MetroloPy built-in physical constants

Constants are accessed by passing the name or alias of a physical constant as a string to the constant function. This function returns a GummyConstant instance that can be used like a gummy in calculations:

from metrolopy import constant

constant('G')

G = 6.674 30(15) × 10^-11 m³/(kg s²)

The constant definitions include correlations. So, for example, even though relative atomic masses are not in the constant library, dividing the mass of a particle by the atomic mass constant gives the particle mass in atomic units with the correct uncertainty.

The constants below are mostly based on the 2018 CODATA recommended values. See the .description attribute of each constant for source information.

Most constants with exact values are stored as integers or the ratio of integers. However constants such as ℏ are exact in theory, but since the numerical value of π cannot be relized exactly on a computer, they may be listed with an uncertainty below.

To get a listing of all built-in constants use the search_constants function with no argument:

from metrolopy import search_constants
search_constants()

• 1990 conventional value of Josephson constant K_J-90 = 4.835 979 × 10¹⁴ Hz/V, alias: K(J-90)
• 1990 conventional value of von Klitzing constant R_K-90 = 25812.807 Ω, alias: R(K-90)
• alpha particle mass m_α = 6.644 657 335 7(20) × 10^-27 kg, aliases: m(alpha), m(α)
• Angstrom star Å^* = 1.000 014 95(90) × 10^-10 m, aliases: A*, Å*
• atomic mass constant m_u = 1.660 539 066 60(50) × 10^-27 kg, alias: m(u)
• Avogadro constant N_A = 6.022 140 76 × 10²³ 1/mol, alias: N(A)
• Bohr magneton μ_B = 9.274 010 078 3(28) × 10^-24 J/T, aliases: mu(B), μ(B)
• Bohr radius a₀ = 5.291 772 109 03(80) × 10^-11 m, alias: a(0)
• Boltzmann constant k = 1.380 649 × 10^-23 J/K, alias: k
• classical electron radius r_r = 2.817 940 326 2(13) × 10^-15 m, alias: r(e)
• Compton wavelength λ_C = 2.426 310 238 68(73) × 10^-12 m, aliases: lambda(C), λ(C)
• conductance quantum G₀ = 7.748 091 729 863 65 × 10^-5 S, alias: G(0)
• copper x unit xu(CuKα₁) = 1.002 076 97(28) × 10^-13 m, aliases: xu(Cu), xu(CuKalpha1), xu(CuKα1)
• Coulomb constant k_e = 8.987 551 792 3(14) × 10⁹ N m²/C², alias: k(e)
• deuteron g factor g_d = 0.857 438 233 8(22), alias: g(d)
• deuteron magnetic moment μ_d = 4.330 735 095(11) × 10^-27 J/T, aliases: mu(d), μ(d)
• deuteron mass m_d = 3.343 583 772 4(10) × 10^-27 kg, alias: m(d)
• deuteron rms charge radius r_d = 2.127 99(74) × 10^-15, alias: r(d)
• electron g factor g_e^- = -2.002 319 304 362 56(36), alias: g(e-)
• electron gyromagnetic ratio γ_e = 1.760 859 630 23(53) × 10¹¹ 1/(T s), aliases: gamma(e), γ(e)
• electron magnetic moment μ_e = -9.284 764 704 4(28) × 10^-24 J/T, aliases: mu(e), μ(e)
• electron magnetic moment anomaly a_e = 0.001 159 652 181 28(18), alias: a(e)
• electron mass m_e = 9.109 383 701 5(27) × 10^-31 kg, alias: m(e)
• elementary charge e = 1.602 176 634 × 10^-19 C, alias: e
• Faraday constant F = 96485.332 123 310 01... C/mol, alias: F
• Fermi coupling constant G_F/(ℏc)³ = 1.166 378 70(60) × 10^-5 1/GeV², alias: G(F)/(hbar*c)**3
• fine-structure constant α = 0.007 297 352 569 3(11), alias: alpha
• first radiation constant c₁ = 3.741 771 852 192 757... × 10^-16 W m² ± 1.8 × 10^-32 W m², alias: c(1)
• first radiation constant for spectral radiance c_1L = 1.191 042 972 397 188 5 × 10^-16 W m²/sr, alias: c(1L)
• float64 representation of Euler's number e e = 2.718 281 828 459 045... ± 1.3 × 10^-16, aliases: Euler, euler, math e, math_e
• float64 representation of pi π = 3.141 592 653 589 793... ± 1.5 × 10^-16, aliases: pi, π
• float64 representation of sqrt(2) sqrt(2) = 1.414 213 562 373 095... ± 6.6 × 10^-17, alias: sqrt(2)
• Hartree energy E_h = 4.359 744 722 207 2(83) × 10^-18 J, alias: E(h)
• helion g factor g_h = -4.255 250 615(50), alias: g(h)
