UnitConversion

Natural unit systems are measurement systems with selected physical constants set to 1, a practice that has proven useful in physics research. The Mathematica package “UnitConversion” is designed for unit conversion within customizable natural unit systems. The package includes predefined units and parameters commonly used in particle physics and cosmology, enabling efficient and flexible calculations across various physical systems. The default natural unit system is the one with $c=\hbar=\varepsilon_0=k_\mathrm{B}=1$ (light speed = reduced Planck constant = vacuum permittivity = Boltzmann constant = 1).

Installation/update

Method 1: One can directly import the package from the web every time, using

Import["https://raw.githubusercontent.com/hongyi18/UnitConversion/main/UnitConversion.wl"]

Method 2: Download the package to the Applications subdirectory of $UserBaseDirectory, using

URLDownload["https://raw.githubusercontent.com/hongyi18/UnitConversion/main/UnitConversion.wl", FileNameJoin[{$UserBaseDirectory, "Applications", "UnitConversion.wl"}]]

To load the package, simply run

<<UnitConversion`

Note: If the installation/update fails, please try again or check your internet connection by following the guide Troubleshooting Internet Connectivity Problems.

Documentation/tutorial

Documentation can be found on zenodo:14086594. A 3-minute line-by-line tutorial is available here.

Cheatsheet

• Join[$BaseUnits, Keys@$Units]: Print the full list of the symbols of named units.
• ?H0: Check if the unit symbol H0 is supported; the meaning of the symbol will be printed if it is supported.
• UnitList[]: Print the full list of named units and their meanings.
• NaturalUnitInfo[]: Information about the current natural unit system.
• UC[quantity]: Automatically simplify the quantity in terms of the SI base units.
• UC[quantity, targetunit]: Convert the quantity in terms of the target unit.
• SetNaturalUnit[DefiningConstants->{c==1, GN==1}]: Use the natural system with the defining constant $c=G_\mathrm{N}=1$ (geometrized units).

Basic info about the package

The values of constants are taken based on Particle Physics Booklet by Particle Data Group and the wikipedia page International System of Units.

Only named units and parameters are supported. The current list of named units include five SI base units $\{ \mathrm{s}, \mathrm{m}, \mathrm{kg}, \mathrm{A}, \mathrm{K} \}$, their derived units, and some useful constants and parameters in particle physics and cosmology. The other two SI base units $\{ \mathrm{mol}, \mathrm{cd} \}$ and their derived units are not supported yet.

Contact

If you find any bugs or would like to make suggestions for its improvement, please contact me via the email address displayed on my website.