The UnitSystem

Metric = MetricSystem(milli,𝟐*τ/𝟏𝟎^7)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Standard Metric system based on exact molarmass and vacuumpermeability.

julia> boltzmann(Metric) # J⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2⁴5³ = 1.38064899953(43) × 10⁻²³ [J⋅K⁻¹] Metric

julia> planckreduced(Metric) # J⋅s⋅rad⁻¹
𝘩⋅τ⁻¹ = 1.0545718176461565×10⁻³⁴ [J⋅s] Metric

julia> lightspeed(Metric) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] Metric

julia> vacuumpermeability(Metric) # H⋅m⁻¹
τ⋅2⁻⁶5⁻⁷ = 1.2566370614359173×10⁻⁶ [H⋅m⁻¹] Metric

julia> electronmass(Metric) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg] Metric

julia> molarmass(Metric) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] Metric

julia> luminousefficacy(Metric) # lm⋅W⁻¹
Kcd = 683.01969009009 [lm⋅W⁻¹] Metric

SI2019 = MetricSystem(Mᵤ,μ₀)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Systeme International d'Unites based on approximate molarmass and vacuumpermeability.

julia> boltzmann(SI2019) # J⋅K⁻¹
kB = 1.380649×10⁻²³ [J⋅K⁻¹] SI2019

julia> planckreduced(SI2019) # J⋅s⋅rad⁻¹
𝘩⋅τ⁻¹ = 1.0545718176461565×10⁻³⁴ [J⋅s] SI2019

julia> lightspeed(SI2019) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] SI2019

julia> vacuumpermeability(SI2019) # H⋅m⁻¹
𝘩⋅𝘤⁻¹𝘦⁻²α⋅2 = 1.25663706212(19) × 10⁻⁶ [H⋅m⁻¹] SI2019

julia> electronmass(SI2019) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg] SI2019

julia> molarmass(SI2019) # kg⋅mol⁻¹
NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2 = 0.00099999999966(31) [kg⋅mol⁻¹] SI2019

julia> luminousefficacy(SI2019) # lm⋅W⁻¹
Kcd = 683.01969009009 [lm⋅W⁻¹] SI2019

SI1976 = MetricSystem(milli,𝟐*τ/𝟏𝟎^7,8.31432)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Reference UnitSystem with universal gas constant of 8.31432 from 1976 standard atmosphere.

julia> boltzmann(SI1976) # J⋅K⁻¹
𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2⁴5³⋅8.31432 = 1.38062531722(43) × 10⁻²³ [kg⋅m²s⁻²K⁻¹] SI1976

julia> planckreduced(SI1976) # J⋅s⋅rad⁻¹
𝘩⋅τ⁻¹ = 1.0545718176461565×10⁻³⁴ [kg⋅m²s⁻¹] SI1976

julia> lightspeed(SI1976) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] SI1976

julia> vacuumpermeability(SI1976) # H⋅m⁻¹
τ⋅2⁻⁶5⁻⁷ = 1.2566370614359173×10⁻⁶ [kg⋅m⋅C⁻²] SI1976

julia> electronmass(SI1976) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg] SI1976

julia> molarmass(SI1976) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] SI1976

julia> luminousefficacy(SI1976) # lm⋅W⁻¹
Kcd = 683.01969009009 [kg⁻¹m⁻²s³lm] SI1976

Engineering = MetricSystem(milli,𝟐*τ/𝟏𝟎^7,Rᵤ,g₀)
F=F, M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=A, R=𝟙, C=𝟙

Standard Metric Engineering system based on kilogram and kilopond (kilogram-force) units.

julia> boltzmann(Engineering) # kgf⋅m⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹2⁴5³ = 1.40787016925(43) × 10⁻²⁴ [kgf⋅m⋅K⁻¹] Engineering

julia> planckreduced(Engineering) # kgf⋅m⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹τ⁻¹ = 1.0753639802033891×10⁻³⁵ [kgf⋅m⋅s⋅rad⁻¹] Engineering

julia> lightspeed(Engineering) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] Engineering

julia> vacuumpermeability(Engineering) # kgf⋅s²⋅C⁻²
g₀⁻¹τ⋅2⁻⁶5⁻⁷ = 1.2814131853751459×10⁻⁷ [kgf⋅s²C⁻²] Engineering

julia> electronmass(Engineering) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg] Engineering

julia> molarmass(Engineering) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] Engineering

julia> luminousefficacy(Engineering) # lm⋅s⋅m⁻¹⋅kgf⁻¹
Kcd⋅g₀ = 6698.135043821981 [kgf⁻¹m⁻¹s⋅lm] Engineering

julia> gravity(Engineering) # kg⋅m⋅kgf⁻¹⋅s⁻²
g₀ = 9.80665 [kgf⁻¹kg⋅m⋅s⁻²] Engineering

Conventional = ConventionalSystem(RK1990,KJ2014)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Conventional electronic UnitSystem with 1990 tuned josephson and klitzing constants.

julia> josephson(Conventional) # Hz⋅V⁻¹
KJ90 = 4.835979×10¹⁴ [Hz⋅V⁻¹] Conventional

julia> klitzing(Conventional) # Ω
RK90 = 25812.807 [Ω] Conventional

julia> boltzmann(Conventional) # J⋅K⁻¹
kB⋅NA⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹RK90⁻¹KJ90⁻²2⁶5³ = 1.38064872956(43) × 10⁻²³ [J⋅K⁻¹] Conventional

julia> planckreduced(Conventional) # J⋅s⋅rad⁻¹
RK90⁻¹KJ90⁻²τ⁻¹2² = 1.0545716114388567×10⁻³⁴ [J⋅s] Conventional

julia> lightspeed(Conventional) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] Conventional

julia> vacuumpermeability(Conventional) # H⋅m⁻¹
𝘤⁻¹α⋅RK90⋅2 = 1.25663703976(19) × 10⁻⁶ [H⋅m⁻¹] Conventional

julia> electronmass(Conventional) # kg
𝘤⁻¹R∞⋅α⁻²RK90⁻¹KJ90⁻²2³ = 9.1093819203(28) × 10⁻³¹ [kg] Conventional

julia> molarmass(Conventional) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] Conventional

julia> luminousefficacy(Conventional) # lm⋅W⁻¹
𝘩⋅Kcd⋅RK90⋅KJ90²2⁻² = 683.0198236454071 [lm⋅W⁻¹] Conventional

CODATA = ConventionalSystem(RK2014,KJ2014,Rᵤ2014)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Reference UnitSystem based on Committee on Data of the International Science Council.

julia> josephson(CODATA) # Hz⋅V⁻¹
KJ = 4.835978525(30) × 10¹⁴ [Hz⋅V⁻¹] CODATA

julia> klitzing(CODATA) # Ω
RK = 25812.8074555(59) [Ω] CODATA

julia> boltzmann(CODATA) # J⋅K⁻¹
𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹RK⁻¹KJ⁻²Rᵤ2014⋅2⁶5³ = 1.38064851(80) × 10⁻²³ [J⋅K⁻¹] CODATA

julia> planckreduced(CODATA) # J⋅s⋅rad⁻¹
RK⁻¹KJ⁻²τ⁻¹2² = 1.054571800(13) × 10⁻³⁴ [J⋅s] CODATA

julia> lightspeed(CODATA) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] CODATA

julia> vacuumpermeability(CODATA) # H⋅m⁻¹
𝘤⁻¹α⋅RK⋅2 = 1.25663706194(35) × 10⁻⁶ [H⋅m⁻¹] CODATA

julia> electronmass(CODATA) # kg
𝘤⁻¹R∞⋅α⁻²RK⁻¹KJ⁻²2³ = 9.10938355(11) × 10⁻³¹ [kg] CODATA

julia> molarmass(CODATA) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] CODATA

julia> luminousefficacy(CODATA) # lm⋅W⁻¹
𝘩⋅Kcd⋅RK⋅KJ²2⁻² = 683.0197015(85) [lm⋅W⁻¹] CODATA

International = ElectricSystem(Metric,Ωᵢₜ = 1.000495,Vᵢₜ = 1.00033)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

International UnitSystem with United States measurements of Ωᵢₜ and Vᵢₜ.

