m}$	$1$
solid angle	esteradian	$\mathrm{sr}$	$\mathrm{m^{2} / m^{2}}$	$1$
force, weight	newton	$\mathrm{N}$	$\mathrm{kg \cdot m/s^{2}}$	$\mathrm{kg \cdot m \cdot s^{-2}}$
pressure, stress	pascal	$\mathrm{Pa}$	$\mathrm{N/m^{2}}$	$\mathrm{kg \cdot m^{-1} \cdot s^{-2}}$
energy, work, heat	joule	$\mathrm{J}$	$\mathrm{m \cdot N,\ C \cdot V,\ W \cdot s}$	$\mathrm{kg \cdot m^{2} \cdot s^{-2} }$
power, radiant flux	watt	$\mathrm{W}$	$\mathrm{J/s, V \cdot A}$	$\mathrm{kg \cdot m^{2} \cdot s^{-3} }$
electric charge	coulomb	$\mathrm{C}$	$\mathrm{s \cdot A, F \cdot V}$	$\mathrm{s \cdot A}$
voltage, electrical potential difference, electromotive force	volt	$\mathrm{V}$	$\mathrm{W/A, J/C}$	$\mathrm{kg \cdot m^{2} \cdot s^{-3}\cdot A^{-1}}$
electrical capacitance	farad	$\mathrm{F}$	$\mathrm{C/V, s/\Omega}$	$\mathrm{kg^{-1}\cdot m^{-2} \cdot s^{4} \cdot A^{2}}$
electrical resistance, impedance, reactance	ohm	$\Omega$	$\mathrm{1/S, V/A}$	$\mathrm{kg \cdot m^{2} \cdot s^{-3}⋅A^{-2}}$
electrical conductance	siemens	$\mathrm{S}$	$\mathrm{1/ \Omega, A/V}$	$\mathrm{kg^{-1} \cdot m^{-2} \cdot s^{3} \cdot A^{2} }$
magnetic flux	weber	$\mathrm{Wb}$	$\mathrm{J/A, T \cdot m^{2},V \cdot s}$	$\mathrm{kg \cdot m^{2} \cdot s^{-2} \cdot A^{-1} }$
magnetic induction, magnetic flux density	tesla	$\mathrm{T}$	$\mathrm{V \cdot s/m^{2}, Wb/m^{2}, N/(A \cdot m)}$	$\mathrm{kg \cdot s^{-2} \cdot A^{-1} }$
electrical inductance	henry	$\mathrm{H}$	$\mathrm{V \cdot s/A, \Omega \cdot s, Wb/A}$	$\mathrm{kg \cdot m^{2} \cdot s^{-2} \cdot A^{-2}}$
temperature relative to $273.15\ \mathrm{K}$	degree Celsius	$^{\circ}\mathrm{C}$	$\mathrm{K}$	$\mathrm{K}$
luminous flux	lumen	$\mathrm{lm}$	$\mathrm{cd \cdot sr}$	$\mathrm{cd}$
illuminance	lux	$\mathrm{lx}$	$\mathrm{ lm/m^{2}}$	$\mathrm{cd \cdot m^{-2}}$
radioactivity	becquerel	$\mathrm{Bq}$	$\mathrm{1/s}$	$\mathrm{s^{-1}}$
absorbed dose	gray	$\mathrm{Gy}$	$\mathrm{J/kg}$	$\mathrm{m^{2} \cdot s^{-2}}$
equivalent dose	sievert	$\mathrm{Sv}$	$\mathrm{J/kg}$	$\mathrm{m^{2} \cdot s^{-2}}$
catalytic activity	katal	$\mathrm{kat}$	$\mathrm{mol/s}$	$\mathrm{s^{-1} \cdot mol}$

