Physical Constants

Version 1.2.2 (64.8 KB) by Jorg Woehl
2022 CODATA recommended values of the fundamental constants in physics and chemistry
54 Downloads
Updated 13 May 2024

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Physical Constants

Constants for MATLAB provides easy access to the 2022 CODATA recommended values of nearly 150 fundamental constants from physics and chemistry, along with their uncertainties, units, names, and other metadata.

Constants has full symbolic math support and contains all historical CODATA datasets back to 1998.

Key Features and Benefits

  • Convenient: Simple dot notation with short, symbol-based variable names.
  • 100% Accurate: Programmatically generated from the official CODATA source.
  • Rich Metadata: Access properties like uncertainty, units, names, and historical datasets back to 1998.
  • Symbolic Math Support: Perform arbitrary-precision calculations, unit conversions, and unit consistency checks using standard MATLAB functions.
  • Future-Proof: Designed to seamlessly accommodate future CODATA adjustments and higher-precision arithmetic in MATLAB.

Basic Usage

Load the latest (2022) values of physical constants:

const = Constants;

Tip

For easy access, save Constants.m to your userpath or add its parent folder to the MATLAB search path.

Access individual constants:

format long;
const.R   % Molar gas constant
% >> 8.314462618153240

const.NA  % Avogadro constant
% >> 6.02214076e+23

Constants have SI units unless the variable name ends in inUnit:

const.hbar             % Reduced Planck constant in SI units (J s)
% >> 1.054571817646156e-34

const.hbarineVseconds  % Reduced Planck constant in eV s
% >> 6.582119569509066e-16

Look up a constant:

const.find('charge')

Output:

    Variable                    Constant                     Unit
    ________    _________________________________________    ____
     ralpha     Alpha particle rms charge radius              m  
     rd         Deuteron rms charge radius                    m  
     e          Elementary charge (atomic unit of charge)     C  
     rp         Proton rms charge radius                      m

Get a list of available constants:

const.info

Output:

            Variable                                           Constant                                           Unit       
    ________________________    _______________________________________________________________________    __________________
    malpha                      Alpha particle mass                                                        kg                
    malphainu                   Alpha particle mass in u                                                   u                 
    Malpha                      Alpha particle molar mass                                                  kg mol^{-1}       
    ralpha                      Alpha particle rms charge radius                                           m                 
    angstromstar                Angstrom star                                                              m                 
    mu                          Atomic mass constant                                                       kg                
               :                                                   :                                               :         
    epsilonzero                 Vacuum electric permittivity                                               F m^{-1}          
    muzero                      Vacuum magnetic permeability                                               N A^{-2}          
    RK                          Von Klitzing constant                                                      ohm               
    sinsquaredthetaW            Weak mixing angle                                                          (unitless)        
    bprime                      Wien frequency displacement law constant                                   Hz K^{-1}         
    b                           Wien wavelength displacement law constant                                  m K               
	Display all 146 rows.

Advanced Usage

Properties and Metadata

Load all properties and metadata:

const = Constants('all');
const.me  % Properties and metadata for the electron mass

Output:

  struct with fields:

          id: 'electron mass (atomic unit of mass, natural unit of mass)'
        year: 2022
       value: 9.109383713900000e-31
       uncty: 2.800000000000000e-40
        unit: "kg"
        name: "electron mass (atomic unit of mass, natural unit of mass)"
     isExact: 0
       isIrr: 0
    symvalue: 0.00000000000000000000000000000091093837139
     symunit: [kg]
         sym: 0.00000000000000000000000000000091093837139*[kg]
Property Description
id Current name (and other names, if applicable)
year Dataset year
value Value
uncty Uncertainty
unit Unit
name Name (and other names, if applicable) in dataset
isExact true if the constant is exact
isIrr true if the constant is irrational and exact
symvalue Symbolic value (*)
symunit Symbolic unit (*)
sym Symbolic constant with unit (*)

(*) Requires a Symbolic Math Toolbox license.

Access individual properties:

const.me.value   % Value of the electron mass
% >> 9.1093837139e-31

const.me.uncty   % ... its associated uncertainty
% >> 2.8e-40

const.me.unit    % ... and units
% >> "kg"

Load individual properties:

uncty = Constants('uncty');
uncty.me         % Uncertainty in the value of the electron mass
% >> 2.8e-40

Note

The default is value. Calling Constants is equivalent to calling Constants('value').

