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


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:

Peter J. Mohr and Barry N. Taylor (1999):
CODATA Recommended Values of the Fundamental Physical Constants: 1998. Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000. See also

CODATA is the Committee on Data for Science and Technology.

Main Author:
Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e. V. (DLR)
Postfach 11 16
D-82230 Weßling

Copyright © 1998-2010, Modelica Association and DLR.

This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the Modelica License 2. For license conditions (including the disclaimer of warranty) see Modelica.UsersGuide.ModelicaLicense2 or visit

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

Package Content

D2R=pi/180Degree to Radian
R2D=180/piRadian to Degree
eps=1.e-15Biggest number such that 1.0 + eps = 1.0
small=1.e-60Smallest number such that small and -small are representable on the machine
inf=1.e+60Biggest Real number such that inf and -inf are representable on the machine
Integer_inf=2147483647Biggest Integer number such that Integer_inf and -Integer_inf are representable on the machine
c=299792458Speed of light in vacuum
g_n=9.80665Standard acceleration of gravity on earth
G=6.6742e-11Newtonian constant of gravitation
F=9.64853399e4Faraday constant, C/mol
h=6.6260693e-34Planck constant
k=1.3806505e-23Boltzmann constant
R=8.314472Molar gas constant
sigma=5.670400e-8Stefan-Boltzmann constant
N_A=6.0221415e23Avogadro constant
mue_0=4*pi*1.e-7Magnetic constant
epsilon_0=1/(mue_0*c*c)Electric constant
T_zero=-273.15Absolute zero temperature

Types and constants

  final constant Real e=Modelica.Math.exp(1.0);

  final constant Real pi=2*Modelica.Math.asin(1.0);

  final constant Real D2R=pi/180 "Degree to Radian";

  final constant Real R2D=180/pi "Radian to Degree";

  final constant Real gamma=0.57721566490153286060 

  final constant Real eps=1.e-15 "Biggest number such that 1.0 + eps = 1.0";

  final constant Real small=1.e-60 
  "Smallest number such that small and -small are representable on the machine";

  final constant Real inf=1.e+60 
  "Biggest Real number such that inf and -inf are representable on the machine";

  final constant Integer Integer_inf=2147483647 
  "Biggest Integer number such that Integer_inf and -Integer_inf are representable on the machine";

  final constant SI.Velocity c=299792458 "Speed of light in vacuum";

  final constant SI.Acceleration g_n=9.80665 
  "Standard acceleration of gravity on earth";

  final constant Real G(final unit="m3/(kg.s2)") = 6.6742e-11 
  "Newtonian constant of gravitation";

  final constant SI.FaradayConstant F = 9.64853399e4 "Faraday constant, C/mol";

  final constant Real h(final unit="J.s") = 6.6260693e-34 "Planck constant";

  final constant Real k(final unit="J/K") = 1.3806505e-23 "Boltzmann constant";

  final constant Real R(final unit="J/(mol.K)") = 8.314472 "Molar gas constant";

  final constant Real sigma(final unit="W/(m2.K4)") = 5.670400e-8 
  "Stefan-Boltzmann constant";

  final constant Real N_A(final unit="1/mol") = 6.0221415e23 
  "Avogadro constant";

  final constant Real mue_0(final unit="N/A2") = 4*pi*1.e-7 "Magnetic constant";

  final constant Real epsilon_0(final unit="F/m") = 1/(mue_0*c*c) 
  "Electric constant";

  final constant NonSI.Temperature_degC T_zero=-273.15 
  "Absolute zero temperature";

Automatically generated Fri Nov 12 16:31:49 2010.