Constants

View all mathematical and physical constants

Acceleration due to gravity

The acceleration experienced by an object falling freely near the Earth's surface. This is a standard value, and may vary slightly depending on location. Units are meters per second squared (m/s²).

g
= 9.80665

Avogadro's number

The number of constituent particles (atoms, molecules, ions, etc.) that are contained in one mole of a substance. It's a fundamental constant in chemistry. Units are per mole (mol⁻¹).

N_A
= 6.0221408e+23

Planck's constant

A fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. Units are Joule-seconds (J⋅s).

h_P
= 6.6260701e-34

Speed of light in vacuum

The speed at which light travels in a vacuum. It's a universal constant in physics. Units are meters per second (m/s).

c_{light}
= 2.9979246e+8

Boltzmann constant

Relates the average kinetic energy of particles in a gas to the absolute temperature. It's a fundamental constant in thermodynamics and statistical mechanics. Units are Joules per Kelvin (J/K).

k_B
= 1.380649e-23

Elementary charge

The magnitude of the electric charge carried by a single proton or electron. It's a fundamental constant in physics. Units are Coulombs (C).

q_e
= 1.6021766e-19

Permittivity of free space

A constant that relates the electric field to electric displacement in a vacuum. It's a fundamental constant in electromagnetism. Units are Farads per meter (F/m).

ε_0
= 8.8541878e-12

Permeability of free space

A constant that relates the magnetic field to magnetic flux density in a vacuum. It's a fundamental constant in electromagnetism. Units are Henrys per meter (H/m) or Tesla-meters per ampere (T⋅m/A).

μ_0
= 0.00000126

Gas constant

The ideal gas constant, relating the pressure, volume, temperature, and number of moles of an ideal gas. Units are Joules per mole-Kelvin (J/(mol⋅K)).

R
= 8.31446262

Atomic mass unit

A standard unit of mass used to express the mass of atoms and molecules. One atomic mass unit is approximately equal to the mass of one proton or neutron. Units are kilograms (kg).

m_{amu}
= 1.6605391e-27

Rydberg constant

A fundamental constant in atomic physics that relates to the atomic spectra of hydrogen. Units are per meter (m⁻¹).

R_y
= 10973731.56800000

Fine-structure constant

A dimensionless physical constant that characterizes the strength of the electromagnetic interaction. It's related to the elementary charge, speed of light, and Planck's constant. It is dimensionless.

α
= 0.00729735

Bohr radius

The approximate radius of the electron's orbit in the ground state of the hydrogen atom. Units are meters (m).

a_0
= 5.2917721e-11

Electron mass

The mass of an electron. Units are kilograms (kg).

m_e
= 9.1093837e-31

Proton mass

The mass of a proton. Units are kilograms (kg).

m_p
= 1.6726219e-27

Neutron mass

The mass of a neutron. Units are kilograms (kg).

m_n
= 1.6749275e-27

Magnetic constant

Relates the magnetic field to its sources. Units are Henrys per meter (H/m) or Tesla-meters per ampere (T⋅m/A).

μ
= 0.00000126

Atmospheric pressure (standard)

The standard atmospheric pressure at sea level. Units are Pascals (Pa).

P_atm
= 101325

Molar mass of carbon-12

The mass of one mole of carbon-12 atoms. Units are kilograms per mole (kg/mol).

M_C12
= 0.012

Faraday constant

The amount of electric charge carried by one mole of electrons. Units are Coulombs per mole (C/mol).

F_A
= 96485.33212000

Speed of sound in air (at 20°C)

The speed of sound in air at approximately 20°C. This value can vary slightly with temperature and air pressure. Units are meters per second (m/s).

v_s
= 343

Golden ratio

An irrational mathematical constant approximately equal to 1.6180339887. It appears in many areas of mathematics, nature, and art. It is dimensionless.

φ
= 1.61803399
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