Fundamental Physical Constants

Examples of When They May Be Used

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The speed of light, which is how fast light travels in a vacuum, is an important physical constant. Artur Debat/Getty Images

Physics is described in the language of mathematics, and the equations of this language make use of a wide array of physical constants. In a very real sense, the values of these physical constants define our reality. A universe in which they were different would be radically altered from the one that we actually inhabit.

The constants are generally arrived at by observation, either directly (as when one measures the charge of an electron or the speed of light) or by describing a relationship that is measurable and then deriving the value of the constant (as in the case of the gravitational constant).

This listing is of significant physical constants, along with some commentary on when they are used, is not at all exhaustive, but should be helpful in trying to understand how to think about these physical concepts.

It should also be noted that these constants are all sometimes written in different units, so if you find another value that isn't exactly the same as this one, it may be that it has been converted into another set of units.

Speed of Light

Even before Albert Einstein came along, physicist James Clerk Maxwell had described the speed of light in free space in his famous Maxwell's equations describing electromagnetic fields. As Albert Einstein developed his theory of relativity, the speed of light took on relevance as a constant underlying important elements of the physical structure of reality.

c = 2.99792458 x 108 meters per second 

Charge of Electron

Our modern world runs on electricity, and the electrical charge of an electron is the most fundamental unit when talking about the behavior of electricity or electromagnetism.

e = 1.602177 x 10-19 C

Gravitational Constant

The gravitational constant was developed as part of the law of gravity developed by Sir Isaac Newton. The measurement of the gravitational constant is a common experiment conducted by introductory physics students, by measuring the gravitational attraction between two objects.

G = 6.67259 x 10-11 N m2/kg2

Planck's Constant

The physicist Max Planck began the entire field of quantum physics by explaining the solution to the "ultraviolet catastrophe" in exploring blackbody radiation problem. In doing so, he defined a constant that became known as Planck's constant, which continued to show up across various applications throughout the quantum physics revolution.

h = 6.6260755 x 10-34 J s

Avogadro's Number

This constant is used much more actively in chemistry than in physics, but it relates the number of molecules that are contained in one mole of a substance.

NA = 6.022 x 1023 molecules/mol

Gas Constant

This is a constant that shows up in a lot of equations related to the behavior of gases, such as the Ideal Gas Law as part of the kinetic theory of gases.

R = 8.314510 J/mol K

Boltzmann's Constant

Named after Ludwig Boltzmann, this is used to relate the energy of a particle to the temperature of a gas. It is the ratio of the gas constant R to Avogadro's number NA:

k = R / NA = 1.38066 x 10-23 J/K

Particle Masses

The universe is made up of particles, and the masses of those particles also show up in a lot of different places throughout the study of physics. Though there are a lot more fundamental particles than just these three, they're the most relevant physical constants that you'll come across:

Electron mass = me = 9.10939 x 10-31 kg 
Neutron mass = mn = 1.67262 x 10-27 kg 
Proton mass = mp = 1.67492 x 10-27 kg 

Permittivity of Free Space

This is a physical constant that represents the ability of a classical vacuum to permit electric field lines. It is also known as epsilon naught.

ε0 = 8.854 x 10-12 C2/N m2

Coulomb's Constant

The permittivity of free space is then used to determine Coulomb's constant, which is a key feature of Coulomb's equation that governs the force created by interacting electrical charges.

k = 1/(4πε0) = 8.987 x 109 N m2/C2

Permeability of Free Space

This constant is similar to the permittivity of free space, but relates to the magnetic field lines permitted in a classical vacuum, and comes into play in Ampere's law describing the force of magnetic fields:

μ0 = 4 π x 10-7 Wb/A m