julia> resistance(International,Metric) # Ω⋅Ω⁻¹
Ωᵢₜ = 1.000495 [kg⋅m⋅s⁻²C⁻²]/[kg⋅m⋅s⁻²C⁻²] International -> Metric

julia> electricpotential(International,Metric) # V⋅V⁻¹
Vᵢₜ = 1.00033 [V⋅m⁻¹]/[V⋅m⁻¹] International -> Metric

julia> boltzmann(International) # J⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹Ωᵢₜ⋅Vᵢₜ⁻²2⁴5³ = 1.38042119247(42) × 10⁻²³ [J⋅K⁻¹] International

julia> planckreduced(International) # J⋅s⋅rad⁻¹
𝘩⋅Ωᵢₜ⋅Vᵢₜ⁻²τ⁻¹ = 1.0543978133151816×10⁻³⁴ [J⋅s] International

julia> lightspeed(International) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] International

julia> vacuumpermeability(International) # H⋅m⁻¹
Ωᵢₜ⁻¹τ⋅2⁻⁶5⁻⁷ = 1.2560153338456637×10⁻⁶ [H⋅m⁻¹] International

julia> electronmass(International) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²Ωᵢₜ⋅Vᵢₜ⁻²2 = 9.1078806534(28) × 10⁻³¹ [kg] International

julia> molarmass(International) # kg⋅mol⁻¹
Ωᵢₜ⋅Vᵢₜ⁻²2⁻³5⁻³ = 0.0009998350000179567 [kg⋅mol⁻¹] International

julia> luminousefficacy(International) # lm⋅W⁻¹
Kcd⋅Ωᵢₜ⁻¹Vᵢₜ² = 683.1324069249656 [lm⋅W⁻¹] International

InternationalMean = ElectricSystem(Metric,1.00049,1.00034)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

International UnitSystem with mean measurements of Ωᵢₜ and Vᵢₜ.

julia> resistance(InternationalMean,Metric) # Ω⋅Ω⁻¹
1.00049 = 1.00049 [kg⋅m⋅s⁻²C⁻²]/[kg⋅m⋅s⁻²C⁻²] InternationalMean -> Metric

julia> electricpotential(InternationalMean,Metric) # V⋅V⁻¹
1.00034 = 1.00034 [V⋅m⁻¹]/[V⋅m⁻¹] InternationalMean -> Metric

julia> boltzmann(InternationalMean) # J⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2⁴5³/1.0001900224889804 = 1.38038669501(42) × 10⁻²³ [J⋅K⁻¹] InternationalMean

julia> planckreduced(InternationalMean) # J⋅s⋅rad⁻¹
𝘩⋅τ⁻¹/1.0001900224889804 = 1.0543714633563797×10⁻³⁴ [J⋅s] InternationalMean

julia> lightspeed(InternationalMean) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] InternationalMean

julia> vacuumpermeability(InternationalMean) # H⋅m⁻¹
τ⋅2⁻⁶5⁻⁷/1.00049 = 1.2560216108466022×10⁻⁶ [H⋅m⁻¹] InternationalMean

julia> electronmass(InternationalMean) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2/1.0001900224889804 = 9.1076530427(28) × 10⁻³¹ [kg] InternationalMean

julia> molarmass(InternationalMean) # kg⋅mol⁻¹
2⁻³5⁻³/1.0001900224889804 = 0.0009998100136127059 [kg⋅mol⁻¹] InternationalMean

julia> luminousefficacy(International) # lm⋅W⁻¹
Kcd⋅Ωᵢₜ⁻¹Vᵢₜ² = 683.1324069249656 [lm⋅W⁻¹] International

EMU = GaussSystem(Metric,𝟏,𝟐*τ)
F=MLT⁻², M=M, L=L, T=T, Q=M¹ᐟ²L¹ᐟ², Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Centimetre-gram-second UnitSystem variant based on EMU (non-rationalized).

julia> boltzmann(EMU) # erg⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2¹¹5¹⁰ = 1.38064899953(43) × 10⁻¹⁶ [erg⋅K⁻¹] EMU

julia> planckreduced(EMU) # erg⋅s⋅rad⁻¹
𝘩⋅τ⁻¹2⁷5⁷ = 1.0545718176461565×10⁻²⁷ [erg⋅s] EMU

julia> lightspeed(EMU) # cm⋅s⁻¹
𝘤⋅2²5² = 2.99792458×10¹⁰ [cm⋅s⁻¹] EMU

julia> vacuumpermeability(EMU) # abH⋅cm⁻¹
𝟏 = 1.0 [𝟙] EMU

julia> electronmass(EMU) # g
𝘩⋅𝘤⁻¹R∞⋅α⁻²2⁴5³ = 9.1093837016(28) × 10⁻²⁸ [g] EMU

julia> molarmass(EMU) # g⋅mol⁻¹
𝟏 = 1.0 [g⋅mol⁻¹] EMU

julia> luminousefficacy(EMU) # lm⋅s⋅erg⁻¹
Kcd⋅2⁻⁷5⁻⁷ = 6.830196900900899×10⁻⁵ [lm⋅s⋅erg⁻¹] EMU

julia> rationalization(EMU)
τ⋅2 = 12.566370614359172 [𝟙] EMU

ESU = GaussSystem(Metric,(𝟏𝟎*𝘤)^-2,𝟐*τ)
F=MLT⁻², M=M, L=L, T=T, Q=M¹ᐟ²L³ᐟ²T⁻¹, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Centimetre-gram-second UnitSystem variant based on ESU (non-rationalized).

julia> boltzmann(ESU) # erg⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2¹¹5¹⁰ = 1.38064899953(43) × 10⁻¹⁶ [erg⋅K⁻¹] ESU

julia> planckreduced(ESU) # erg⋅s⋅rad⁻¹
𝘩⋅τ⁻¹2⁷5⁷ = 1.0545718176461565×10⁻²⁷ [erg⋅s] ESU

julia> lightspeed(ESU) # cm⋅s⁻¹
𝘤⋅2²5² = 2.99792458×10¹⁰ [cm⋅s⁻¹] ESU

julia> vacuumpermeability(ESU) # statH⋅cm⁻¹
𝘤⁻²2⁻⁴5⁻⁴ = 1.1126500560536184×10⁻²¹ [cm⁻²s²] ESU

julia> electronmass(ESU) # g
𝘩⋅𝘤⁻¹R∞⋅α⁻²2⁴5³ = 9.1093837016(28) × 10⁻²⁸ [g] ESU

julia> molarmass(ESU) # g⋅mol⁻¹
𝟏 = 1.0 [g⋅mol⁻¹] ESU

julia> luminousefficacy(ESU) # lm⋅s⋅erg⁻¹
Kcd⋅2⁻⁷5⁻⁷ = 6.830196900900899×10⁻⁵ [lm⋅s⋅erg⁻¹] ESU

julia> rationalization(ESU)
τ⋅2 = 12.566370614359172 [𝟙] ESU

Gauss = GaussSystem(Metric,𝟏,𝟐*τ,𝟏𝟎^-2/𝘤)
F=MLT⁻², M=M, L=L, T=T, Q=M¹ᐟ²L³ᐟ²T⁻¹, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=LT⁻¹

Centimetre-gram-second UnitSystem variant CGS (Gauss-Lorentz, non-rationalized).

julia> boltzmann(Gauss) # erg⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2¹¹5¹⁰ = 1.38064899953(43) × 10⁻¹⁶ [erg⋅K⁻¹] Gauss

julia> planckreduced(Gauss) # erg⋅s⋅rad⁻¹
𝘩⋅τ⁻¹2⁷5⁷ = 1.0545718176461565×10⁻²⁷ [erg⋅s] Gauss

julia> lightspeed(Gauss) # cm⋅s⁻¹
𝘤⋅2²5² = 2.99792458×10¹⁰ [cm⋅s⁻¹] Gauss

julia> vacuumpermeability(Gauss) # statH⋅cm⁻¹
𝟏 = 1.0 [𝟙] Gauss

julia> electronmass(Gauss) # g
𝘩⋅𝘤⁻¹R∞⋅α⁻²2⁴5³ = 9.1093837016(28) × 10⁻²⁸ [g] Gauss

julia> molarmass(Gauss) # g⋅mol⁻¹
𝟏 = 1.0 [g⋅mol⁻¹] Gauss

julia> luminousefficacy(Gauss) # lm⋅s⋅erg⁻¹
Kcd⋅2⁻⁷5⁻⁷ = 6.830196900900899×10⁻⁵ [lm⋅s⋅erg⁻¹] Gauss

julia> rationalization(Gauss)
τ⋅2 = 12.566370614359172 [𝟙] Gauss

julia> lorentz(Gauss)
𝘤⁻¹2⁻²5⁻² = 3.335640951981521×10⁻¹¹ [cm⁻¹s] Gauss

LorentzHeaviside = GaussSystem(Metric,𝟏,𝟏,centi/𝘤)
F=MLT⁻², M=M, L=L, T=T, Q=M¹ᐟ²L³ᐟ²T⁻¹, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=LT⁻¹

Centimetre-gram-second UnitSystem variant HLU (Heaviside-Lorentz, rationalized).