Historical Data

Calling Constants with a second argument provides access to any of these datasets:

  • 1998
  • 2002
  • 2006
  • 2010
  • 2014
  • 2018
  • 2022

Load values for a specific dataset:

const = Constants('value', '2006');
const.pg  % 2006 value of the proton g factor
% >> 5.585694713

Load values for the latest (2022) dataset:

const = Constants('value', 'latest');
const.Vm  % Current value of the molar volume of an ideal gas (273.15 K, 100 kPa)
% >> 0.022710954641486

Note

This is the default. Calling Constants(arg1) without a second argument is equivalent to calling Constants(arg1, 'latest').

Load values for all datasets (from oldest to most recent):

const = Constants('value', 'all');
const.h(1)    % 1998 value of the Planck constant
% >> 6.62606876e-34

const.h(4)    % 2010 value of the Planck constant
% >> 6.62606957e-34

const.h(end)  % Current (2022) value of the Planck constant
% >> 6.62607015e-34

Load all properties and metadata for all datasets:

const = Constants('all', 'all');
const.alpha   % Properties and metadata for the fine-structure constant (1998 to date)

Output:

  struct with fields:

          id: 'fine-structure constant'
        year: [1998 2002 2006 2010 2014 2018 2022]
       value: [0.007297352533000 0.007297352568000 0.007297352537600 0.007297352569800 0.007297352566400 … ] (1×7 double)
       uncty: [2.700000000000000e-11 2.400000000000000e-11 5.000000000000000e-12 2.400000000000000e-12 … ] (1×7 double)
        unit: [""    ""    ""    ""    ""    ""    ""]
        name: ["fine-structure constant"    "fine-structure constant"    "fine-structure constant"    …    ] (1×7 string)
     isExact: [0 0 0 0 0 0 0]
       isIrr: [0 0 0 0 0 0 0]
    symvalue: [1×7 sym]
     symunit: [1    1    1    1    1    1    1]
         sym: [1×7 sym]

Example 1

const = Constants('all', 'all');
plot(const.NA.year, const.NA.uncty, ':o', 'LineWidth',2);
title(const.NA.id);
xlabel('Year');
ylabel("Uncertainty (" + const.NA.unit(end) + ")");
xticks(const.NA.year);
grid on;

Plot of uncertainty versus year for the Avogadro constant

The Avogadro constant was defined as an exact value (uncertainty: 0) when the SI Units were redefined in 2017.

Symbolic Math

Constants also provides symbolic representations of all values, units, and constants (values & units) to carry out symbolic manipulations and perform calculations with arbitrary accuracy.

symvalue: Symbolic Values

Exact constants, whose values are defined rather than experimentally determined, can be displayed with an arbitrary number of significant digits.

svalue = Constants('symvalue', '2018');
vpa(svalue.R, 150)     % 2018 value of the molar gas constant, rounded to 150 significant digits
vpa(svalue.hbar, 150)  % 2018 value of the reduced Planck constant, rounded to 150 significant digits

Output:

8.3144626181532399999999999999999999999986025942636401108474665474304748280360408924463157254169942689259187318384647369384765625
0.0000000000000000000000000000000001054571817646156391262428003302280744722889961594431207605200865210242417652521623612880705649658442982842269265184440305099090648037855420322457436

The first value, defined as R = NA k in the 2018 dataset, is rational and has 128 significant digits. (Both the Avogadro constant NA and the Boltzmann constant k are have exact, rational values in the dataset.)

The second value, defined as h / (2 π) in the 2018 dataset, is exact but irrational because pi is involved. (The Planck constant h has an exact, rational value in this dataset.)

Note

Even the 64-bit (double precision) floating-point values (value) of exact constants are computed from their definitions in Constants. This makes Constants future-proof should MATLAB ever be released with support for 128-bit (quadruple precision) or 256-bit (octuple precision) arithmetic.

symunit: Symbolic Units

Example 2

Verify units for the Rydberg constant, given by me e4 / (8 ε02 h3 c) according to the Bohr model of the H atom:

sunit = Constants('symunit');
simplify(sunit.me * sunit.e^4 / (sunit.epsilonzero^2 * sunit.h^3 * sunit.c))
% >> 1/[m]

Caution

Choose your variable names wisely; sym and symunit are names of commands from the Symbolic Math Toolbox!

sym: Symbolic Constants

sconst = Constants('sym');
u = symunit;
speed = unitConvert(sconst.c, u.km/u.year)  % Speed of light in vacuum in km/year
% >> (47303652362904/5)*([km]/[year_Julian])

double(separateUnits(speed))                % Extract value and convert to double
% >> 9.460730472580801e+12

Example 3

According to Planck's blackbody radiation law, the proportionality constant between the total power flux and T4 is given by σ = 2 π5 k4 / (15 c2 h3) :

sigma = sym('2')*sym(pi)^sym('5')*sconst.k^sym('4') / ...
	(sym('15')*sconst.c^sym('2')*sconst.h^sym('3'))
	
