Physical constants

The units library comes with a number of physical constants with appropriate units defined. All the physical constants are specified as Precise measurements and in the namespace units::constants In general the most recent definition was chosen which includes the 2019 redefinition of some SI units this matches with the rest of the library and the defined units. Inspiration for the different constants was taken from wikipedia and NIST. Defined constants. The 2019 redefinition of the SI system was used where applicable. All common constants listed from NIST are included

Defined constants

Values are taken from NIST 2018 CODATA unless otherwise noted

  • Standard gravity - g0

  • Gravitational constant - G

  • Speed of light - c

  • Elementary Charge (2019 redefinition) - e

  • hyperfine structure transition frequency of the caesium-133 atom - fCs

  • fine structure constant - alpha

  • Planck constant (2019 redefinition) - h

  • Reduced Planck constant (2019 redefinition) - hbar

  • Boltzman constant (2019 redefinition) - k

  • Avogadros constant (2019 redefinition) - Na

  • Luminous efficiency - kcd

  • Permittivity of free space - eps0

  • Permeability of free space - mu0

  • Gas Constant - R

  • Stephan Boltzmann constant -s

  • Hubble constant 69.8 km/s/Mpc - H0

  • Mass of an electron - me

  • Mass of a proton - mp

  • Bohr Radius - a0

  • Faraday’s constant - F

  • Atomic mass constant - mu

  • Conductance quantum - G0

  • Josephson constant - Kj

  • Magnetic flux quantum - phi0

  • von Kiltzing constant - Rk

  • Rydberg constant - Rinf

Planck Units

These units are found in the units::constants::planck namespace and include length, mass, time, charge, and temperature.

Atomic units

These physical constants are values related to an electron or atomic measurements They include length, mass, time, charge- same as e above, energy, and action. The atomic constants are defined in the units::constants::atomic namespace.


There are a few numbers that are used in the library and include definitions in the units::constants namespace. They are represented as doubles and are defined as constexpr

  • pi (3.14159265358979323846)

  • tau (2.0*pi)

  • invalid_conversion (signaling NaN)

  • infinity

  • standard_gravity the numerical value of g0, earth standard gravity in m/s/sec

  • speed_of_light The numerical value of the speed of light in m/s

The last two are used in several other units and some conversions so it seemed better to just define the numerical value and use that rather than use the same number in several places.

Planetary masses

The masses of some of the solar system bodies are included in units::constants::Planetary::mass

  • solar

  • earth

  • moon

  • jupiter

  • mars

From Strings

All constants listed here are available for conversion from strings by wrapping in brackets For example the luminous efficiency would be converted to a unit by using [kcd] The planck constants are available as [planck::XXXXX] or planckXXXXXX and the atomic constants are available as `[atomic::XXXX]


Certain physical constants have uncertainties associated with them and have an additional uncertain_measurement associated with them see uncertain_measurments. These can be found in the units::constants::uncertain namespace and include:

  • Gravitational constant - G

  • Permittivity of free space - eps0

  • Permeability of free space - u0

  • Hubble constant 69.8 km/s/Mpc - H0

  • Mass of an electron - me

  • Mass of a proton - mp

  • Atomic mass constant - mu

  • mass of nuetron - mn

  • Rydberg constant - Rinf

  • fine structure constant - alpha

NOTE: A few of the uncertain constants have more precision than supported in uncertain_measurments but were included for completeness