By field of application

Kinematics

Quantity	Name	Symbol	SI Equivalents
speed, velocity	metre per second	$\mathrm{m/s}$	$\mathrm{m \cdot s^{-1}}$
acceleration	metre per second squared	$\mathrm{m/s^{2}}$	$\mathrm{m \cdot s^{-2}}$
jerk, jolt	metre per second cubed	$\mathrm{m/s^{3}}$	$\mathrm{m \cdot s^{-3}}$
snap,jounce	metre per second to the fourth	$\mathrm{m/s^{4}}$	$\mathrm{m \cdot s^{-4}}$
crackle	metre per second to the fifth	$\mathrm{m/s^{5}}$	$\mathrm{m \cdot s^{-5}}$
pop	metre per second to the sixth	$\mathrm{m/s^{6}}$	$\mathrm{m \cdot s^{-6}}$
angular velocity	radian per second	$\mathrm{rad/s}$	$\mathrm{s^{-1}}$
angular acceleration	radian per second squared	$\mathrm{rad/s^{2}}$	$\mathrm{s^{-2}}$
frequency drift	hertz per second	$\mathrm{Hz/s}$	$\mathrm{s^{-2}}$
volumetric flow	cubic metre per second	$\mathrm{m^{3}/s}$	$\mathrm{m^{3} \cdot s^{-1}}$

Mechanics

Quantity	Name	Symbol	SI Equivalents
area	square metre	$\mathrm{m^{2}}$	$\mathrm{m^{2}}$
volume	cubic metre	$\mathrm{m^{3}}$	$\mathrm{m^{3}}$
momentum, impulse	newton-second	$\mathrm{N \cdot s}$	$\mathrm{m \cdot kg \cdot s^{-1}}$
angular momentum	newton metre second	$\mathrm{N \cdot m \cdot s}$	$\mathrm{m^{2} \cdot kg \cdot s^{-1}}$
torque, moment of force	newton-metre	$\mathrm{N \cdot m = J/rad}$	$\mathrm{m^{2} \cdot kg \cdot s^{-2}}$
yank	newton per second	$\mathrm{N/s}$	$\mathrm{m \cdot kg \cdot s^{-3}}$
wavenumber, optical power, curvature, spatial frequency	reciprocal metre	$\mathrm{m^{-1}}$	$\mathrm{m^{-1}}$
area density	kilogram per square metre	$\mathrm{kg/m^{2}}$	$\mathrm{m^{2}\cdot kg}$
density	kilogram per cubic metre	$\mathrm{kg/m^{3}}$	$\mathrm{m^{-3} \cdot kg}$
specific volume	cubic metre per kilogram	$\mathrm{m^{3}/kg}$	$\mathrm{m^{3} \cdot kg^{-1}}$
action	joule-second	$\mathrm{J \cdot s}$	$\mathrm{m^{2} \cdot kg \cdot s^{-1}}$
specific energy	joule per kilogram	$\mathrm{J/kg}$	$\mathrm{m^{2} \cdot s^{-2}}$
energy density	joule per cubic metre	$\mathrm{J/m^{3}}$	$\mathrm{m^{-1} \cdot kg \cdot s^{-2}}$
surface tension, stiffness	newton per metre	$\mathrm{N/m = J/m^{2}}$	$\mathrm{kg \cdot s^{-2}}$
heat flux density, irradiance	watt per square metre	$\mathrm{W/m^{2}}$	$\mathrm{kg \cdot s^{-3}}$
kinematic viscosity, thermal diffusivity, diffusion coefficient	square metre per second	$\mathrm{m^{2}/s}$	$\mathrm{m^{2} \cdot s^{-1}}$
dynamic viscosity	pascal-second	$\mathrm{Pa \cdot s = N \cdot s/m^{2}}$	$\mathrm{m^{-1} \cdot kg \cdot s^{-1}}$
linear mass density	kilogram per metre	$\mathrm{kg/m}$	$\mathrm{m^{-1} \cdot kg}$
mass flow rate	kilogram per second	$\mathrm{kg/s}$	$\mathrm{kg \cdot s^{-1}}$
radiance	watt per steradian square metre	$\mathrm{W/\left(sr\cdot m^{2}\right)}$	$\mathrm{kg \cdot s^{-3}}$
radiance	watt per steradian cubic metre	$\mathrm{W/\left(sr\cdot m^{3}\right)}$	$\mathrm{m^{-1} kg \cdot s^{-3}}$
spectral power	watt per metre	$\mathrm{W/m}$	$\mathrm{m \cdot kg \cdot s^{-3}}$
absorbed dose rate	gray per second	$\mathrm{Gy/s}$	$\mathrm{m^{2} \cdot s^{-3}}$
fuel efficiency	metre per cubic metre	$\mathrm{m/m^{3}}$	$\mathrm{m^{-2}}$
spectral irradiance, power density	watt per cubic metre	$\mathrm{W/m^{3}}$	$\mathrm{m^{-1} \cdot kg \cdot s^{-3}}$
energy flux density	joule per square metre second	$\mathrm{J/\left( m^{2} \cdot s\right)}$	$\mathrm{kg \cdot s^{-3}}$
compressibility	reciprocal pascal	$\mathrm{Pa^{-1}}$	$\mathrm{m \cdot kg^{-1} \cdot s^{2}}$
radiant exposure	joule per square metre	$\mathrm{J/m^{2}}$	$\mathrm{kg \cdot s^{-2}}$
moment of inertia	kilogram square metre	$\mathrm{kg \cdot m^{2}}$	$\mathrm{m^{2} \cdot kg}$
specific angular momentum	newton metre second per kilogram	$\mathrm{N \cdot m \cdot s/kg}$	$\mathrm{m^{2} \cdot s^{-1}}$
radiant intensity	watt per steradian	$\mathrm{W/sr}$	$\mathrm{m^{2} \cdot kg \cdot s^{-3}}$
spectral intensity	watt per steradian metre	$\mathrm{W/\left( sr \cdot m \right)}$	$\mathrm{m \cdot kg \cdot s^{-3}}$

