Mathematical Constants

You will notice that there may be minor discrepancies between some of the constants listed below and publicly available values. This is due to CalQlata's policy of publishing mathematically verifiable values (see reference publications below) in preference to those that are not supported.
For example;
Newton's gravitational constant 'G': This constant, which has remained elusive for more than three-hundred years, has at last been established to CalQlata's satisfaction; formula, value and units. On the other hand, the generally recognised value issued by Codata is not only unsupported, its units are incorrect.
CalQlata has therefore elected to publish the verified value.

Primary Constants

The following Table contains the primary constants from which all other constants may be derived; without exception.

NameSymbolValueUnits
electron massmₑ9.1093897E-31kilogram (kg)
electron chargee1.60217648753E-19Coulomb (C)
neutronic radius {© 01/10/18}Rₙ2.81793795383896E-15metre (m)
neutronic period {© 01/10/18}tₙ5.90596121302193E-23second (s)
static ratio {© 15/07/19}ξₘ1836.15115053207
dynamic ratio {© 15/07/19}ξᵥ1722.0458764934
universal constant {© 15/07/19}Σ3E-91m⁶ #

1 Joule = 1 kilogram.metre / second²
# can also have no units (see Further Reading below)

All constants - including electricity - can be explained using the above four dimensions;
mass (magnetic charge) [kg]; electrical charge [C]; distance [m]; time [s];
and they are all related via the static and/or dynamic ratios.

Temperature Constants

The following Table contains the constants used to define temperature.

NameSymbolFormulaValueUnits
heat transfer constant {© 15/07/19}Y³√[½.ξᵥ]9.51345439232503
Boltzmann's constantKB1.38065156E-23J/K
neutronic temperature {© 15/07/19}Ṯₙmₑ.c² / Y.KB6.23316124717178E+08K
Avogadro's numberNA0.001/mₙ6.02214129E+23/mol

Temperature is not a genuine property, it is simply a convenient method of measuring the heat (EME) emitted by the innermost proton-electron pairs in any atom.
Ṯ = X.PE / mₑ
where; 'PE' is the potential energy in the proton-electron pair
PE = mₑ.v²
where; 'v' is the orbital velocity of the electron.

Particle Constants

The following Table contains the constants that define the properties of the basic atomic particles; electrons and protons and neutrons.

NameSymbolFormulaValueUnits
ultimate densityρᵤmₑ.√[ξₘ/Σ]7.1266079635045E+16kg/m³
electron volumeVₑmₑ/ρᵤ1.27822236702922E-47
electron radiusrₑ³√[3.Vₑ/4π]1.45046059426276E-16m
electron constant of motionhₑRₙ.c8.4479654849081E-07m²/s
proton massmₚξₘ.mₑ1.67262163783E-27kg
proton volumeVₚmₚ/ρᵤ2.34700946985653E-44
proton radiusrₚ³√[3.Vₚ/4π]1.77613270336827E-15m
proton constant of motionhₚRₙ.c / √ξₘ1.97150515178454E-08m²/s
proton charge (operational) {© 15/07/19}e'e.ξᵥ.√[Ṯ/Ṯₙ]C
neutron mass {© 15/07/19}mₙmₚ+mₑ1.6735325768E-27kg
neutron volumeVₙmₙ/ρᵤ2.34828769222356E-44
neutron radiusrₙ³√[3.Vₙ/4π]1.77645508248591E-15m²/s

Principal Constants

The following Table contains general constants that have been developed by scientists of the past.