% Compare this with the (exact and irrational) Stefan-Boltzmann constant from 'Constants'
sconst.sigma

Output:

0.00000000018529443369510835899732062307541*pi^5*(([Hz]^3*[J]*[s]^2)/([K]^4*[m]^2))
0.00000000018529443369510835899732062307541*pi^5*([W]/([K]^4*[m]^2))

The values are obviously identical. Let's check if their units match as well:

checkUnits(sigma == sconst.sigma)

Output:

Consistent: 0
Compatible: 0

MATLAB thinks they are different, perhaps because sigma has messy units. Let's simplify it and try again:

sigma = simplify(sigma)

checkUnits(sigma == sconst.sigma)

Output:

0.000000056703744191844294539709967318892*(([Hz]*[kg])/([K]^4*[s]^2))

Consistent: 1
Compatible: 1

That's a match!

Background

Constants was built by scientists for scientists and engineers with a focus on ease of use, accuracy, and completeness.

The internationally recommended values of the basic constants and conversion factors of physics and chemistry are established by the Committee on Data of the International Science Council's (CODATA) Task Group on Fundamental Physical Constants. CODATA recommended values are adjusted in a four-year cycle and available on the National Institute of Standards and Technology (NIST) website. The 2022 CODATA recommended values were published on May 9, 2024 on the NIST website.

For each adjustment since 1998, NIST provides an ASCII file of all values. Constants.m is generated automatically by scraping the data from these ASCII files to avoid copy & paste errors and guarantee accuracy.

Frequently Asked Questions

A list of frequently asked questions is maintained separately from this README file.