Chemistry

Quantity	Name	Symbol	SI Equivalents
molarity, amount of substance concentration	mole per cubic metre	$\mathrm{mol / m^{3}}$	$\mathrm{m^{-3} \cdot mol}$
molar volume	cubic metre per mole	$\mathrm{m^{3} / mol}$	$\mathrm{m^{3} \cdot mol^{-1}}$
molar heat capacity, molar entropy	joule per kelvin mole	$\mathrm{J/\left(K \cdot mol\right) }$	$\mathrm{m^{2} \cdot kg \cdot s^{-2} \cdot K^{-1} \cdot mol^{-1}}$
molar energy	joule per mole	$\mathrm{J/ mol}$	$\mathrm{m^{2} \cdot kg \cdot s^{-2} \cdot mol^{-1}}$
molar conductivity	siemens square metre per mole	$\mathrm{S \cdot m^{2} / mol}$	$\mathrm{kg^{-1} \cdot s^{3} \cdot A^{2} \cdot mol^{-1}}$
molality	mole per kilogram	$\mathrm{mol / kg}$	$\mathrm{kg^{-1} \cdot mol}$
molar mass	kilogram per mole	$\mathrm{kg/mol}$	$\mathrm{kg \cdot mol^{-1}}$
catalytic efficiency	cubic metre per mole second	$\mathrm{m^{3}/\left( mol \cdot s \right)}$	$\mathrm{m^{3} \cdot s^{-1} \cdot mol^{-1} }$

