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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:

In [1]:

from metrolopy import constant

constant('G')

Out[1]:

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 2022 CODATA recommended values (though there are some differences in the last digit from the tabulated CODATA values for some constants due to rounding errors). 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 realized 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:

In [2]:

from metrolopy import search_constants
search_constants()

Out[2]:

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 = 25 812.807 Ω, alias: R(K-90)
alpha particle mass m_α = 6.644 657 345 0(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 = 1.660 539 068 93(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 = 9.274 010 065 6(28) × 10^-24 J/T, aliases: mu(B), μ(B)
Bohr radius a₀ = 5.291 772 105 41(80) × 10^-11 m, alias: a(0)
Boltzmann constant k = 1.380 649 × 10^-23 J/K, alias: k
classical electron radius r_r = 2.817 940 320 4(13) × 10^-15 m, alias: r(e)
Compton wavelength λ_C = 2.426 310 235 35(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 = 8.987 551 786 1(14) × 10⁹ N m²/C², alias: k(e)
deuteron g factor g_d = 0.857 438 233 5(20), alias: g(d)
deuteron magnetic moment μ_d = 4.330 735 087(10) × 10^-27 J/T, aliases: mu(d), μ(d)
deuteron mass m_d = 3.343 583 776 8(10) × 10^-27 kg, alias: m(d)
deuteron rms charge radius r_d = 2.127 78(27) × 10^-15 m, alias: r(d)
electron g factor g_e^- = -2.002 319 304 360 92(36), alias: g(e-)
electron gyromagnetic ratio γ_e = 1.760 859 627 82(53) × 10¹¹ 1/(T s), aliases: gamma(e), γ(e)
electron magnetic moment μ_e = -9.284 764 691 6(28) × 10^-24 J/T, aliases: mu(e), μ(e)
electron magnetic moment anomaly a_e = 0.001 159 652 180 46(18), alias: a(e)
electron mass m_e = 9.109 383 714 0(27) × 10^-31 kg, alias: m(e)
elementary charge e = 1.602 176 634 × 10^-19 C, alias: e
Faraday constant F = 96 485.332 123 310 018 4 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 = 0.007 297 352 564 3(11), alias: alpha
first radiation constant c₁ = 3.741 771 852 192 757 33(18) × 10^-16 W m², alias: c(1)
first radiation constant for spectral radiance c_1L = 1.191 042 972 397 19 × 10^-16 W m²/sr, alias: c(1L)
float64 representation of Euler's number e e = 2.718 281 828 459 045 09(13), aliases: Euler, euler, math e, math_e
float64 representation of pi π = 3.141 592 653 589 793 12(15), aliases: pi, π
float64 representation of sqrt(2) sqrt(2) = 1.414 213 562 373 095 145(66), alias: sqrt(2)
Hartree energy E_h = 4.359 744 722 206 0(48) × 10^-18 J, alias: E(h)
helion g factor g_h = -4.255 250 699 5(34), alias: g(h)
helion magnetic moment μ_h = -1.074 617 551 96(92) × 10^-26 J/T, aliases: mu(h), μ(h)
helion mass m_h = 5.006 412 786 2(15) × 10^-27 kg, alias: m(h)
helion shielding shift σ_h = 5.996 702 9(23) × 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 84 × 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 93 × 10^-15 Wb, alias: Phi(0)
mass of Jupiter M_J = 1.898 518(43) × 10²⁷ kg, alias: M(J)
mass of the earth M_E = 5.972 17(13) × 10²⁴ kg, alias: M(E)
mass of the sun M_S = 1.988 410(45) × 10³⁰ kg, alias: M(S)
molar gas constant R = 8.314 462 618 153 24 J/(K mol), alias: R
molar mass constant M_u = 0.001 000 000 001 06(30) kg/mol, alias: M(u)
molar mass of carbon-12 M(¹²C) = 0.012 000 000 012 7(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 24(82), 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 62(41), 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 = 1.319 590 903 81(66) × 10^-15 m, aliases: lambda(n), λ(n)
neutron g factor g_n = -3.826 085 52(90), alias: g(n)
neutron gyromagnetic ratio γ_n = 1.832 471 74(43) × 10⁸ 1/(T s), aliases: gamma(n), γ(n)
neutron magnetic moment μ_n = -9.662 365 3(23) × 10^-27 J/T, aliases: mu(n), μ(n)
neutron mass m_n = 1.674 927 500 58(83) × 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 = 5.050 783 739 2(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 = 2.675 221 870 8(11) × 10⁸ 1/(T s), aliases: gamma(p), γ(p)
proton magnetic moment μ_p = 1.410 606 795 44(59) × 10^-26 J/T, aliases: mu(p), μ(p)
proton magnetic shielding correction σ′_p = 2.567 15(41) × 10^-5, aliases: sigma'(p), σ′(p)
proton mass m_p = 1.672 621 925 97(50) × 10^-27 kg, alias: m(p)
reduced Planck constant ℏ = 1.054 571 817 646 156 472(49) × 10^-34 J s, aliases: hbar, h-bar
Rydberg constant R_∞ = 10 973 731.568 157(12) 1/m, aliases: R(inf), R(∞)
second radiation constant c₂ = 0.014 387 768 775 039 338 021... 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 1(13) × 10^-8 W/(m² K⁴), aliases: sigma, σ
Thomson cross section σ_e = 6.652 458 704 8(60) × 10^-29 m², aliases: sigma(e), σ(e)
triton g factor g_t = 5.957 924 930(12), alias: g(t)
triton magnetic moment μ_t = 1.504 609 517 8(31) × 10^-26 J/T, aliases: mu(t), μ(t)
triton mass m_t = 5.007 356 751 3(15) × 10^-27 kg, alias: m(t)
vacuum electric permittivity ε₀ = 8.854 187 818 8(13) × 10^-12 F/m, aliases: epsilon(0), ε(0)
vacuum impedance Z₀ = 376.730 313 410(57) Ω, alias: Z(0)
vacuum magnetic permeability μ₀ = 1.256 637 061 26(19) × 10^-6 N/A², aliases: mu(0), μ(0)
von Klitzing constant R_K = 25 812.807 459 304 506 660... J s/C², alias: R(K)
W to Z mass ratio m_W/m_Z = 0.881 45(13), alias: m(W)/m(Z)
weak mixing angle sin² Θ_W = 0.223 05(23), aliases: sin2(Theta(W)), sin2(ϴ(W))