List of Constants

Variable Constant Unit
malpha Alpha particle mass kg
malphainu Alpha particle mass in u u
Malpha Alpha particle molar mass kg mol-1
ralpha Alpha particle rms charge radius m
angstromstar Angstrom star m
mu Atomic mass constant kg
NA Avogadro constant mol-1
muB Bohr magneton J T-1
muBineVpertesla Bohr magneton in eV/T eV T-1
azero Bohr radius (atomic unit of length) m
k Boltzmann constant J K-1
kineVperkelvin Boltzmann constant in eV/K eV K-1
Zzero Characteristic impedance of vacuum ohm
re Classical electron radius m
lambdaC Compton wavelength m
Gzero Conductance quantum S
KJninety Conventional value of Josephson constant Hz V-1
Aninety Conventional value of ampere-90 A
Cninety Conventional value of coulomb-90 C
Fninety Conventional value of farad-90 F
Hninety Conventional value of henry-90 H
Omeganinety Conventional value of ohm-90 ohm
Vninety Conventional value of volt-90 V
RKninety Conventional value of von Klitzing constant ohm
Wninety Conventional value of watt-90 W
xuCu Copper x unit m
gd Deuteron g factor (unitless)
mud Deuteron magnetic moment J T-1
md Deuteron mass kg
mdinu Deuteron mass in u u
Md Deuteron molar mass kg mol-1
rd Deuteron rms charge radius m
ge Electron g factor (unitless)
gammae Electron gyromagnetic ratio s-1 T-1
gammaeinMHzpertesla Electron gyromagnetic ratio in MHz/T MHz T-1
mue Electron magnetic moment J T-1
ae Electron magnetic moment anomaly (unitless)
me Electron mass (atomic unit of mass, natural unit of mass) kg
meinu Electron mass in u u
Me Electron molar mass kg mol-1
eV Electron volt J
eVinhartree Electron volt-hartree relationship E_h
e Elementary charge (atomic unit of charge) C
F Faraday constant C mol-1
alpha Fine-structure constant (unitless)
cone First radiation constant W m^2
coneL First radiation constant for spectral radiance W m^2 sr-1
Eh Hartree energy (atomic unit of energy) J
EhineV Hartree energy in eV eV
gh Helion g factor (unitless)
muh Helion magnetic moment J T-1
mh Helion mass kg
mhinu Helion mass in u u
Mh Helion molar mass kg mol-1
sigmah Helion shielding shift (unitless)
DeltanuCs Hyperfine transition frequency of Cs-133 Hz
KJ Josephson constant Hz V-1
jouleineV Joule-electron volt relationship eV
jouleinhartree Joule-hartree relationship E_h
kginu Kilogram-atomic mass unit relationship u
a Lattice parameter of silicon m
dtwotwozero Lattice spacing of ideal Si (220) m
nzero Loschmidt constant (273.15 K, 100 kPa) m-3
nzeroSTPold Loschmidt constant (273.15 K, 101.325 kPa) m-3
Kcd Luminous efficacy lm W-1
Phizero Magnetic flux quantum Wb
R Molar gas constant J mol-1 K-1
Mu Molar mass constant kg mol-1
MtwelveC Molar mass of carbon-12 kg mol-1
Vm Molar volume of ideal gas (273.15 K, 100 kPa) m^3 mol-1
VmSTPold Molar volume of ideal gas (273.15 K, 101.325 kPa) m^3 mol-1
VmSi Molar volume of silicon m^3 mol-1
xuMo Molybdenum x unit m
lambdaCmu Muon Compton wavelength m
gmu Muon g factor (unitless)
mumu Muon magnetic moment J T-1
amu Muon magnetic moment anomaly (unitless)
mmu Muon mass kg
mmuinu Muon mass in u u
Mmu Muon molar mass kg mol-1
lambdaCn Neutron Compton wavelength m
gn Neutron g factor (unitless)
gamman Neutron gyromagnetic ratio s-1 T-1
gammaninMHzpertesla Neutron gyromagnetic ratio in MHz/T MHz T-1
mun Neutron magnetic moment J T-1
mn Neutron mass kg
mninu Neutron mass in u u
Mn Neutron molar mass kg mol-1
G Newtonian constant of gravitation m^3 kg-1 s-2
muN Nuclear magneton J T-1
muNineVpertesla Nuclear magneton in eV/T eV T-1
h Planck constant J Hz-1
hineVseconds Planck constant in eV/Hz eV Hz-1
lP Planck length m
mP Planck mass kg
TP Planck temperature K
tP Planck time s
lambdaCp Proton Compton wavelength m
gp Proton g factor (unitless)
gammap Proton gyromagnetic ratio s-1 T-1
gammapinMHzpertesla Proton gyromagnetic ratio in MHz/T MHz T-1
mup Proton magnetic moment J T-1
sigmapprime Proton magnetic shielding correction (unitless)
mp Proton mass kg
mpinu Proton mass in u u
Mp Proton molar mass kg mol-1
rp Proton rms charge radius m
lambdabarC Reduced Compton wavelength (natural unit of length) m
hbar Reduced Planck constant (atomic unit of action, natural unit of action) J s
hbarineVseconds Reduced Planck constant in eV s (natural unit of action in eV s) eV s
lambdabarCmu Reduced muon Compton wavelength m
lambdabarCn Reduced neutron Compton wavelength m
lambdabarCp Reduced proton Compton wavelength m
lambdabarCtau Reduced tau Compton wavelength m
Rinfinity Rydberg constant m-1
ctwo Second radiation constant m K
gammahprime Shielded helion gyromagnetic ratio s-1 T-1
gammahprimeinMHzpertesla Shielded helion gyromagnetic ratio in MHz/T MHz T-1
muhprime Shielded helion magnetic moment J T-1
gammapprime Shielded proton gyromagnetic ratio s-1 T-1
gammapprimeinMHzpertesla Shielded proton gyromagnetic ratio in MHz/T MHz T-1
mupprime Shielded proton magnetic moment J T-1
sigmadp Shielding difference of d and p in HD (unitless)
sigmatp Shielding difference of t and p in HT (unitless)
c Speed of light in vacuum (natural unit of velocity) m s-1
gzero Standard acceleration of gravity m s-2
atm Standard atmosphere Pa
ssp Standard-state pressure Pa
sigma Stefan-Boltzmann constant W m-2 K-4
lambdaCtau Tau Compton wavelength m
mtau Tau mass kg
mtauinu Tau mass in u u
Mtau Tau molar mass kg mol-1
sigmae Thomson cross section m^2
gt Triton g factor (unitless)
mut Triton magnetic moment J T-1
mt Triton mass kg
mtinu Triton mass in u u
Mt Triton molar mass kg mol-1
u Unified atomic mass unit kg
epsilonzero Vacuum electric permittivity F m-1
muzero Vacuum magnetic permeability N A-2
RK Von Klitzing constant ohm
sinsquaredthetaW Weak mixing angle (unitless)
bprime Wien frequency displacement law constant Hz K-1
b Wien wavelength displacement law constant m K

Cite As

Jorg Woehl (2024). Physical Constants (https://github.com/JorgWoehl/Constants/releases/tag/v1.2.2), GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2023b
Compatible with R2023b and later releases
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.2.2

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/v1.2.2

1.2.1

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/v1.2.1

1.2

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/v1.2

1.1.2

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/1.1.2

1.1.1

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/v1.1.1

1.1.0

See release notes for this release on GitHub: https://github.com/JorgWoehl/Constants/releases/tag/v1.1.0

1.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.