constants

This repository contains a collection of mathematical and physical constants. Additional information about the constants provided—and their values— see the associated README files.

Note: For the mathematical constants, their values are actually given in three places in this repository:

1. in the associated README.md files;
2. in the header file that defines the value for C++; and
3. in the files used to test/verify the values. While every effort is made to ensure that each of these values are the same, inconsistencies may appear. If discovered, please file an issue.

Using the constants

Here is an example of how the mathematical constants can be used.

#include "constants.hpp"

double r{1.0};

auto area = njoy::constants::pi*r**2;

auto CODATA = njoy::constants::CODATA2018;

auto c = CODATA[c];
auto cUncertainty = CODATA.uncertainty[c]; // 0.0
auto h = CODATA[Planck];
auto hUncertainty = CODATA.uncertainty[Planck];

Mathematical Constants

The (short) list of mathematical constants was taken from Wikipedia:Mathematical constant. While there are many more constants given there, we have limited this initially to the Basic mathematical constants.

Name	Variable name	Value	Reference	Reference Date
Archimedes constant (π)	pi	3.141 592 653 589 793	http://mathworld.wolfram.com/Pi.html	2018-09-13
Euler's number (e)	e	2.718 281 828 459 045	http://mathworld.wolfram.com/e.html	2018-09-13
Pythagoras' constant (√2)	root2	1.414 213 562 373 095	http://mathworld.wolfram.com/PythagorassConstant.html	2018-09-13

Physical Constants

Unlike mathematical constants, physical constants can change based on the current understanding and measurement capabilities of physics. Thus we can have different versions of the constants.

The worldwide standard for the physical constants is maintained by Committee on Data of the International Council for Science (CODATA). We have taken our physical constant values from their publication.

For each CODATA release, we provide two maps; one for the data values and one for their associated uncertainty. The keys are the same in both maps. There are some physical constants that are defined to be exact (e.g., the speed of light). Their uncertainty, is, therefore, zero.

CODATA2018

The raw data for this is contained in CODATA2018.txt which was downloaded from https://physics.nist.gov/cuu/Constants/Table/allascii.txt on 2019-07-05.

Constants

Quantity	Variable name	Value	Uncertainty	Unit
Avogadro constant	avogadro	6.022 140 76 e23	0.0	mol^-1
Boltzmann constant	boltzmann	1.380 649 e-23	0.0	J K^-1
Boltzmann constant	k	1.380 649 e-23	0.0	J K^-1
conductance quantum	conductanceQuantum	7.748 091 729 e-5	0.0	S
conductance quantum	G0	7.748 091 729 e-5	0.0	S
Elementary charge	elementaryCharge	1.602 176 6234 e-19	0.0	C
classical electron radius	electronRadius	2.817 940 3227 e-15	0.000 000 0019 e-15	m
Faraday constant	faraday	96 485.332 89	0.000 59	C mol^-1
fine-structure constant	fineStructure	7.297 352 5664 e-3	0.000 000 0017 e-3	--
magnetic constant	magnetic	12.566 370 614... e-7	0.0	N A^-2
magnetic flux quantum	magneticFluxQuantum	2.067 833 831 e-15	0.000 000 013 e-15	Wb
molar gas constant	molarGas	8.314 4598	0.000 0048	J mol^-1 K^-1
Newtonian constant of gravitation	G	6.674 08 e-11	0.000 31 e-11	m^3 kg^-1 s^-2
Newtonian constant of gravitation	newtonianGravity	6.674 08 e-11	0.000 31 e-11	m^3 kg^-1 s^-2
Planck constant	planck	6.626 070 15 e-34	0.0	J s
Planck constant	h	6.626 070 15 e-34	0.0	J s
Planck constant over 2 pi	reducedPlanck	1.054 571 817 e-34	0.0	J s
Planck constant over 2 pi	hbar	1.054 571 817 e-34	0.0	J s
Rydberg constant	rydberg	10 973 731.568 160	0.000 021	m^-1
Speed of light in a vacuum	c	299 792 458	0.0	m s^-1
Speed of light in a vacuum	speedOfLight	299 792 458	0.0	m s^-1
Stefan-Boltzmann constant	stefanBoltzmann	5.670 374 419 e-8	0.0	W m^-2 K^-4