NameSymbolFormulaValueUnits
fine structure constantαe²/4π2.04272942122269E-39
velocity-of-light (EME)c2π.Rₙ/tₙ2.99792459E+08m/s
Rydberg radiusaₒRₙ.(ξᵥ/4π)²5.2917721067E-11m
Planck's constanth½.Rₙ.mₑ.c.ξᵥ6.62607174469163E-34kg.m²/s
Planck's constant (mod'd by Dirac)ħh/2π1.05457207144921E-34kg.m²/s
Planck's constant (mod'd by KDR) {© 15/07/19}h'½.Rₙ.mₑ.c²1.15353857232684E-28J.m
magnetic constant (fundamental) {© 15/07/19}μRₙ.mₑ/e²1E-07kg.m/C²
magnetic constantμₒ4π.μ1.25663706143592E-06kg.m/C²
Newton's gravitational constant {© 15/07/19}Gaₒ.c²/mᵤ6.67359232004334E-11m³ / s².kg
Coulomb's constant (electron) {© 15/07/19}kc².μ8.98755184732667E+09J.m/C²
Coulomb's constant (proton) {© 15/07/19}k'k/ξₘ²4.89477777726648E+06J.m/C²
coupling ratio {© 15/07/19}φG.mₑ.mₚ / k.e²4.40742111792334E-40
permittivity of a vacuum {© 15/07/19}εₒ1 / μₒ.c²8.85418775855161E-12C² / J.m
Rydberg's wave number {© 15/07/19}R1 / aₒ.ξᵥ1.09737269561359E+07/m
Rydberg's energy constant {© 15/07/19}RγRₙ/aₒ . ½.mₑ.c²2.17987197684936E-18J
heat transfer coefficient (velocity) {© 15/07/19}Xmₑ / Y.KB6.9353271647894E-09K.s²/m²
heat transfer coefficient (radial) {© 15/07/19}XRRₙ.Ṯₙ1.75646616508035E-06K.m
structural constant {© 15/07/19}Amₚ / Y.Rₙ.Ṯₙ3.55212512357916E-08kg / K.m²

Planck Constants

The following Table contains the atomic constants that have been derived from Planck's original constants; mass, length & time.

NameSymbolFormulaValueUnits
Planck's massm√[ħ.c / G]2.1765500017459E-08kg
Planck's lengthλ√[ħ.G / c³]1.61616952231127E-35m
Planck's timet√[ħ.G / c⁵]5.39096122598358E-44s
Planck's force {© 15/07/19}Fc⁴/G1.21038391820525E+44N
Planck's energy {© 15/07/19}E√[ħ.c⁵ / G]1.95618559889903E+09J
minimum orbital radius {© 15/07/19}RₒRₙ.ξᵥ²8.35643156381571E-09m
mean orbital radius {© 15/07/19}RₘRₙ.ξᵥ4.85261843362263E-12m
neutronic orbital radius {© 15/07/19}RₙG.mₚ / φ.c²2.81793795383896E-15m
minimum orbital velocity {© 15/07/19}vₒc.√[Rₙ/Rₒ]174090.866621084m/s
mean orbital velocity {© 15/07/19}vₘ√[c.vₒ]7224342.80705004m/s
neutronic orbital velocity {© 15/07/19}vₙc2.99792459E+08m/s
minimum temperature {© 15/07/19}ṮₒX.vₒ²210.193328535837K
mean temperature {© 15/07/19}ṮₘX.vₘ²361962.554671561K
neutronic temperature {© 15/07/19}ṮₙX.vₙ²623316124.717178K

Heat and Charge Constants

The following Table contains the heat and charge capacity constants.