julia> boltzmann(LorentzHeaviside) # erg⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2¹¹5¹⁰ = 1.38064899953(43) × 10⁻¹⁶ [erg⋅K⁻¹] LorentzHeaviside

julia> planckreduced(LorentzHeaviside) # erg⋅s⋅rad⁻¹
𝘩⋅τ⁻¹2⁷5⁷ = 1.0545718176461565×10⁻²⁷ [erg⋅s] LorentzHeaviside

julia> lightspeed(LorentzHeaviside) # cm⋅s⁻¹
𝘤⋅2²5² = 2.99792458×10¹⁰ [cm⋅s⁻¹] LorentzHeaviside

julia> vacuumpermeability(HLU) # hlH⋅cm⁻¹
𝟏 = 1.0 [𝟙] LorentzHeaviside

julia> electronmass(LorentzHeaviside) # g
𝘩⋅𝘤⁻¹R∞⋅α⁻²2⁴5³ = 9.1093837016(28) × 10⁻²⁸ [g] LorentzHeaviside

julia> molarmass(LorentzHeaviside) # g⋅mol⁻¹
𝟏 = 1.0 [g⋅mol⁻¹] LorentzHeaviside

julia> luminousefficacy(LorentzHeaviside) # lm⋅s⋅erg⁻¹
Kcd⋅2⁻⁷5⁻⁷ = 6.830196900900899×10⁻⁵ [lm⋅s⋅erg⁻¹] LorentzHeaviside

julia> rationalization(LorentzHeaviside)
𝟏 = 1.0 [𝟙] LorentzHeaviside

julia> lorentz(LorentzHeaviside)
𝘤⁻¹2⁻²5⁻² = 3.335640951981521×10⁻¹¹ [cm⁻¹s] LorentzHeaviside

Gravitational = EntropySystem(Metric,𝟏,𝟏,g₀)
F=F, M=FL⁻¹T², L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Standard Gravitational system based on hyl and kilopond units.

julia> boltzmann(Gravitational) # kgf⋅m⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹2⁴5³ = 1.40787016925(43) × 10⁻²⁴ [kgf⋅m⋅K⁻¹] Gravitational

julia> planckreduced(Gravitational) # kgf⋅m⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹τ⁻¹ = 1.0753639802033891×10⁻³⁵ [kgf⋅m⋅s] Gravitational

julia> lightspeed(Gravitational) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] Gravitational

julia> vacuumpermeability(Gravitational) # H⋅m⁻¹
g₀⁻¹τ⋅2⁻⁶5⁻⁷ = 1.2814131853751459×10⁻⁷ [kgf⋅s²C⁻²] Gravitational

julia> electronmass(Gravitational) # hyl
𝘩⋅𝘤⁻¹R∞⋅α⁻²g₀⁻¹2 = 9.2889862507(28) × 10⁻³² [hyl] Gravitational

julia> molarmass(Gravitational) # hyl⋅mol⁻¹
g₀⁻¹2⁻³5⁻³ = 0.00010197162129779284 [hyl⋅mol⁻¹] Gravitational

julia> luminousefficacy(Gravitational) # lm⋅s⋅m⁻¹⋅kgf⁻¹
Kcd⋅g₀ = 6698.135043821981 [kgf⁻¹m⁻¹s⋅lm] Gravitational

MTS = EntropySystem(SI2019,𝟏,𝟏,kilo)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Metre-tonne-second UnitSystem variant of Metric system.

julia> boltzmann(MTS) # kJ⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2 = 1.38064899953(43) × 10⁻²⁶ [t⋅m²s⁻²K⁻¹] MTS

julia> planckreduced(MTS) # kJ⋅s⋅rad⁻¹
𝘩⋅τ⁻¹2⁻³5⁻³ = 1.0545718176461566×10⁻³⁷ [t⋅m²s⁻¹] MTS

julia> lightspeed(MTS) # m⋅s⁻¹
𝘤 = 2.99792458×10⁸ [m⋅s⁻¹] MTS

julia> vacuumpermeability(MTS) # kH⋅m⁻¹
τ⋅2⁻⁹5⁻¹⁰ = 1.2566370614359174×10⁻⁹ [t⋅m⋅C⁻²] MTS

julia> electronmass(MTS) # t
𝘩⋅𝘤⁻¹R∞⋅α⁻²2⁻²5⁻³ = 9.1093837016(28) × 10⁻³⁴ [t] MTS

julia> molarmass(MTS) # t⋅mol⁻¹
2⁻⁶5⁻⁶ = 1.0×10⁻⁶ [t⋅mol⁻¹] MTS

julia> luminousefficacy(MTS) # lm⋅kW⁻¹
Kcd⋅2³5³ = 683019.6900900899 [t⁻¹m⁻²s³lm] MTS

KKH = EntropySystem(Metric,HOUR,kilo,𝟏)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Kilometer-kilogram-hour UnitSystem variant of Metric system.

julia> boltzmann(KKH) # kg⋅km²⋅h⁻²⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹2⁶3⁴5 = 1.78932110338(55) × 10⁻²² [kg⋅km²h⁻²K⁻¹] KKH

julia> planckreduced(KKH) # kg⋅km²⋅h⁻¹
𝘩⋅τ⁻¹2⁻²3²5⁻⁴ = 3.7964585435261634×10⁻³⁷ [kg⋅km²h⁻¹] KKH

julia> lightspeed(KKH) # km⋅hr⁻¹
𝘤⋅2⋅3²5⁻¹ = 1.0792528488×10⁹ [km⋅h⁻¹] KKH

julia> vacuumpermeability(KKH) # kg⋅km⋅C⁻²
τ⋅2⁻⁹5⁻¹⁰ = 1.2566370614359174×10⁻⁹ [kg⋅km⋅C⁻²] KKH

julia> electronmass(KKH) # kg
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg] KKH

julia> molarmass(KKH) # kg⋅mol⁻¹
2⁻³5⁻³ = 0.001 [kg⋅mol⁻¹] KKH

julia> luminousefficacy(KKH) # lm⋅h³⋅kg⁻¹⋅km⁻²
Kcd⋅2⁻⁶3⁻⁶ = 0.014639482383618183 [kg⁻¹km⁻²h³lm] KKH

MPH = EntropySystem(FPS,HOUR,mi,𝟏)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Mile-pound-hour specification based on FPS absolute UnitSystem.

julia> boltzmann(MPH) # lbf⋅mi²⋅hr⁻²⋅F⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹ft⁻²lb⁻¹2²5⁶11⁻² = 8.4615956484(26) × 10⁻²³ [lb⋅mi²h⁻²°R⁻¹] MPH

julia> planckreduced(MPH) # lbf⋅mi²⋅hr⁻¹⋅rad⁻¹
𝘩⋅ft⁻²lb⁻¹τ⁻¹2⁻⁶11⁻² = 3.2315817800735083×10⁻³⁷ [lb⋅mi²h⁻¹] MPH

julia> lightspeed(MPH) # mi⋅hr⁻¹
𝘤⋅ft⁻¹2⁻¹3⋅5⋅11⁻¹ = 6.706166293843951×10⁸ [mi⋅h⁻¹] MPH

julia> vacuumpermeability(MPH) # lbm⋅mi⋅C⁻²
ft⁻¹lb⁻¹τ⋅2⁻¹¹3⁻¹5⁻⁸11⁻¹ = 1.7214532710813804×10⁻⁹ [lb⋅mi⋅C⁻²] MPH

julia> electronmass(MPH) # lbm
𝘩⋅𝘤⁻¹R∞⋅α⁻²lb⁻¹2 = 2.00827533796(62) × 10⁻³⁰ [lb] MPH

julia> molarmass(MPH) # lbm⋅lb-mol⁻¹
𝟏 = 1.0 [lb⋅lb-mol⁻¹] MPH

julia> luminousefficacy(MPH) # lm⋅h³⋅lb⁻¹⋅mi⁻²
Kcd⋅ft²lb⋅2⁻²3⁻⁴5⁻⁴11² = 0.017198446999173198 [lb⁻¹mi⁻²h³lm] MPH

Nautical = EntropySystem(Metric,HOUR,nm,em^3,𝟏,τ*𝟑^3/𝟐^10/𝟓^12,milli)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Nautical miles, kilo-earthgram, hour specification based on Meridian definition.

julia> greatcircle(Nautical) # nm
2⁵3³5² = 21600.0 [nm] Nautical

julia> boltzmann(Nautical) # keg⋅nm²⋅hr⁻²⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁵ᐟ²GME⁻⁵ᐟ²τ⁻⁵2⁴⁹3¹⁰5³² = 5.180046618(26) × 10⁻²³ [keg⋅nm²h⁻²K⁻¹] Nautical

julia> planckreduced(Nautical) # keg⋅nm²⋅hr⁻¹⋅rad⁻¹
𝘩⋅g₀⁵ᐟ²GME⁻⁵ᐟ²τ⁻⁶2⁴¹3⁸5²⁷ = 1.0990666907(55) × 10⁻³⁷ [keg⋅nm²h⁻¹] Nautical

julia> lightspeed(Nautical) # nm⋅hr⁻¹
𝘤⋅g₀¹ᐟ²GME⁻¹ᐟ²τ⁻¹2⁹3⁵5⁴ = 5.8195383759(58) × 10⁸ [nm⋅h⁻¹] Nautical

julia> vacuumpermeability(Nautical) # keg⋅nm⋅eC⁻²
τ⋅2⁻¹⁰3³5⁻¹² = 6.785840131753953×10⁻¹⁰ [keg⋅nm⋅eC⁻²] Nautical

julia> electronmass(Nautical) # keg
𝘩⋅𝘤⁻¹R∞⋅α⁻²g₀³ᐟ²GME⁻³ᐟ²τ⁻³2²⁸5²¹ = 9.069925385(27) × 10⁻³¹ [keg] Nautical

julia> molarmass(Nautical) # keg⋅eg-mol⁻¹
2⁻³5⁻³ = 0.001 [keg⋅eg-mol⁻¹] Nautical

julia> luminousefficacy(Nautical) # lm⋅h³⋅keg⁻¹⋅nm⁻²
Kcd⋅g₀⁻⁵ᐟ²GME⁵ᐟ²τ⁵2⁻⁴⁹3⁻¹²5⁻³¹ = 0.05056853095(25) [keg⁻¹nm⁻²h³lm] Nautical