Particle masses

Quantity	Variable name	Value	Uncertainty	Unit
electron mass	electronMass	9.109 383 56 e-31	0.000 000 11 e-31	kg
neutron mass	neutronMass	1.674 927 471 e-27	0.000 000 021 e-27	kg
proton mass	protonMass	1.672 621 898 e-27	0.000 000 021 e-27	kg
deuteron mass	deuteronMass	3.343 583 719 e-27	0.000 000 041 e-27	kg
helion mass	helionMass	5.006 412 700 e-27	0.000 000 062 e-27	kg
triton mass	tritonMass	5.007 356 665 e-27	0.000 000 062 e-27	kg
alpha particle mass	alphaMass	6.644 657 230 e-27	0.000 000 082 e-27	kg

CODATA2014

The raw data for this is contained in CODATA2014.txt which was downloaded from https://physics.nist.gov/cuu/Constants/Table/allascii.txt on 2018-09-13.

Constants

Quantity	Variable name	Value	Uncertainty	Unit
Avogadro constant	avogadro	6.022 140 857 e23	0.000 000 074 e23	mol^-1
Boltzmann constant	boltzmann	1.380 648 52 e-23	0.000 000 79 e-23	J K^-1
Boltzmann constant	k	1.380 648 52 e-23	0.000 000 79 e-23	J K^-1
conductance quantum	conductanceQuantum	7.748 091 7310 e-5	0.000 000 0018 e-5	S
conductance quantum	G0	7.748 091 7310 e-5	0.000 000 0018 e-5	S
Elementary charge	elementaryCharge	1.602 176 6208 e-19	0.000 000 0098 e-19	C
classical electron radius	electronRadius	2.817 940 3262 e-15	0.000 000 0013 e-15	m
Faraday constant	faraday	96 485.332 12	0.0	C mol^-1
fine-structure constant	fineStructure	7.297 352 5693 e-3	0.000 000 0011 e-3	--
magnetic constant	magnetic	1.256 637 062 12 e-6	0.000 000 000 19 e-6	N A^-2
magnetic flux quantum	magneticFluxQuantum	2.067 833 848 e-15	0.0	Wb
molar gas constant	molarGas	8.314 462 618	0.0	J mol^-1 K^-1
Newtonian constant of gravitation	G	6.674 30 e-11	0.000 15 e-11	m^3 kg^-1 s^-2
Newtonian constant of gravitation	newtonianGravity	6.674 30 e-11	0.000 15 e-11	m^3 kg^-1 s^-2
Planck constant	planck	6.626 070 040 e-34	0.000 000 081 e-34	J s
Planck constant	h	6.626 070 040 e-34	0.000 000 081 e-34	J s
Planck constant over 2 pi	reducedPlanck	1.054 571 800 e-34	0.000 000 013 e-34	J s
Planck constant over 2 pi	hbar	1.054 571 800 e-34	0.000 000 013 e-34	J s
Rydberg constant	rydberg	10 973 731.568 508	0.000 065	m^-1
Speed of light in a vacuum	c	2.997 924 58 e8	0.0	m s^-1
Speed of light in a vacuum	speedOfLight	2.997 924 58 e8	0.0	m s^-1
Stefan-Boltzmann constant	stefanBoltzmann	5.670 367 e-8	0.000 013 e-8	W m^-2 K^-4

Particle masses

Quantity	Variable name	Value	Uncertainty	Unit
electron mass	electronMass	9.109 383 7015 e-31	0.000 000 0028 e-31	kg
neutron mass	neutronMass	1.674 927 498 04 e-27	0.000 000 000 95 e-27	kg
proton mass	protonMass	1.672 621 923 69 e-27	0.000 000 021 e-27	kg
deuteron mass	deuteronMass	3.343 583 7724 e-27	0.000 000 0010 e-27	kg
helion mass	helionMass	5.006 412 7796 e-27	0.000 000 0015 e-27	kg
triton mass	tritonMass	5.007 356 7446 e-27	0.000 000 0015 e-27	kg
alpha particle mass	alphaMass	6.644 657 3357 e-27	0.000 000 0020 e-27	kg

Derived Constants

Some constants are derived from others, but used sufficiently often that it is worth pre-computing the values. Their values are not listed here, but the variable names are.

Quanitity	Variable Name	Unit
2π	twopi	--
Reduced Planck	hbar	J s
Planck length	planckLength	m

A note on floating point arithmetic

Some values of these constants are known to much greater precision than what we have reported here (e.g., pi and e.) We have limited the number of significant digits in this repository to 16 as anything more would be insignificant in floating point arithmetic.

LICENSE

This software is copyrighted by Los Alamos National Laboratory and distributed according to the conditions in the accompanying LICENSE file.