• helion magnetic moment μ_h = -1.074 617 532(13) × 10^-26 J/T, aliases: mu(h), μ(h)
• helion mass m_h = 5.006 412 779 6(15) × 10^-27 kg, alias: m(h)
• helion shielding shift σ_h = 5.996 743(10) × 10^-5, aliases: sigma(h), σ(h)
• hyperfine transition frequency of Cs-133 Δν_Cs = 9.192 631 77 × 10⁹ Hz, aliases: hf(Cs), Δν(Cs)
• Josephson constant K_J = 4.835 978 484 169 836 6 × 10¹⁴ Hz/V, alias: K(J)
• lattice parameter of silicon a = 5.431 020 511(89) × 10^-10 m, alias: a
• lattice spacing of ideal Si (220) d₂₂₀) = 1.920 155 716(31) × 10^-10 m, alias: d(220)
• luminous efficacy K_cd = 683 lm/W, alias: K(cd)
• magnetic flux quantum Φ₀ = 2.067 833 848 461 929 4 × 10^-15 Wb, alias: Phi(0)
• molar gas constant R = 8.314 462 618 153 24 J/(K mol), alias: R
• molar mass constant M_u = 9.999 999 996 5(30) × 10^-4 kg/mol, alias: M(u)
• molar mass of carbon-12 M(¹²C) = 0.011 999 999 995 8(36) kg/mol, alias: M(12C)
• molar volume of silicon V_m(Si) = 1.205 883 199(59) × 10^-5 1/mol, alias: Vm(Si)
• molybdenum x unit xu(MoKα₁) = 1.002 099 52(53) × 10^-13 m, aliases: xu(Mo), xu(MoKalpha1), xu(MoKα1)
• muon Compton wavelength λ_μ = 1.173 444 110(26) × 10^-14 m, aliases: lambda(mu), λ(μ)
• muon g factor g_μ^- = -2.002 331 841 8(13), aliases: g(mu-), g(μ-)
• muon magnetic moment μ_μ = -4.490 448 30(10) × 10^-26 J/T, aliases: mu(mu), μ(μ)
• muon magnetic moment anomaly a_μ = 0.001 165 920 89(63), aliases: a(mu), a(μ)
• muon mass m_μ = 1.883 531 627(42) × 10^-28 kg, aliases: m(mu), m(μ)
• neutron Compton wavelength λ_n = 1.319 590 905 81(75) × 10^-15 m, aliases: lambda(n), λ(n)
• neutron g factor g_n = -3.826 085 45(90), alias: g(n)
• neutron gyromagnetic ratio γ_n = 1.832 471 71(43) × 10⁸ 1/(T s), aliases: gamma(n), γ(n)
• neutron magnetic moment μ_n = -9.662 365 1(23) × 10^-27 J/T, aliases: mu(n), μ(n)
• neutron mass m_n = 1.674 927 498 04(96) × 10^-27 kg, alias: m(n)
• Newtonian constant of gravitation G = 6.674 30(15) × 10^-11 m³/(kg s²), aliases: constant of gravitation, G
• nuclear magneton μ_N = 5.050 783 746 1(15) × 10^-27 J/T, aliases: mu(N), μ(N)
• Planck constant h = 6.626 070 15 × 10^-34 J s, alias: h
• proton g factor g_p = 5.585 694 689 3(16), alias: g(p)
• proton gyromagnetic ratio γ_p = 2.675 221 874 5(11) × 10⁸ 1/(T s), aliases: gamma(p), γ(p)
• proton magnetic moment μ_p = 1.410 606 797 37(59) × 10^-26 J/T, aliases: mu(p), μ(p)
• proton magnetic shielding correction σ′_p = 2.5689(11) × 10^-5, aliases: sigma'(p), σ′(p)
• proton mass m_p = 1.672 621 923 68(51) × 10^-27 kg, alias: m(p)
• reduced Planck constant ℏ = 1.054 571 817 646 156... × 10^-34 J s ± 4.9 × 10^-51 J s, aliases: hbar, h-bar
• Rydberg constant R_∞ = 10 973 731.568 160(21) 1/m, aliases: R(inf), R(∞)
• second radiation constant c₂ = 0.014 387 768 775 039 34... m K, alias: c(2)
• speed of light in vacuum c = 2.997 924 58 × 10⁸ m/s, alias: c
• standard atmosphere atm = 101 325 Pa, alias: atm
• standard-state pressure ssp = 100 000 Pa, alias: ssp
• Stefan-Boltzmann constant σ = 5.670 374 419 184 428... × 10^-8 W/(m² K⁴) ± 1.3 × 10^-23 W/(m² K⁴), aliases: sigma, σ
• Thomson cross section σ_e = 6.652 458 732 2(60) × 10^-29 m², aliases: sigma(e), σ(e)
• triton g factor g_t = 5.957 924 931(12), alias: g(t)
• triton magnetic moment μ_t = 1.504 609 520 1(31) × 10^-26 J/T, aliases: mu(t), μ(t)
• triton mass m_t = 5.007 356 744 6(15) × 10^-27 kg, alias: m(t)
• vacuum electric permittivity ε₀ = 8.854 187 812 8(13) × 10^-12 F/m, aliases: epsilon(0), ε(0)
• vacuum impedance Z₀ = 376.730 313 668(57) Ω, alias: Z(0)
• vacuum magnetic permeability μ₀ = 1.256 637 062 12(19) × 10^-6 N/A², aliases: mu(0), μ(0)
• von Klitzing constant R_K = 25812.807 459 304 51... J s/C², alias: R(K)
• W to Z mass ratio m_W/m_Z = 0.881 53(17), alias: m(W)/m(Z)
• weak mixing angle sin² Θ_W = 0.222 90(30), aliases: sin2(Theta(W)), sin2(ϴ(W))

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