Electromagnetics

Quantity	Name	Symbol	SI Equivalents
electric displacement field, polarization density	coulomb per square metre	$\mathrm{C/m^{2}}$	$\mathrm{m^{-2} \cdot s \cdot A }$
electric charge density	coulomb per cubic metre	$\mathrm{C/m^{3}}$	$\mathrm{m^{-3} \cdot s \cdot A }$
electric current density	ampere per square metre	$\mathrm{A/m^{2}}$	$\mathrm{m^{-2} \cdot A}$
electrical conductivity	siemens per metre	$\mathrm{S/m}$	$\mathrm{m^{-3} \cdot kg^{-1} \cdot s^{3} \cdot A^{2}}$
permitivity	farad per metre	$\mathrm{F/m}$	$\mathrm{m^{-3} \cdot kg^{-1} \cdot s^{4} \cdot A^{2} }$
magnetic permeability	henry per metre	$\mathrm{H/m}$	$\mathrm{m \cdot kg \cdot s^{-2} \cdot A^{-2} }$
electric field strength	volt per metre	$\mathrm{V/m}$	$\mathrm{m \cdot kg \cdot s^{-3} \cdot A^{-2}}$
magnetization, magnetic field strength	ampere per metre	$\mathrm{A/m}$	$\mathrm{m^{-1} \cdot A }$
exposure (X and $\gamma$ rays)	coulomb per kilogram	$\mathrm{C/kg}$	$\mathrm{kg^{-1} \cdot s \cdot A }$
resistivity	ohm metre	$\mathrm{\Omega \cdot m}$	$\mathrm{m^{3} \cdot kg \cdot s^{-3} \cdot A^{-2}}$
linear charge density	coulomb per metre	$\mathrm{C/m}$	$\mathrm{m^{-1} \cdot s \cdot A }$
magnetic dipole moment	joule per tesla	$\mathrm{J/T}$	$\mathrm{m^{2} \cdot A}$
electron mobility	square metre per volt second	$\mathrm{m^{2}/\left( V \cdot s \right)}$	$\mathrm{kg^{-1} \cdot s^{2} \cdot A }$
magnetic reluctance	reciprocal henry	$\mathrm{H^{-1}}$	$\mathrm{m^{-2} \cdot kg^{-1} \cdot s^{2} \cdot A^{2}}$
magnetic vector potential	weber per metre	$\mathrm{Wb/m}$	$\mathrm{m \cdot kg \cdot s^{-2} \cdot A^{-1}}$
magnetic moment	weber metre	$\mathrm{Wb \cdot m}$	$\mathrm{m^{3} \cdot kg \cdot s^{-2} \cdot A^{-1}}$
magnetic rigidity	tesla metre	$\mathrm{T \cdot m}$	$\mathrm{m \cdot kg \cdot s^{-2} \cdot A^{-1}}$
magnetomotive force	ampere radian	$\mathrm{A \cdot rad}$	$\mathrm{A}$
magnetic susceptibility	metre per henry	$\mathrm{m/H}$	$\mathrm{m^{-1} \cdot kg^{-1} \cdot s^{2} \cdot A^{2}}$
piezoelectric constant	coulombs per newton	$C/N$	$\mathrm{m^{-1} \cdot kg^{-1} \cdot s^{3} \cdot A}$

Photometry

Quantity	Name	Symbol	SI Equivalents
luminous energy	lumen second	$\mathrm{lm \cdot s}$	$\mathrm{s \cdot cd}$
luminous exposure	lux second	$\mathrm{lx \cdot s}$	$\mathrm{m^{-2} \cdot s \cdot cd}$
luminance	candela per square metre	$\mathrm{cd/m^{2}}$	$\mathrm{m^{-2} \cdot cd}$
luminous efficacy	lumen per watt	$\mathrm{lm / W}$	$\mathrm{m^{-2} \cdot kg^{-1} \cdot s^{3} \cdot cd}$

Optics

Quantity	Name	Symbol	SI Equivalents
optical power	diopter	$D$	$\mathrm{m^{-1}}$

Thermodynamics

Quantity	Name	Symbol	SI Equivalents
heat capacity, entropy	joule per kilogram	$\mathrm{J/kg}$	$\mathrm{m^{2} \cdot s^{-2}}$
heating value (energy value, calorific value)	joule per kilogram, joule per cubic metre, joule per mole	$\mathrm{J/kg}$ $\mathrm{J/m^{3}}$ $\mathrm{J/mol}$	$\mathrm{m^{2} \cdot s^{-2}}$ $\mathrm{kg \cdot m^{-1} \cdot s^{-2}}$ $\mathrm{kg \cdot m^{2} \cdot mol^{-1} \cdot s^{-2}}$
specific heat capacity, specific entropy	joule per kilogram kelvin	$\mathrm{J/\left( K \cdot kg \right)}$	$\mathrm{m^{2} \cdot s^{-2} \cdot K^{-1}}$
thermal conductivity	watt per metre kelvin	$\mathrm{W/\left( m \cdot K \right)}$	$\mathrm{kg \cdot m \cdot s^{-3} \cdot K^{-1}}$
thermal resistance	kelvin per watt	$\mathrm{K/W}$	$\mathrm{s^{3} \cdot K \cdot kg^{-1} \cdot m^{-2}}$
thermal expansion coefficient	reciprocal kelvin	$\mathrm{K^{-1}}$	$\mathrm{K^{-1}}$
temperature gradient	kelvin per metre	$\mathrm{K/m}$	$\mathrm{K \cdot m^{-1}}$

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