physical constants

Fundamental Physical Constants

List of Fundamental Physical Constants with Definitions, SI Unit Values and 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 but did you realize hundreds of physical constants have been discovered, measured, defined and are being used every day. As measurement techniques have improved accuracy and the level of uncertainty has been reduced. Researchers, metrologists and standards organizations worldwide continuously refine the constant values. The latest fundamental physical constant values, based on CODATA 2014 data, are publicly available, we like the searchable NIST database. To make ADDucation’s list of key physical constants useful we focused on:

  • Identifying the SI-Units for each constant and we’ve done our best to explain the units in words.
  • Attempting to explain the definitions of fundamental physical constants “for dummies”, in layman’s terms, so anyone interested has a better chance to understand them, please help us improve them.
  • Values for physical constants in exponential notation format which students can enter directly into scientific calculators.

ADDucation Tips: Click arrows in column headings to sort physical constants. Click the + icon to expand columns on tablets and mobiles. Set your browser to full screen and zoom out to display all physical constants. Start typing in the Filter table box to find anything inside the table.

Key Physical ConstantsSymbol/sSI / CODATA value/sSI units in wordsScientific Notation ValuePhysical Constant Definitions in Words
Avogadro constantNA6.022140857 x 1023 mol-1per mole6.022140857E+23The number of atoms or molecules in a mole of a substance.
Bohr magnetonµB927.400 9994(57) x 10-24 J T-1
joule per tesla927.4009994E-24Bohr magneton is a physical constant used to express the magnetic moment of an electron caused by its orbital or spin angular momentum.
Bohr radiusao0.529 177 210 67(12) x 10-10 mmeter0.52917721067E-10The 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 constantk1.380 648 52(79) x 10-23 J K-1joule per kelvin1.38064852E-23Boltzmann’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 / NA)
electron mass / electron rest massme9.109 383 56(11) x 10-31 kgkilogram9.10938356E-31The 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 chargeelectron charge magnitudee or
qe
1.602 176 6208(98) x 10-19 Ccoulomb1.6021766208E-19The 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 constantɑ7.297 352 5664(17) x 10-3number7.2973525664E-3The 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 gravitationG6.674 08(31) x 10-11 m3 kg-1 s-2meters cubed per kilogram per second squared6.67408E-11The 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 constant1/ɑ137.035 999 139(31)number137.035999139Refer to the fine structure constant (above).
neutron rest mass / neutron massmn1.674 927 471(21) x 10-27 kgkilogram1.674927471E-27The 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 magnetonµn5.050 783 699(31) x 10-27 J T-1joule per tesla5.050783699E-27The 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 constantµo4 π x 10-7 N A-2newton per ampere squared12.566370614E-7The 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 constantεo8.854 187 817… x 10-12 F m-1farad per meter8.854187817E-12Permittivity 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”.
piπ3.141592653…number3.141592653Pi is a constant number which can be calculated by dividing the circumference of a circle by its diameter (or radius squared).
Planck constanth6.626 070 040(81) x 10-34 Jsjoule second6.626070040E-34Planck’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 massmp1.672 621 898(21) x 10-27 kgkilogram1.672621898E-27The 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 vacuumc299 792 458 m s-1meters per second299792458The 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 constantσ5.670 367(13) x 10-8 W m-2 K-4watt per meter squared
per kelvin to the fourth
5.670367E-8The 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.
unified atomic mass unit / daltonu or Da1.660 539 040(20) × 10-27 kgkilogram1.66053904E-27Standard 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.

SI Base Unit Redefinition

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 and will formally come into force on 20th May 2019, as part of World Metrology Day celebrations. The precise values of physical constants will change and updated in the next official CODATA physical constants list. The other Base SI units (the meter, second and candela) were already defined in terms of physical constants from nature.

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