Meridian = EntropySystem(Metric,𝟏,em,em^3,𝟏,τ/𝟐^6/𝟓^7,milli)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Modern ideal Meridian system defined by France's original earthmeter definition.

julia> greatcircle(Meridian) # em
2⁹5⁷ = 4.0×10⁷ [em] Meridian

julia> boltzmann(Meridian) # eJ⋅K⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁵ᐟ²GME⁻⁵ᐟ²τ⁻⁵2⁴⁹5³⁸ = 1.3706960050(69) × 10⁻²³ [eJ⋅K⁻¹] Meridian

julia> planckreduced(Meridian) # eJ⋅s⋅rad⁻¹
𝘩⋅g₀⁵ᐟ²GME⁻⁵ᐟ²τ⁻⁶2⁴⁵5³⁵ = 1.0469694890(53) × 10⁻³⁴ [eJ⋅s] Meridian

julia> lightspeed(Meridian) # em⋅s⁻¹
𝘤⋅g₀¹ᐟ²GME⁻¹ᐟ²τ⁻¹2⁹5⁷ = 2.9935896996(3) × 10⁸ [em⋅s⁻¹] Meridian

julia> vacuumpermeability(Meridian) # kegf⋅s²⋅eC⁻²
τ⋅2⁻⁶5⁻⁷ = 1.2566370614359173×10⁻⁶ [eH⋅em⁻¹] Meridian

julia> electronmass(Meridian) # keg
𝘩⋅𝘤⁻¹R∞⋅α⁻²g₀³ᐟ²GME⁻³ᐟ²τ⁻³2²⁸5²¹ = 9.069925385(27) × 10⁻³¹ [keg] Meridian

julia> molarmass(Meridian) # keg⋅eg-mol⁻¹
2⁻³5⁻³ = 0.001 [keg⋅eg-mol⁻¹] Meridian

julia> luminousefficacy(Meridian) # lm⋅W⁻¹
Kcd⋅g₀⁻⁵ᐟ²GME⁵ᐟ²τ⁵2⁻⁴⁵5⁻³⁵ = 687.9792808(35) [lm⋅eW⁻¹] Meridian

FPS = RankineSystem(Metric,ft,lb)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Absolute English UnitSystem based on the foot, pound, second, and poundal.

julia> boltzmann(FPS) # ft⋅pdl⋅°R⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹ft⁻²lb⁻¹2⁴3⁻²5⁴ = 1.82018324169(56) × 10⁻²² [lb⋅ft²s⁻²°R⁻¹] FPS

julia> planckreduced(FPS) # ft⋅pdl⋅s⋅rad⁻¹
𝘩⋅ft⁻²lb⁻¹τ⁻¹ = 2.5025369304889247×10⁻³³ [lb⋅ft²s⁻¹] FPS

julia> lightspeed(FPS) # ft⋅s⁻¹
𝘤⋅ft⁻¹ = 9.835710564304461×10⁸ [ft⋅s⁻¹] FPS

julia> vacuumpermeability(FPS) # lb⋅ft⋅C⁻²
ft⁻¹lb⁻¹τ⋅2⁻⁶5⁻⁷ = 9.089273271309687×10⁻⁶ [lb⋅ft⋅C⁻²] FPS

julia> electronmass(FPS) # lb
𝘩⋅𝘤⁻¹R∞⋅α⁻²lb⁻¹2 = 2.00827533796(62) × 10⁻³⁰ [lb] FPS

julia> molarmass(FPS) # lb⋅lb-mol⁻¹
𝟏 = 1.0 [lb⋅lb-mol⁻¹] FPS

julia> luminousefficacy(FPS) # lm⋅s³⋅lb⁻¹⋅ft⁻²
Kcd⋅ft²lb = 28.78252493663283 [lb⁻¹ft⁻²s³lm] FPS

IPS = RankineSystem(Metric,ft/𝟐^2/𝟑,lb*g₀*𝟐^2*𝟑/ft)
F=F, M=FL⁻¹T², L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

British Gravitational UnitSystem historically used in the United States of America.

julia> boltzmann(IPS) # in⋅lb⋅°R⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹ft⁻¹lb⁻¹2⁶3⁻¹5⁴ = 6.7887629566(21) × 10⁻²³ [lb⋅in⋅°R⁻¹] IPS

julia> planckreduced(IPS) # in⋅lb⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹ft⁻¹lb⁻¹τ⁻¹2²3 = 9.333747076683978×10⁻³⁴ [lb⋅in⋅s] IPS

julia> lightspeed(IPS) # in⋅s⁻¹
𝘤⋅ft⁻¹2²3 = 1.1802852677165354×10¹⁰ [in⋅s⁻¹] IPS

julia> vacuumpermeability(IPS) # slinch⋅in⋅C⁻²
g₀⁻¹lb⁻¹τ⋅2⁻⁶5⁻⁷ = 2.8250324964133447×10⁻⁷ [lb⋅s²C⁻²] IPS

julia> electronmass(IPS) # slinch
𝘩⋅𝘤⁻¹R∞⋅α⁻²g₀⁻¹ft⋅lb⁻¹2⁻¹3⁻¹ = 5.2015921425(16) × 10⁻³³ [slinch] IPS

julia> molarmass(IPS) # slinch⋅slinch-mol⁻¹
𝟏 = 1.0 [slinch-slinch-mol⁻¹] IPS

julia> luminousefficacy(IPS) # lm⋅s⋅in⁻¹⋅lb⁻¹
Kcd⋅g₀⋅ft⋅lb⋅2⁻²3⁻¹ = 77.17086290732456 [lb⁻¹in⁻¹s⋅lm] IPS

British = RankineSystem(Metric,ft,slug)
F=F, M=FL⁻¹T², L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

British Gravitational UnitSystem historically used by Britain and United States.

julia> boltzmann(British) # ft⋅lb⋅°R⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹ft⁻¹lb⁻¹2⁴3⁻²5⁴ = 5.6573024638(17) × 10⁻²⁴ [lb⋅ft⋅°R⁻¹] British

julia> planckreduced(British) # ft⋅lb⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹ft⁻¹lb⁻¹τ⁻¹ = 7.778122563903315×10⁻³⁵ [lb⋅ft⋅s] British

julia> lightspeed(British) # ft⋅s⁻¹
𝘤⋅ft⁻¹ = 9.835710564304461×10⁸ [ft⋅s⁻¹] British

julia> vacuumpermeability(British) # slug⋅ft⋅C⁻²
g₀⁻¹lb⁻¹τ⋅2⁻⁶5⁻⁷ = 2.8250324964133447×10⁻⁷ [lb⋅s²C⁻²] British

julia> electronmass(British) # slugs
𝘩⋅𝘤⁻¹R∞⋅α⁻²g₀⁻¹ft⋅lb⁻¹2 = 6.2419105710(19) × 10⁻³² [slug] British

julia> molarmass(British) # slug⋅slug-mol⁻¹
𝟏 = 1.0 [slug⋅slug-mol⁻¹] British

julia> luminousefficacy(British) # lm⋅s⋅ft⁻¹⋅lb⁻¹
Kcd⋅g₀⋅ft⋅lb = 926.0503548878947 [lb⁻¹ft⁻¹s⋅lm] British

English = RankineSystem(Metric,ft,lb,g₀/ft)
F=F, M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=A, R=𝟙, C=𝟙

English Engineering UnitSystem historically used in the United States of America.