NameSymbolFormulaValueUnits
relative charge capacity {© 15/07/19}RCe/mₑ1.75881869180545E+11C/kg
charge [emission] capacity {© 15/07/19}Rc√[G/k]8.61706029887134E-11C/kg
gas constant (ideal)RᵢKB.NA8.24992342031355J / K.mole
gas constantRₐRᵢ/RAMJ / K.kg
gas constantRRₐ.mJ/K
gas constantRₚcₚ.RAMJ / K.mol
heat capacity (constant temperature)cₜmₑ.KB & mₚ.KB15156356.3034305J / kg.K
heat capacity (constant volume)cᵥ1.5 . cₜ22558018.7907087J / kg.K
heat capacity (constant pressure)cₚ2.5 . cₜ37596697.9845145J / kg.K
heat capacity (constant temperature)Cₜmₑ.cₜ1.38065156E-23J/K
heat capacity (constant volume)Cᵥmₑ.cᵥ2.07097734E-23J/K
heat capacity (constant pressure)Cₚmₑ.cₚ3.4516289E-23J/K
charge capacity (constant temperature)Qₜe.qₜ1.38065156E-23J/K
charge capacity (constant volume)Qᵥe.qᵥ2.05489784024488E-23J/K
charge capacity (constant pressure)Qₚe.qₚ3.42482973374147E-23J/K
microstate (constant temperature)Nₜexp(2.5 . Ln(Ṯ) / Rₐ)
microstate (constant volume)Nᵥcᵥ/Rₐ & qᵥ/Rₐ
microstate (constant pressure)Nₚcₚ/Rₐ & qₚ/Rₐ
Faraday's ConstantFe.NA96485.3317942158C/mol

Various Constants

The following Table contains various miscellaneous constants.

NameSymbolFormulaValueUnits
natural logarithme2.71828182845905
golden ratioΦ1.61803398874989
circular ratioπC/D #3.14159265358979
gravitational accelerationg9.80663139027614m/s²

# C = circumference; D = Diameter

Ultimate Constants

The following two Tables demonstrate the relationship between all of the historic scientific constants if the Primary Constants are set to unity.

Primary Constants

The following Table contains the primary constants set to unity at the neutronic condition.

NameSymbolValueUnits
electron massmₑ1kilogram (kg)
electron chargee1Coulomb (C)
neutronic radius {© 01/10/18}Rₙ1metre (m)
neutronic period {© 01/10/18}tₙ1second (s)
static ratio {© 15/07/19}ξₘ1836.15115053207
dynamic ratio {© 15/07/19}ξᵥ1722.0458764934
universal constant {© 15/07/19}Σ5.99146043769661E-04m⁶ #

# can also have no units (see Further Reading below)

Principal Constants

Below are listed the formulas for the above Principal Constants

NameSymbolFormulaValueUnits
fine structure constantα1/4π0.0795774715459477
velocity-of-light (EME)c6.28318530717959m/s
Rydberg radiusaₒ(ξᵥ / 4π)²18778.8808461551m
Planck's constanthπ.ξᵥ5409.96667473626kg.m²/s
Planck's constant (mod'd by Dirac)ħ½.ξᵥ861.0229382467kg.m²/s
Planck's constant (mod'd by KDR) {© 15/07/19}h'2.π²19.7392088021787J.m
magnetic constant (fundamental) {© 15/07/19}μRₙ.mₑ/e²1kg.m/C²
magnetic constantμₒ12.5663706143592kg.m/C²
Newton's gravitational constant {© 15/07/19}G¼.ξᵥ² . √[∑/ξₘ]423.488456181401m³ / s².kg
Coulomb's constant {© 15/07/19}k(2π)²39.4784176043574J.m/C²
coupling ratio {© 15/07/19}φ(ξᵥ / 4π)² . √[∑.ξₘ]19696.5548074223
permittivity of a vacuum {© 15/07/19}εₒ1 / 2.(2π)³2.01572090207497E-03C² / J.m
Rydberg's wave number {© 15/07/19}R(4π)² / ξᵥ³3.09232816847610E-08/m
Rydberg's energy constant {© 15/07/19}Rγ2.(4π²/ξᵥ0.00105113872141216J
heat transfer coefficient (velocity) {© 15/07/19}XṮₙ / (2π)²1.57887818849249E+07K.s²/m²
heat transfer coefficient (radial) {© 15/07/19}XRṮₙ6.23316124717178E+08K.m

The above constants have been applied to the properties of all 92 elements and reproduce exactly the same results as those in the Tables above. Therefore, everything in the universe can legitimately be claimed to comprise two particles that are related by two ratios.

Further Reading

You will find further reading on this subject in various reference publications(70 & 73)