# Fundamental Physical Constants

## Examples of When They May Be Used

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 inhabit.

## Discovering Constants

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). Note that these constants are sometimes written in different units, so if you find another value that isn't exactly the same as it is here, it may have been converted into another set of units.

This list of significant physical constants⁠—along with some commentary on when they are used⁠—is not exhaustive. These constants should help you understand how to think about these physical concepts.

## 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 equations describing electromagnetic fields. As Einstein developed the theory of relativity, the speed of light became relevant as a constant that underlies many important elements of the physical structure of reality.

c = 2.99792458 x 108 meters per second

## Charge of Electron

The 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. Measuring 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

Physicist Max Planck began the 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

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 constant relates 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 physical constant 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, 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

Similar to the permittivity of free space, this constant relates to the magnetic field lines permitted in a classical vacuum. It comes into play in Ampere's law describing the force of magnetic fields:

μ0 = 4 π x 10-7 Wb/A m