julia> boltzmann(English) # ft⋅lbf⋅°R⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹ft⁻¹lb⁻¹2⁴3⁻²5⁴ = 5.6573024638(17) × 10⁻²⁴ [lbf⋅ft⋅°R⁻¹] English

julia> planckreduced(English) # ft⋅lbf⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹ft⁻¹lb⁻¹τ⁻¹ = 7.778122563903315×10⁻³⁵ [lbf⋅ft⋅s⋅rad⁻¹] English

julia> lightspeed(English) # ft⋅s⁻¹
𝘤⋅ft⁻¹ = 9.835710564304461×10⁸ [ft⋅s⁻¹] English

julia> vacuumpermeability(English) # lbm⋅ft⋅C⁻²
g₀⁻¹lb⁻¹τ⋅2⁻⁶5⁻⁷ = 2.8250324964133447×10⁻⁷ [lbf⋅s²C⁻²] English

julia> electronmass(English) # lbm
𝘩⋅𝘤⁻¹R∞⋅α⁻²lb⁻¹2 = 2.00827533796(62) × 10⁻³⁰ [lbm] English

julia> molarmass(English) # lbm⋅lb-mol⁻¹
𝟏 = 1.0 [lbm⋅lb-mol⁻¹] English

julia> luminousefficacy(English) # lm⋅s⋅ft⁻¹⋅lbf⁻¹
Kcd⋅g₀⋅ft⋅lb = 926.0503548878947 [lbf⁻¹ft⁻¹s⋅lm] English

julia> gravity(English) # lbm⋅ft⋅lbf⁻¹⋅s⁻²
g₀⋅ft⁻¹ = 32.17404855643044 [lbf⁻¹lbm⋅ft⋅s⁻²] English

Survey = RankineSystem(Metric,ftUS,lb,g₀/ftUS)
F=F, M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=A, R=𝟙, C=𝟙

English Engineering UnitSystem based on the geophysical US survey foot (1200/3937).

julia> boltzmann(Survey) # ftUS⋅lbf⋅°R⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹g₀⁻¹ftUS⁻¹lb⁻¹2⁴3⁻²5⁴ = 5.6572911492(17) × 10⁻²⁴ [lbf⋅ft⋅°R⁻¹] Survey

julia> planckreduced(Survey) # ftUS⋅lbf⋅s⋅rad⁻¹
𝘩⋅g₀⁻¹ftUS⁻¹lb⁻¹τ⁻¹ = 7.77810700765819×10⁻³⁵ [lbf⋅ft⋅s⋅rad⁻¹] Survey

julia> lightspeed(Survey) # ftUS⋅s⁻¹
𝘤⋅ftUS⁻¹ = 9.835690892883334×10⁸ [ft⋅s⁻¹] Survey

julia> vacuumpermeability(Survey) # lbm⋅ftUS⋅C⁻²
g₀⁻¹lb⁻¹τ⋅2⁻⁶5⁻⁷ = 2.8250324964133447×10⁻⁷ [lbf⋅s²C⁻²] Survey

julia> electronmass(Survey) # lbm
𝘩⋅𝘤⁻¹R∞⋅α⁻²lb⁻¹2 = 2.00827533796(62) × 10⁻³⁰ [lbm] Survey

julia> molarmass(Survey) # lbm⋅lb-mol⁻¹
𝟏 = 1.0 [lbm⋅lb-mol⁻¹] Survey

julia> luminousefficacy(Survey) # lm⋅s⋅ft⁻¹⋅lbf⁻¹
Kcd⋅g₀⋅ftUS⋅lb = 926.0522069923087 [lbf⁻¹ft⁻¹s⋅lm] Survey

julia> gravity(Survey) # lbm⋅ftUS⋅lbf⁻¹⋅s⁻²
g₀⋅ftUS⁻¹ = 32.17398420833334 [lbf⁻¹lbm⋅ft⋅s⁻²] Survey

FFF = EntropySystem(Metric,𝟐*𝟕*DAY,fur,𝟐*𝟑^2*𝟓*lb,°R,0,𝟏)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Furlong–firkin–fortnight FFF is a humorous UnitSystem based on unusal impractical units.

julia> boltzmann(FFF) # fir⋅fur²⋅ftn⁻²⋅F⁻¹
kB⋅NA⋅𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹ft⁻²lb⁻¹2¹⁵5⁵7²11⁻² = 6.7931043720(21) × 10⁻¹⁸ [fir⋅fur²ftn⁻²°R⁻¹] FFF

julia> planckreduced(FFF) # fir⋅fur²⋅ftn⁻¹⋅rad⁻¹
𝘩⋅ft⁻²lb⁻¹τ⁻¹2³3⁻¹5⁻¹7⋅11⁻² = 7.721326066522302×10⁻³⁵ [fir⋅fur²ftn⁻¹] FFF

julia> lightspeed(FFF) # fur⋅ftn⁻¹
𝘤⋅ft⁻¹2⁶3²5⋅7⋅11⁻¹ = 1.8026174997852542×10¹² [fur⋅ftn⁻¹] FFF

julia> vacuumpermeability(FFF) # fir⋅fur⋅Inf⁻²
𝟏/Inf = 0.0 [fir⋅fur⋅Inf⁻²] FFF

julia> electronmass(FFF) # fir
𝘩⋅𝘤⁻¹R∞⋅α⁻²lb⁻¹3⁻²5⁻¹ = 2.23141704217(68) × 10⁻³² [fir] FFF

julia> molarmass(FFF) # fir⋅fir-mol⁻¹
𝟏 = 1.0 [fir⋅fir-mol⁻¹] FFF

julia> luminousefficacy(FFF) # lm⋅ftn³⋅fir⁻¹⋅fur⁻²
Kcd⋅ft²lb⋅2⁻¹⁹3⁻⁵5⁻³7⁻³11² = 6.375788993269436×10⁻¹⁰ [fir⁻¹fur⁻²ftn³lm] FFF

IAU☉ = EntropySystem(Metric,DAY,au,GM☉/G)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Solar UnitSystem defined by International Astronomical Union and solarmass.

julia> boltzmann(IAU) # M⊙⋅au²⋅D⁻²⋅K⁻¹
kB⋅NA⋅𝘩²R∞⋅α⁻²μₑᵤ⁻¹au⁻⁵kG⁻²mP⁻²τ⁻³2⁴⁶3²⁰5¹⁷ = 2.316083(51) × 10⁻⁶⁶ [M☉⋅au²D⁻²K⁻¹] IAU☉

julia> planckreduced(IAU) # M⊙⋅au²⋅D⁻¹⋅rad⁻¹
𝘩²𝘤⋅au⁻⁵kG⁻²mP⁻²τ⁻⁴2³⁵3¹⁷5¹² = 2.047544(45) × 10⁻⁸² [M☉⋅au²D⁻¹] IAU☉

julia> lightspeed(IAU) # au⋅D⁻¹
𝘤⋅au⁻¹2⁷3³5² = 173.1446326742(35) [au⋅D⁻¹] IAU☉

julia> vacuumpermeability(IAU) # M⊙⋅au²⋅C⁻²
𝘩⋅𝘤⋅au⁻⁴kG⁻²mP⁻²τ⁻²2²²3¹⁴5³ = 4.224533(93) × 10⁻⁴⁸ [M☉⋅au⋅C⁻²] IAU☉

julia> electronmass(IAU) # M⊙
𝘩²R∞⋅α⁻²au⁻³kG⁻²mP⁻²τ⁻³2²⁹3¹⁴5¹⁰ = 4.58124(10) × 10⁻⁶¹ [M☉] IAU☉

julia> molarmass(IAU) # M☉⋅mol⁻¹
𝘩⋅𝘤⋅au⁻³kG⁻²mP⁻²τ⁻³2²⁵3¹⁴5⁷ = 5.02915(11) × 10⁻³⁴ [M☉⋅mol⁻¹] IAU☉

julia> luminousefficacy(IAU) # lm⋅D³⋅M☉⁻¹⋅au⁻²
𝘩⁻¹𝘤⁻¹Kcd⋅au⁵kG²mP²τ³2⁻⁴⁹3⁻²³5⁻¹⁶ = 4.71247(10) × 10⁴⁰ [M☉⁻¹au⁻²D³lm] IAU☉

julia> gaussgravitation(IAU) # D⁻¹
kG⋅τ⋅2⁻⁷3⁻⁴5⁻³ = 0.017202098964713464 [D⁻¹] IAU☉

IAUE = EntropySystem(Metric,DAY,LD,GME/G)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Astronomical (Earth) UnitSystem defined by lunardistance around the earthmass.

