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hepunits: units and constants in the HEP system of units

Scikit-HEP PyPI version Conda-forge version Zenodo DOI

GitHub Actions Status: CI Code Coverage

hepunits collects the most commonly used units and constants in the HEP System of Units, as derived from the basic units originally defined by the CLHEP project, which are not the same as the SI system of units:

Quantity Name Unit
Length millimeter mm
Time nanosecond ns
Energy Mega electron Volt MeV
Positron charge eplus  
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
Plane angle radian rad
Solid angle steradian sr

It is largely based on the international system of units (SI)

Quantity Name Unit
Length meter m
Time second s
Mass kilogram kg
Electric current ampere A
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd

but augments it with handy definitions, changing the basic length and time units.

This HEP system of units is in use in many software libraries such as GEANT4 and Gaudi.

Note that many units are now exact, such as the speed of light in vacuum. The package is in agreement with the values in the 2020 Particle Data Group review.


Install hepunits like any other Python package, typically:

python -m pip install hepunits

The package is also available on conda-forge, and installable with

conda install -c conda-forge hepunits

Getting started

The package contains 2 modules, constants and units, whose names are self-explanatory. It may be more readable to import quantities explicitly from each of the modules though everything is available from the top-level as from hepunits import ....

The module hepunits.constants contains 2 sorts of constants: physical constants and commonly used constants.

The typical usage is the following:

>>> from hepunits.constants import c_light
>>> from hepunits.units     import picosecond, micrometer
>>> tau_Bs = 1.5 * picosecond    # a particle lifetime, say the Bs meson's
>>> ctau_Bs = c_light * tau_Bs   # ctau of the particle, ~450 microns
>>> print ctau_Bs                # result in HEP units, so mm
>>> print ctau_Bs / micrometer   # result in micrometers

Typical usage of the hepunits.units module:

>>> # add two quantities with length units and get the result in meters
>>> from hepunits import units as u
>>> (1 * u.meter + 5 * / u.meter
>>> # the default result is, of course, in HEP units, so mm
>>> 1 * u.meter + 5 *

Fancier usage

When working with data the user should not need to know what units are used in their internal representation (it makes sense, though, and is important, to be consistent throughout the "data storages"!).

These simple rules are enough - exemplified in the code below:

  • Dimensioned quantities in the "data stores" abide to the HEP system of units.
  • All definitions of dimensioned quantities are dimensioned by multiplying by the units, as in mass_window = 500 * keV.
  • All output of dimensioned quantities is converted to the required units by dividing by the units, as in energy_resolution() / GeV.

For the sake of argument, let's consider below a function returning a dimensioned quantity. the function below stores a dimensioned quantity defined in keV (the actual value is represented in MeV, which is the standard unit) and the caller simply needs to ensure an explicit conversion to the desired unit dividing by it (GeV in the example):

>>> from hepunits.units import keV, MeV, GeV
>>> mass_window = 1 * GeV    # define a 1 GeV mass window
>>> def energy_resolution():
...    # returns the energy resolution of 500 keV
...    return 500. * keV  # numerical value is 0.5
>>> energy_resolution() / GeV # get the energy resolution in GeV