Modelica.Constants

Library of mathematical constants and constants of nature (e.g., pi, eps, R, sigma)

Information

This package provides often needed constants from mathematics, machine dependent constants and constants from nature. The latter constants (name, value, description) are from the following source (based on the second source):

Michael Stock, Richard Davis, Estefanía de Mirandés and Martin J T Milton:
The revision of the SI-the result of three decades of progress in metrology in Metrologia, Volume 56, Number 2. https://iopscience.iop.org/article/10.1088/1681-7575/ab0013/pdf, 2019.
D B Newell, F Cabiati, J Fischer, K Fujii, S G Karshenboim, H S Margolis , E de Mirandés, P J Mohr, F Nez, K Pachucki, T J Quinn, B N Taylor, M Wang, B M Wood and Z Zhang:
The CODATA 2017 values of h, e, k, and NA for the revision of the SI in Metrologia, Volume 55, Number 1. https://iopscience.iop.org/article/10.1088/1681-7575/aa950a/pdf, 2017.

BIPM is Bureau International des Poids et Mesures (they publish the SI-standard).

CODATA is the Committee on Data for Science and Technology.

Main Author:
Martin Otter
Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Institut für Systemdynamik und Regelungstechnik (SR)
Münchener Straße 20
D-82234 Weßling
Germany
email: Martin.Otter@dlr.de

Copyright © 1998-2025, Modelica Association and contributors

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name Description
e=Modelica.Math.exp(1.0)  
pi=2*Modelica.Math.asin(1.0)  
D2R=pi/180 Degree to Radian
R2D=180/pi Radian to Degree
gamma=0.57721566490153286061 See http://en.wikipedia.org/wiki/Euler_constant
eps=ModelicaServices.Machine.eps The difference between 1 and the least value greater than 1 that is representable in the given floating point type
small=ModelicaServices.Machine.small Minimum normalized positive floating-point number
inf=ModelicaServices.Machine.inf Maximum representable finite floating-point number
Integer_inf=ModelicaServices.Machine.Integer_inf Biggest Integer number such that Integer_inf and -Integer_inf are representable on the machine
c=299792458 Speed of light in vacuum
g_n=9.80665 Standard acceleration of gravity on earth
G=6.67430e-11 Newtonian constant of gravitation
q=1.602176634e-19 Elementary charge
F=q*N_A Faraday constant, C/mol
h=6.62607015e-34 Planck constant
k=1.380649e-23 Boltzmann constant
R=k*N_A Molar gas constant
sigma=2*pi^5*k^4/(15*h^3*c^2) Stefan-Boltzmann constant
N_A=6.02214076e23 Avogadro constant
mu_0=1.25663706212e-6 Magnetic constant
epsilon_0=1/(mu_0*c*c) Electric constant
T_zero=-273.15 Absolute zero temperature
Automatically generated Tue Feb 24 16:59:32 2026.