julia> boltzmann(IAUE) # ME⋅LD²⋅D⁻²⋅K⁻¹
kB⋅NA⋅𝘩²R∞⋅α⁻²μₑᵤ⁻¹mP⁻²GME⁻¹τ⁻¹2¹²5/202692169 = 1.167923(26) × 10⁻⁵⁵ [ME⋅LD²D⁻²K⁻¹] IAUE

julia> planckreduced(IAUE) # ME⋅LD²⋅D⁻¹⋅rad⁻¹
𝘩²𝘤⋅mP⁻²GME⁻¹τ⁻²2⋅3⁻³5⁻⁴/202692169 = 1.032508(23) × 10⁻⁷¹ [ME⋅LD²D⁻¹] IAUE

julia> lightspeed(IAUE) # LD⋅D⁻¹
𝘤⋅2⁴5⁻¹/14237 = 67383.2876027253 [LD⋅D⁻¹] IAUE

julia> vacuumpermeability(IAUE) # ME⋅LD²⋅C⁻²
𝘩⋅𝘤⋅mP⁻²GME⁻¹2⁻⁹3⁻³5⁻¹⁰/14237 = 5.47389(12) × 10⁻⁴⁰ [ME⋅LD⋅C⁻²] IAUE

julia> electronmass(IAUE) # ME
𝘩²R∞⋅α⁻²mP⁻²GME⁻¹τ⁻¹2 = 1.525306(34) × 10⁻⁵⁵ [ME] IAUE

julia> molarmass(IAUE) # ME⋅mol⁻¹
𝘩⋅𝘤⋅mP⁻²GME⁻¹τ⁻¹2⁻³5⁻³ = 1.674434(37) × 10⁻²⁸ [ME⋅mol⁻¹] IAUE

julia> luminousefficacy(IAUE) # lm⋅D³⋅ME⁻¹⋅LD⁻²
𝘩⁻¹𝘤⁻¹Kcd⋅mP²GME⋅τ⋅2⁻¹⁵3⁻³⋅202692169 = 9.34520(21) × 10²⁹ [ME⁻¹LD⁻²D³lm] IAUE

julia> turn(IAU)/gaussianmonth(IAU) # D⁻¹
GME¹ᐟ²2⁵ᐟ²3⁻³ᐟ²5⁻⁵ᐟ²/1.6987431854323947×10⁶ = 0.22888074402(23) [D⁻¹] IAU☉

IAUJ = EntropySystem(Metric,DAY,JD,GMJ/G)
F=MLT⁻², M=M, L=L, T=T, Q=Q, Θ=Θ, N=N, J=J, A=𝟙, R=𝟙, C=𝟙

Astronomical (Jupiter) UnitSystem defined by jupiterdistance around the solarmass.

julia> boltzmann(IAUJ) # MJ⋅JD²⋅D⁻²⋅K⁻¹
kB⋅NA⋅𝘩²R∞⋅α⁻²μₑᵤ⁻¹mP⁻²GMJ⁻¹τ⁻¹2⁶3⁴5⁻⁵/67336617049 = 8.95968(20) × 10⁻⁶⁵ [MJ⋅JD²D⁻²K⁻¹] IAUJ

julia> planckreduced(IAUJ) # MJ⋅JD²⋅D⁻¹⋅rad⁻¹
𝘩²𝘤⋅mP⁻²GMJ⁻¹τ⁻²2⁻⁵3⋅5⁻¹⁰/67336617049 = 7.92084(17) × 10⁻⁸¹ [MJ⋅JD²D⁻¹] IAUJ

julia> lightspeed(IAUJ) # JD⋅D⁻¹
𝘤⋅2⋅3²5⁻⁴/259493 = 33.272661653300865 [JD⋅D⁻¹] IAUJ

julia> vacuumpermeability(IAUJ) # MJ⋅JD²⋅C⁻²
𝘩⋅𝘤⋅mP⁻²GMJ⁻¹2⁻¹²3⁻¹5⁻¹³/259493 = 8.50430(19) × 10⁻⁴⁶ [MJ⋅JD⋅C⁻²] IAUJ

julia> electronmass(IAUJ) # MJ
𝘩²R∞⋅α⁻²mP⁻²GMJ⁻¹τ⁻¹2 = 4.79915(11) × 10⁻⁵⁸ [MJ] IAUJ

julia> molarmass(IAUJ) # MJ⋅mol⁻¹
𝘩⋅𝘤⋅mP⁻²GMJ⁻¹τ⁻¹2⁻³5⁻³ = 5.26836(12) × 10⁻³¹ [MJ⋅mol⁻¹] IAUJ

julia> luminousefficacy(IAUJ) # lm⋅D³⋅MJ⁻¹⋅JD⁻²
𝘩⁻¹𝘤⁻¹Kcd⋅mP²GMJ⋅τ⋅2⁻⁹3⁻⁷5⁶⋅67336617049 = 1.218177(27) × 10³⁹ [MJ⁻¹JD⁻²D³lm] IAUJ

julia> sqrt(gravitation(IAUJ)*solarmass(IAUJ)/jupiterdistance(IAUJ)^3) # D⁻¹
au³ᐟ²kG⋅τ⋅2⁻¹⁶3⁻¹¹ᐟ²5⁻¹²/1.3218691602384917×10⁸ = 0.001449102839405(44) [D⁻¹] IAUJ

Hubble = AstronomicalSystem(Metric,th,𝘤*th,mₑ)
F=T⁻¹, M=𝟙, L=T, T, Q, Θ=𝟙, N=𝟙, J=T⁻¹, A=𝟙, R=𝟙, C=𝟙

Hubble UnitSystem defined by hubble parameter.

julia> boltzmann(Hubble)
𝟏 = 1.0 [𝟙] Hubble

julia> planckreduced(Hubble)
𝘤⁻¹R∞⁻¹α²H0⋅au⁻¹2⁻¹¹3⁻⁴5⁻⁶ = 2.824(18) × 10⁻³⁹ [T] Hubble

julia> lightspeed(Hubble)
𝟏 = 1.0 [𝟙] Hubble

julia> vacuumpermeability(Hubble)
τ⋅2 = 12.566370614359172 [TQ⁻²] Hubble

julia> electronmass(Hubble)
𝟏 = 1.0 [𝟙] Hubble

julia> molarmass(Hubble)
𝟏 = 1.0 [𝟙] Hubble

julia> luminousefficacy(Hubble)
𝟏 = 1.0 [𝟙] Hubble

julia> hubble(Hubble)
𝟏 = 1.0 [T⁻¹] Hubble

julia> cosmological(Hubble)
ΩΛ⋅3 = 2.067(17) [T⁻²] Hubble

Cosmological = AstronomicalSystem(Metric,lc/𝘤,lc,mc)
F=MT⁻¹, M, L=T, T, Q, Θ=M, N=M, J, A=𝟙, R=𝟙, C=𝟙

Cosmological scale UnitSystem defined by darkenergydensity.

julia> boltzmann(Cosmological)
𝟏 = 1.0 [𝟙] Cosmological

julia> planckreduced(Cosmological)
𝘩²𝘤⁻⁴ΩΛ⋅H0²au⁻²mP⁻²2⁻²⁰3⁻⁷5⁻¹² = 2.888(43) × 10⁻¹²² [MT] Cosmological

julia> lightspeed(Cosmological)
𝟏 = 1.0 [𝟙] Cosmological

julia> vacuumpermeability(Cosmological)
τ⋅2 = 12.566370614359172 [MTQ⁻²] Cosmological

julia> electronmass(Cosmological)
𝘩²𝘤⁻³R∞⋅α⁻²ΩΛ¹ᐟ²H0⋅au⁻¹mP⁻²τ¹ᐟ²2⁻⁸3⁻⁷ᐟ²5⁻⁶ = 3.566(26) × 10⁻⁸³ [M] Cosmological

julia> molarmass(Cosmological)
𝟏 = 1.0 [𝟙] Cosmological

julia> luminousefficacy(Cosmological)
𝟏 = 1.0 [M⁻¹TJ] Cosmological

julia> hubble(Cosmological)
ΩΛ⁻¹ᐟ²τ¹ᐟ²2⋅3⁻¹ᐟ² = 3.487(14) [T⁻¹] Cosmological

julia> cosmological(Cosmological)
τ⋅2² = 25.132741228718345 [T⁻²] Cosmological

CosmologicalQuantum = AstronomicalSystem(Metric,tcq,lcq,mcq)
F=M², M, L=M⁻¹, T=M⁻¹, Q, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Cosmological quantum scale UnitSystem defined by darkenergydensity.

julia> boltzmann(CosmologicalQuantum)
𝟏 = 1.0 [𝟙] CosmologicalQuantum

julia> planckreduced(CosmologicalQuantum)
𝟏 = 1.0 [𝟙] CosmologicalQuantum

julia> lightspeed(CosmologicalQuantum)
𝟏 = 1.0 [𝟙] CosmologicalQuantum

julia> vacuumpermeability(CosmologicalQuantum)
τ⋅2 = 12.566370614359172 [𝘦ₙ⁼²] CosmologicalQuantum

julia> electronmass(CosmologicalQuantum)
𝘩¹ᐟ²R∞⋅α⁻²ΩΛ⁻¹ᐟ⁴H0⁻¹ᐟ²au¹ᐟ²mP⁻¹ᐟ²τ¹ᐟ⁴2¹³ᐟ²3⁷ᐟ⁴5³ = 2.2733(84) × 10⁸ [M] CosmologicalQuantum

julia> molarmass(CosmologicalQuantum)
𝟏 = 1.0 [𝟙] CosmologicalQuantum

julia> luminousefficacy(CosmologicalQuantum)
𝟏 = 1.0 [𝟙] CosmologicalQuantum

Planck = UnitSystem(𝟏,𝟏,𝟏,𝟏,√(𝟐*τ*αG))
F=M², M, L=M⁻¹, T=M⁻¹, Q=𝟙, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Planck UnitSystem with the electronmass value √(4π*αG) using gravitational coupling.

