# 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.

 Name Symbol Value Units electron mass mₑ 9.1093897E-31 kilogram (kg) electron charge e 1.60217648753E-19 Coulomb (C) neutronic radius {© 01/10/18} Rₙ 2.81793795383896E-15 metre (m) neutronic period {© 01/10/18} tₙ 5.90596121302193E-23 second (s) static ratio {© 15/07/19} ξₘ 1836.15115053207 dynamic ratio {© 15/07/19} ξᵥ 1722.0458764934 universal constant {© 15/07/19} Σ 3E-91 m⁶ #

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.

 Name Symbol Formula Value Units heat transfer constant {© 15/07/19} Y ³√[½.ξᵥ] 9.51345439232503 Boltzmann's constant KB 1.38065156E-23 J/K neutronic temperature {© 15/07/19} Ṯₙ mₑ.c² / Y.KB 6.23316124717178E+08 K Avogadro's number NA 0.001/mₙ 6.02214129E+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.

 Name Symbol Formula Value Units ultimate density ρᵤ mₑ.√[ξₘ/Σ] 7.1266079635045E+16 kg/m³ electron volume Vₑ mₑ/ρᵤ 1.27822236702922E-47 m³ electron radius rₑ ³√[3.Vₑ/4π] 1.45046059426276E-16 m electron constant of motion hₑ Rₙ.c 8.4479654849081E-07 m²/s proton mass mₚ ξₘ.mₑ 1.67262163783E-27 kg proton volume Vₚ mₚ/ρᵤ 2.34700946985653E-44 m³ proton radius rₚ ³√[3.Vₚ/4π] 1.77613270336827E-15 m proton constant of motion hₚ Rₙ.c / √ξₘ 1.97150515178454E-08 m²/s proton charge (operational) {© 15/07/19} e' e.ξᵥ.√[Ṯ/Ṯₙ] C neutron mass {© 15/07/19} mₙ mₚ+mₑ 1.6735325768E-27 kg neutron volume Vₙ mₙ/ρᵤ 2.34828769222356E-44 m³ neutron radius rₙ ³√[3.Vₙ/4π] 1.77645508248591E-15 m²/s

## Principal Constants

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

## Planck Constants

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

## Heat and Charge Constants

The following Table contains the heat and charge capacity constants.

 Name Symbol Formula Value Units relative charge capacity {© 15/07/19} RC e/mₑ 1.75881869180545E+11 C/kg charge [emission] capacity {© 15/07/19} Rc √[G/k] 8.61706029887134E-11 C/kg gas constant (ideal) Rᵢ KB.NA 8.24992342031355 J / K.mole gas constant Rₐ Rᵢ/RAM J / K.kg gas constant R Rₐ.m J/K gas constant Rₚ cₚ.RAM J / K.mol heat capacity (constant temperature) cₜ mₑ.KB & mₚ.KB 15156356.3034305 J / kg.K heat capacity (constant volume) cᵥ 1.5 . cₜ 22558018.7907087 J / kg.K heat capacity (constant pressure) cₚ 2.5 . cₜ 37596697.9845145 J / kg.K heat capacity (constant temperature) Cₜ mₑ.cₜ 1.38065156E-23 J/K heat capacity (constant volume) Cᵥ mₑ.cᵥ 2.07097734E-23 J/K heat capacity (constant pressure) Cₚ mₑ.cₚ 3.4516289E-23 J/K charge capacity (constant temperature) Qₜ e.qₜ 1.38065156E-23 J/K charge capacity (constant volume) Qᵥ e.qᵥ 2.05489784024488E-23 J/K charge capacity (constant pressure) Qₚ e.qₚ 3.42482973374147E-23 J/K microstate (constant temperature) Nₜ exp(2.5 . Ln(Ṯ) / Rₐ) microstate (constant volume) Nᵥ cᵥ/Rₐ & qᵥ/Rₐ microstate (constant pressure) Nₚ cₚ/Rₐ & qₚ/Rₐ Faraday's Constant F e.NA 96485.3317942158 C/mol

## Various Constants

The following Table contains various miscellaneous constants.

 Name Symbol Formula Value Units natural logarithm e 2.71828182845905 golden ratio Φ 1.61803398874989 circular ratio π C/D # 3.14159265358979 gravitational acceleration g 9.80663139027614 m/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.

 Name Symbol Value Units electron mass mₑ 1 kilogram (kg) electron charge e 1 Coulomb (C) neutronic radius {© 01/10/18} Rₙ 1 metre (m) neutronic period {© 01/10/18} tₙ 1 second (s) static ratio {© 15/07/19} ξₘ 1836.15115053207 dynamic ratio {© 15/07/19} ξᵥ 1722.0458764934 universal constant {© 15/07/19} Σ 5.99146043769661E-04 m⁶ #

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

### Principal Constants

Below are listed the formulas for the above Principal Constants