Physical Units

Class Quantity and its derivates, Unit and Constant, can be used in many scientific applications, because they enable easy manipulation and calculations with physical quantities. Among the most interesting features are:

  • Concise and regularized unit notation with arbitrary unit prefixes.

  • Conversion of units with the same, or inverse dimensionality (SI, CGS, natural units and more…).

  • Conversion of temperatures (K, degR, degC, degF).

  • Conversion of logarithmic units (dB, Np, dBmW,…).

  • Integration with numpy arrays and functions.

  • Usage of float or Decimal precision.

  • Quantity is a self-content class that does not need initialization in a header, or use of registries. Quantities can be pickled and are compatible when created in different parts of the code.

  • Support of fractional powers

All available units, constants and prefixes with their corresponding symbols and definitions are listed in settings.py. In this text, we will refer to them without extensive introduction. A list of available units and constants can also be printed using the following python command:

>>> import scinumtools.units as su
>>> print(su.Unit())
Units

Prefixes:

Symbol   | Prefix               | Definition
---------+----------------------+---------------------
Y        | yotta                | 1e24
Z        | zetta                | 1e21
E        | exa                  | 1e18
P        | peta                 | 1e15
...

>>> print(su.Constant())
Constants

Symbol   | Unit                 | Definition
---------+----------------------+---------------------
[c]      | velocity of light    | 299792458*m/s
[h]      | Planck const.        | 6.6260755e-34*J*s
[k]      | Boltzmann const.     | 1.380658e-23*J/K
[eps_0]  | permit. of vac.      | 8.854187817e-12*F/m
...

All units used by Quantity are based on 8 fundamental dimensions. These are not identical with any standard metric system (SI, CGS) but conveniently selected for ease of implementation and internal calculations. Six units are physical (m meter, g gram, s second, K Kelvin, C Coulomb, cd candela) and two are numerical (mol mole, rad radian). Derived units use combinations of these dimensions and a numerical value, magnitude.

Units can be used individually, or combined using basic mathematical operations. Multiplication is denoted using asterisk symbol m*m, division using slash symbol m/s, integer powers are indicated with a number after the unit m2 (or m-2) and fractional powers are denoted using two numbers separated by a colon s3:3 (or s-3:3). Units can also have a numerical part 60*s (or 365.25*day, or 1.67e-24*g) and can use parenthesis m3/(kg*s2). No empty spaces in unit expressions are allowed.

  • Units without prefixes: g, J, ly

  • Units with prefixes: mg, MJ, kly

  • Unit expressions: kg*m2/s2, V/(C/s), 1/Hz1:2

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