julia> boltzmann(Planck)
𝟏 = 1.0 [𝟙] Planck

julia> planckreduced(Planck)
𝟏 = 1.0 [𝟙] Planck

julia> lightspeed(Planck)
𝟏 = 1.0 [𝟙] Planck

julia> vacuumpermeability(Planck)
𝟏 = 1.0 [𝟙] Planck

julia> electronmass(Planck)
𝘩⋅𝘤⁻¹R∞⋅α⁻²mP⁻¹τ¹ᐟ²2³ᐟ² = 1.483708(16) × 10⁻²² [M] Planck

PlanckGauss = UnitSystem(𝟏,𝟏,𝟏,𝟐*τ,√αG)
F=M², M=M, L=M⁻¹, T=M⁻¹, Q=Q, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Planck (Gauss) UnitSystem with permeability of 4π and electronmass coupling √αG.

julia> boltzmann(PlanckGauss)
𝟏 = 1.0 [𝟙] PlanckGauss

julia> planckreduced(PlanckGauss)
𝟏 = 1.0 [𝟙] PlanckGauss

julia> lightspeed(PlanckGauss)
𝟏 = 1.0 [𝟙] PlanckGauss

julia> vacuumpermeability(PlanckGauss)
τ⋅2 = 12.566370614359172 [𝘦ₙ⁻²] PlanckGauss

julia> electronmass(PlanckGauss)
𝘩⋅𝘤⁻¹R∞⋅α⁻²mP⁻¹2 = 4.185463(46) × 10⁻²³ [mP] PlanckGauss

The well known PlanckGauss values for length, time, mass, and temperature are:

julia> length(PlanckGauss,SI2019) # ℓP
𝘩⋅𝘤⁻¹mP⁻¹τ⁻¹ = 1.616255(18) × 10⁻³⁵ [m]/[mP⁻¹] PlanckGauss -> SI2019

julia> time(PlanckGauss,SI2019) # tP
𝘩⋅𝘤⁻²mP⁻¹τ⁻¹ = 5.391247(59) × 10⁻⁴⁴ [s]/[mP⁻¹] PlanckGauss -> SI2019

julia> mass(PlanckGauss,SI2019) # mP
mP = 2.176434(24) × 10⁻⁸ [kg]/[mP] PlanckGauss -> SI2019

julia> temperature(PlanckGauss,SI2019) # TP
kB⁻¹𝘤²mP = 1.416784(16) × 10³² [K]/[mP] PlanckGauss -> SI2019

Stoney = UnitSystem(𝟏,𝟏/α,𝟏,𝟐*τ,√(αG/α))
F=MT⁻¹, M, L=T, T, Q, Θ=M, N=M, J, A=𝟙, R=𝟙, C=𝟙

Stoney UnitSystem with permeability of 4π and electronmass coupling √(αG/α).

julia> boltzmann(Stoney)
𝟏 = 1.0 [𝟙] Stoney

julia> planckreduced(Stoney)
α⁻¹ = 137.035999084(21) [MT] Stoney

julia> lightspeed(Stoney)
𝟏 = 1.0 [𝟙] Stoney

julia> vacuumpermeability(Stoney)
τ⋅2 = 12.566370614359172 [MTQ⁻²] Stoney

julia> electronmass(Stoney)
𝘩⋅𝘤⁻¹R∞⋅α⁻⁵ᐟ²mP⁻¹2 = 4.899602(54) × 10⁻²² [M] Stoney

The well known Stoney values for length, time, mass, and charge are:

julia> length(Stoney,SI2019) # lS
𝘩⋅𝘤⁻¹α¹ᐟ²mP⁻¹τ⁻¹ = 1.380679(15) × 10⁻³⁶ [m]/[T] Stoney -> SI2019

julia> time(Stoney,SI2019) # tS
𝘩⋅𝘤⁻²α¹ᐟ²mP⁻¹τ⁻¹ = 4.605448(51) × 10⁻⁴⁵ [s]/[T] Stoney -> SI2019

julia> mass(Stoney,SI2019) # mS
α¹ᐟ²mP = 1.859209(21) × 10⁻⁹ [kg]/[M] Stoney -> SI2019

julia> charge(Stoney,SI2019) # qS
𝘦 = 1.602176634×10⁻¹⁹ [C]/[𝘦] Stoney -> SI2019

Hartree = UnitSystem(𝟏,𝟏,𝟏/α,𝟐*τ*α^2,𝟏)
F=L⁻³, M=𝟙, L=L, T=L², Q=Q, Θ=L⁻², N=𝟙, J=L⁻⁴, A=𝟙, R=𝟙, C=𝟙

Hartree atomic UnitSystem based on bohr radius and elementarycharge scale.

julia> boltzmann(Hartree)
𝟏 = 1.0 [𝟙] Hartree

julia> planckreduced(Hartree)
𝟏 = 1.0 [𝟙] Hartree

julia> lightspeed(Hartree)
α⁻¹ = 137.035999084(21) [a₀⁻¹] Hartree

julia> vacuumpermeability(Hartree)
α²τ⋅2 = 0.00066917625662(21) [a₀⋅𝘦⁻²] Hartree

julia> electronmass(Hartree)
𝟏 = 1.0 [𝟙] Hartree

The well known Hartree atomic unit values for length, time, mass, and charge are:

julia> length(Hartree,SI2019) # lA
R∞⁻¹α⋅τ⁻¹2⁻¹ = 5.29177210902(81) × 10⁻¹¹ [m]/[a₀] Hartree -> SI2019

julia> time(Hartree,SI2019) # tA
𝘤⁻¹R∞⁻¹τ⁻¹2⁻¹ = 2.4188843265857(46) × 10⁻¹⁷ [s]/[a₀²] Hartree -> SI2019

julia> mass(Hartree,SI2019) # mA
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg]/[𝟙] Hartree -> SI2019

julia> charge(Hartree,SI2019) # qA
𝘦 = 1.602176634×10⁻¹⁹ [C]/[𝘦] Hartree -> SI2019

Rydberg = UnitSystem(𝟏,𝟏,𝟐/α,τ/𝟐*α^2,𝟏/𝟐)
F=MLT⁻², M, L, T, Q, Θ=T⁻¹, N=M, J=T², A=𝟙, R=𝟙, C=𝟙

Rydberg UnitSystem with lightspeed of 𝟐/α and permeability of π*α^2.

julia> boltzmann(Rydberg)
𝟏 = 1.0 [ML²T⁻¹] Rydberg

julia> planckreduced(Rydberg)
𝟏 = 1.0 [ML²T⁻¹] Rydberg

julia> lightspeed(Rydberg)
α⁻¹2 = 274.071998168(42) [LT⁻¹] Rydberg

julia> vacuumpermeability(Rydberg)
α²τ⋅2⁻¹ = 0.000167294064155(51) [MLQ⁻²] Rydberg

julia> electronmass(Rydberg)
2⁻¹ = 0.5 [M] Rydberg

The well known Rydberg atomic unit values for length, time, mass, and charge are:

julia> length(Rydberg,SI2019) # lR
R∞⁻¹α⋅τ⁻¹2⁻¹ = 5.29177210902(81) × 10⁻¹¹ [m]/[a₀] Rydberg -> SI2019

julia> time(Rydberg,SI2019) # tR
𝘤⁻¹R∞⁻¹τ⁻¹ = 4.8377686531713(93) × 10⁻¹⁷ [s]/[T] Rydberg -> SI2019

julia> mass(Rydberg,SI2019) # mR
𝘩⋅𝘤⁻¹R∞⋅α⁻²2² = 1.82187674031(56) × 10⁻³⁰ [kg]/[M] Rydberg -> SI2019

julia> charge(Rydberg,SI2019) # qR
𝘦⋅2⁻¹ᐟ² = 1.1329099625600371×10⁻¹⁹ [C]/[Q] Rydberg -> SI2019

Schrodinger = UnitSystem(𝟏,𝟏,𝟏/α,𝟐*τ*α^2,√(αG/α))
F=MLT⁻², M, L, T, Q, Θ=T⁻¹, N=M, J=T², A=𝟙, R=𝟙, C=𝟙

Schrodinger UnitSystem with permeability of 4π/αinv^2 and electronmass of √(αG*αinv).

julia> boltzmann(Schrodinger)
𝟏 = 1.0 [ML²T⁻¹] Schrodinger

julia> planckreduced(Schrodinger)
𝟏 = 1.0 [ML²T⁻¹] Schrodinger

julia> lightspeed(Schrodinger)
α⁻¹ = 137.035999084(21) [LT⁻¹] Schrodinger

julia> vacuumpermeability(Schrodinger)
α²τ⋅2 = 0.00066917625662(21) [MLQ⁻²] Schrodinger

julia> electronmass(Schrodinger)
𝘩⋅𝘤⁻¹R∞⋅α⁻⁵ᐟ²mP⁻¹2 = 4.899602(54) × 10⁻²² [M] Schrodinger

