# Fundamental Physical Constants 🧮

## Fundamental Physical Constants List 🧮 Definitions, SI Unit Values & Symbols

Physical constants are believed to be unchanging over time and universal in nature. Most of us are aware the speed of light is constant (or is it?) and have encountered other physical constants during our studies. Did you know hundreds of physical constants have been discovered? They have been measured, defined and are in use every day. Furthermore, some physical constants are also irrational numbers. As measurement techniques have improved accuracy has reduced the level of uncertainty.

- ADDucation’s commonly used physical constants list is compiled by Joe Connor and last updated 24 Jan 2022.

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Key Physical Constants | Symbol/s | SI / CODATA value/s | SI units in words | Scientific Notation Value | Physical Constant Definitions in Words |
---|---|---|---|---|---|

Avogadro constant |
N_{A} |
6.022140857 x 10^{23} mol^{-1} |
per mole | 6.022140857E+23 | The number of atoms or molecules in a mole of a substance. |

Bohr magneton |
µ_{B} |
927.400 9994(57) x 10^{-24 }J T^{-1
} |
joule per tesla. | 927.4009994E-24 | Bohr magneton is a physical constant used to express the magnetic moment of an electron caused by its orbital or spin angular momentum. |

Bohr radius |
a_{o} |
0.529 177 210 67(12) x 10^{-10} m |
meter | 0.52917721067E-10 | The Bohr radius is a physical constant based on the average distance between an electron in its smallest orbit around the nucleus of a hydrogen atom. |

Boltzmann’s constant |
k |
1.380 648 52(79) x 10^{-23} J K^{-1} |
joule per kelvin. | 1.38064852E-23 | Boltzmann’s constant is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. The Bolzmann constant is the gas constant divided by the Avogadro constant (R / N)_{A} |

electron mass / electron rest mass |
m_{e} |
9.109 383 56(11) x 10^{-31} kg |
kilogram | 9.10938356E-31 | The electron rest mass is a fundamental constant. The mass of an object increases, with its velocity, relative to the observer so its mass is measured when its speed is zero relative to the observer. |

elementary charge / electron charge magnitude |
e orq_{e} |
1.602 176 6208(98) x 10^{-19} C |
coulomb | 1.6021766208E-19 | The elementary charge is a fundamental physical constant. The magnitude of the electric charge carried by a single proton (e) or electron (-e). On completion of SI unit redefinition’s (2019) the value will be exactly 1.602176634 ×10^{-19} |

fine structure constant / Sommerfeld’s constant |
ɑ | 7.297 352 5664(17) x 10^{-3} |
number | 7.2973525664E-3 | The fine-structure constant is a number. It has been determined by experiment yet remains elusive to theoretical proof. The fine-structure constant is the measure of the strength of the electromagnetic force that controls how electrically charged elementary particles and photons (light) interact. |

gravitational constant / Newtonian constant of gravitation |
G |
6.674 08(31) x 10^{-11} m^{3} kg^{-1} s^{-2} |
meters cubed per kilogram per second squared. | 6.67408E-11 | The Newtonian constant of gravitation (aka the universal gravitational constant and the Cavendish gravitational constant) is a physical constant which has been measured but proof it’s a constant remains elusive. G is included in Albert Einstein’s Theory of General Relativity and Sir Isaac Newton’s law of universal gravitation states every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. |

inverse fine structure constant |
1/ɑ | 137.035 999 139(31) | number | 137.035999139 | Refer to the fine structure constant (above). |

neutron rest mass / neutron mass |
m_{n} |
1.674 927 471(21) x 10^{-27} kg |
kilogram | 1.674927471E-27 | The rest mass of a neutron (or any object) will be its minimum mass because, as Relativity theory explains, mass and energy are interchangeable. Any moving object has kinetic energy which increases its mass. |

nuclear magneton |
µ_{n} |
5.050 783 699(31) x 10^{-27} J T^{-1} |
joule per tesla. | 5.050783699E-27 | The nuclear magneton is a physical constant of magnetic moment, the property of a magnet that interacts with an applied field to give a mechanical moment. |

permeability of free space / magnetic constant |
µ_{o} |
4 π x 10^{-7} N A^{-2} |
newton per ampere squared. | 12.566370614E-7 | The permeability of free space (also know as the magnetic constant, vacuum permeability and permeability of vacuum) is a measure of the resistance encountered forming a magnetic field in a vacuum. |

permittivity of free space / electric constant |
ε_{o} |
8.854 187 817… x 10^{-12} F m^{-1} |
farad per meter. | 8.854187817E-12 | Permittivity of free space is a physical constant which describes how easily electric (or magnetic) field lines of force pass through air (or any given substance). In this context permittivity means permits. |

pi |
π | 3.141592653… | irrational number. | 3.14159265358979… | Pi is a constant, also known as Archimedes’ constant, which can be calculated by dividing the circumference of a circle by its diameter (or radius squared). Pi is also an irrational number and a transcendental number. |

Planck constant. |
h |
6.626 070 040(81) x 10^{-34} Js |
joule second. | 6.626070040E-34 | Planck’s constant is a physical constant used to describe the varying sizes of quanta (of matter, electricity, heat and gas) in quantum mechanics. |

proton rest mass / proton mass |
m_{p} |
1.672 621 898(21) x 10^{-27} kg |
kilogram | 1.672621898E-27 | The rest mass of a proton (or any object) will be its minimum mass because, as Relativity theory explains, mass and energy are interchangeable. Any moving object has kinetic energy which increases its mass. |

speed of light in vacuum |
c |
299 792 458 m s^{-1} |
meters per second. | 299792458 | The speed of light in a vacuum is constant and independent of the observer, unlike time and space. However, according to Quantum field theory a vacuum cannot be empty. Elementary particles appear and disappear constantly causing disturbances which could potentially cause variations in the speed of light. |

Stefan-Boltzmann constant. |
σ | 5.670 367(13) x 10^{-8} W m^{-2} K^{-4} |
watt per meter squared per kelvin to the fourth |
5.670367E-8 | The Stefan-Boltzmann constant is typically used to solve equations based on the Stefan Boltzmann law, which states the energy radiated per unit of surface area of a black body per unit time is proportional to the fourth power of the thermodynamic temperature of that body. |

tau |
τ | 2π or 6.28318530718… | irrational number. | 6.28318530718… | Tau is a the circle constant representing the ratio between circumference and radius which is preferred to 2π by some mathematicians. |

unified atomic mass unit / dalton |
u or Da | 1.660 539 040(20) × 10^{-27} kg |
kilogram | 1.66053904E-27 | Standard unit used to quantify mass of atoms and molecules. One unified atomic mass unit is numerically equivalent to 1 g/mol and roughly the mass of one nucleon. |

### 2019 SI Base Unit Redefinitions

At an international meeting of metrologists on 16th November 2018 proposals by the International Committee for Weights and Measures (CIPM) to redefine four of the seven SI Base Units (the kilogram, kelvin, mole and ampere), in terms of physical constants, were unanimously agreed. These formally came into force on 20th May 2019, as part of World Metrology Day celebrations. The precise values of physical constants will change and be updated in the next official CODATA list of physical constants. The other three Base SI units (the meter, second and candela) were already defined in terms of physical constants from nature.

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