Electronic = UnitSystem(𝟏,𝟏/α,𝟏,𝟐*τ,𝟏)
F=T⁻¹, M=𝟙, L=T, T, Q, Θ=𝟙, N=𝟙, J=T⁻¹, A=𝟙, R=𝟙, C=𝟙

Electronic UnitSystem with planckreduced of 1/α and permeability of 4π.

julia> boltzmann(Electronic)
𝟏 = 1.0 [𝟙] Electronic

julia> planckreduced(Electronic)
α⁻¹ = 137.035999084(21) [T] Electronic

julia> lightspeed(Electronic)
𝟏 = 1.0 [𝟙] Electronic

julia> vacuumpermeability(Electronic)
τ⋅2 = 12.566370614359172 [TQ⁻²] Electronic

julia> electronmass(Electronic)
𝟏 = 1.0 [𝟙] Electronic

Natural = UnitSystem(𝟏,𝟏,𝟏,𝟏,𝟏)
F=𝟙, M=𝟙, L=𝟙, T=𝟙, Q=𝟙, Θ=𝟙, N=𝟙, J=𝟙, A=𝟙, R=𝟙, C=𝟙

Natural UnitSystem with all primary constants having unit value.

julia> boltzmann(Natural)
𝟏 = 1.0 [𝟙] Natural

julia> planckreduced(Natural)
𝟏 = 1.0 [𝟙] Natural

julia> lightspeed(Natural)
𝟏 = 1.0 [𝟙] Natural

julia> vacuumpermeability(Natural)
𝟏 = 1.0 [𝟙] Natural

julia> electronmass(Natural)
𝟏 = 1.0 [𝟙] Natural

The well known Natural values for length, time, mass, and charge are:

julia> length(Natural,SI2019)
R∞⁻¹α²τ⁻¹2⁻¹ = 3.8615926796(12) × 10⁻¹³ [m]/[𝟙] Natural -> SI2019

julia> time(Natural,SI2019)
𝘤⁻¹R∞⁻¹α²τ⁻¹2⁻¹ = 1.28808866819(39) × 10⁻²¹ [s]/[𝟙] Natural -> SI2019

julia> mass(Natural,SI2019)
𝘩⋅𝘤⁻¹R∞⋅α⁻²2 = 9.1093837016(28) × 10⁻³¹ [kg]/[𝟙] Natural -> SI2019

julia> charge(Natural,SI2019)
𝘦⋅α⁻¹ᐟ²τ⁻¹ᐟ²2⁻¹ᐟ² = 5.29081768990(41) × 10⁻¹⁹ [C]/[𝟙] Natural -> SI2019

NaturalGauss = UnitSystem(𝟏,𝟏,𝟏,𝟐*τ,𝟏)
F=𝟙, M=𝟙, L=𝟙, T=𝟙, Q=Q, Θ=𝟙, N=𝟙, J=𝟙, A=𝟙, R=𝟙, C=𝟙

Natural (Gauss) UnitSystem with the Gaussian permeability value of 4π.

julia> boltzmann(NaturalGauss)
𝟏 = 1.0 [𝟙] NaturalGauss

julia> planckreduced(NaturalGauss)
𝟏 = 1.0 [𝟙] NaturalGauss

julia> lightspeed(NaturalGauss)
𝟏 = 1.0 [𝟙] NaturalGauss

julia> vacuumpermeability(NaturalGauss)
τ⋅2 = 12.566370614359172 [𝘦ₙ⁻²] NaturalGauss

julia> electronmass(NaturalGauss)
𝟏 = 1.0 [𝟙] NaturalGauss

QCD = UnitSystem(𝟏,𝟏,𝟏,𝟏,𝟏/μₚₑ)
F=M², M=M, L=M⁻¹, T=M⁻¹, Q=𝟙, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Qunatum chromodynamics UnitSystem based on the protonmass scale.

julia> boltzmann(QCD)
𝟏 = 1.0 [𝟙] QCD

julia> planckreduced(QCD)
𝟏 = 1.0 [𝟙] QCD

julia> lightspeed(QCD)
𝟏 = 1.0 [𝟙] QCD

julia> vacuumpermeability(QCD)
𝟏 = 1.0 [𝟙] QCD

julia> electronmass(QCD)
μₑᵤ⋅μₚᵤ⁻¹ = 0.000544617021487(33) [mₚ] QCD

The well known QCD values for length, time, mass, and charge are:

julia> length(QCD,SI2019) # lQCD
R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 2.10308910335(66) × 10⁻¹⁶ [m]/[mₚ⁻¹] QCD -> SI2019

julia> time(QCD,SI2019) # tQCD
𝘤⁻¹R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 7.0151501388(22) × 10⁻²⁵ [s]/[mₚ⁻¹] QCD -> SI2019

julia> mass(QCD,SI2019) # mQCD
𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹μₚᵤ⋅2 = 1.67262192369(52) × 10⁻²⁷ [kg]/[mₚ] QCD -> SI2019

julia> charge(QCD,SI2019) # qQCD
𝘦⋅α⁻¹ᐟ²τ⁻¹ᐟ²2⁻¹ᐟ² = 5.29081768990(41) × 10⁻¹⁹ [C]/[𝟙] QCD -> SI2019

QCDGauss = UnitSystem(𝟏,𝟏,𝟏,𝟐*τ,𝟏/μₚₑ)
F=M², M=M, L=M⁻¹, T=M⁻¹, Q=Q, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Qunatum chromodynamics (Gauss) UnitSystem based on the protonmass scale.

julia> boltzmann(QCDGauss)
𝟏 = 1.0 [𝟙] QCDGauss

julia> planckreduced(QCDGauss)
𝟏 = 1.0 [𝟙] QCDGauss

julia> lightspeed(QCDGauss)
𝟏 = 1.0 [𝟙] QCDGauss

julia> vacuumpermeability(QCDGauss)
τ⋅2 = 12.566370614359172 [𝘦ₙ⁻²] QCDGauss

julia> electronmass(QCDGauss)
μₑᵤ⋅μₚᵤ⁻¹ = 0.000544617021487(33) [mₚ] QCDGauss

The well known QCDGauss values for length, time, mass, and charge are:

julia> length(QCDGauss,SI2019) # lQCD
R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 2.10308910335(66) × 10⁻¹⁶ [m]/[mₚ⁻¹] QCDGauss -> SI2019

julia> time(QCDGauss,SI2019) # tQCD
𝘤⁻¹R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 7.0151501388(22) × 10⁻²⁵ [s]/[mₚ⁻¹] QCDGauss -> SI2019

julia> mass(QCDGauss,SI2019) # mQCD
𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹μₚᵤ⋅2 = 1.67262192369(52) × 10⁻²⁷ [kg]/[mₚ] QCDGauss -> SI2019

julia> charge(QCDGauss,SI2019) # qQCD
𝘦⋅α⁻¹ᐟ² = 1.87554603778(14) × 10⁻¹⁸ [C]/[𝘦ₙ] QCDGauss -> SI2019

QCDoriginal = UnitSystem(𝟏,𝟏,𝟏,𝟐*τ*α,𝟏/μₚₑ)
F=M², M=M, L=M⁻¹, T=M⁻¹, Q=Q, Θ=M, N=M, J=M², A=𝟙, R=𝟙, C=𝟙

Qunatum chromodynamics (original) UnitSystem scaled by protonmass and elementarycharge.

julia> boltzmann(QCDoriginal)
𝟏 = 1.0 [𝟙] QCDoriginal

julia> planckreduced(QCDoriginal)
𝟏 = 1.0 [𝟙] QCDoriginal

julia> lightspeed(QCDoriginal)
𝟏 = 1.0 [𝟙] QCDoriginal

julia> vacuumpermeability(QCDoriginal)
α⋅τ⋅2 = 0.091701236889(14) [𝘦⁻²] QCDoriginal

julia> electronmass(QCDoriginal)
μₑᵤ⋅μₚᵤ⁻¹ = 0.000544617021487(33) [mₚ] QCDoriginal

The well known QCDoriginal values for length, time, mass, and charge are:

julia> length(QCDoriginal,SI2019) # lQCD
R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 2.10308910335(66) × 10⁻¹⁶ [m]/[mₚ⁻¹] QCDoriginal -> SI2019

julia> time(QCDoriginal,SI2019) # tQCD
𝘤⁻¹R∞⁻¹α²μₑᵤ⋅μₚᵤ⁻¹τ⁻¹2⁻¹ = 7.0151501388(22) × 10⁻²⁵ [s]/[mₚ⁻¹] QCDoriginal -> SI2019

julia> mass(QCDoriginal,SI2019) # mQCD
𝘩⋅𝘤⁻¹R∞⋅α⁻²μₑᵤ⁻¹μₚᵤ⋅2 = 1.67262192369(52) × 10⁻²⁷ [kg]/[mₚ] QCDoriginal -> SI2019

julia> charge(QCDoriginal,SI2019) # qQCD
𝘦 = 1.602176634×10⁻¹⁹ [C]/[𝘦] QCDoriginal -> SI2019