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Electromagnetic constants

33 values, each with its units, its uncertainty, and where it came from.

Universal & Atomic 2

Elementary charge exact

e=1.602176634×10−19 Ce = 1.602176634 \times 10^{-19}\ \text{C}

CThe charge of a proton, exactly 1.602 176 634 × 10⁻¹⁹ C — the quantum of free charge and the SI definition of the ampere.

Electron charge-to-mass quotient measured

−e/me=−1.75882000838×1011 C/kg-e/m_{\mathrm{e}} = -1.75882000838 \times 10^{11}\ \text{C/kg}

C/kgThe electron's charge divided by its mass, −1.758 820 008 × 10¹¹ C/kg — the quantity J. J. Thomson measured in 1897 to discover the electron.

Electromagnetic 31

Vacuum magnetic permeability measured

μ0=0.00000125663706127 N/A2 (H/m)\mu_{0} = 0.00000125663706127\ \text{N/A}^{2}\text{ (H/m)}

N/A² (H/m)How strongly a current magnetises empty space — the constant in Ampère's law, no longer exactly 4π×10⁻⁷ since the 2019 SI redefinition.

Vacuum electric permittivity measured

ε0=8.8541878188×10−12 F/m\varepsilon_{0} = 8.8541878188 \times 10^{-12}\ \text{F/m}

F/mThe electric constant of free space, setting the strength of Coulomb's law and the capacitance of every parallel-plate geometry.

Characteristic impedance of vacuum measured

Z0=376.730313412 ΩZ_{0} = 376.730313412\ \text{Ω}

ΩThe ratio of electric to magnetic field strength in a plane wave in free space — the 377 ohms every antenna engineer matches to.

Coulomb constant measured

ke=8987551786.2 N⋅m2/C2k_{e} = 8987551786.2\ \text{N}{\cdot}\text{m}^{2}\text{/C}^{2}

N·m²/C²The proportionality constant 1/(4πε₀) in Coulomb's law, fixing the enormous strength of the electrostatic force between charges.

Bohr magneton measured

μB=9.2740100657×10−24 J/T\mu_{\mathrm{B}} = 9.2740100657 \times 10^{-24}\ \text{J/T}

J/TThe natural quantum of magnetic moment for an electron, eħ/2mₑ — the yardstick for atomic magnetism and electron spin.

Nuclear magneton measured

μN=5.0507837393×10−27 J/T\mu_{\mathrm{N}} = 5.0507837393 \times 10^{-27}\ \text{J/T}

J/TThe magnetic-moment unit for nuclei, eħ/2mₚ — smaller than the Bohr magneton by the full proton-to-electron mass ratio of 1836.

Electron magnetic moment measured

μe=−9.2847646917×10−24 J/T\mu_{\mathrm{e}} = -9.2847646917 \times 10^{-24}\ \text{J/T}

J/TThe magnetic moment of a free electron, negative because its charge is, and about 0.116% larger than one Bohr magneton.

Proton magnetic moment measured

μp=1.41060679545×10−26 J/T\mu_{\mathrm{p}} = 1.41060679545 \times 10^{-26}\ \text{J/T}

J/TThe magnetic moment of the proton, 2.79 nuclear magnetons rather than the 1 a point particle would show — evidence of quark structure.

Neutron magnetic moment measured

μn=−9.6623653×10−27 J/T\mu_{\mathrm{n}} = -9.6623653 \times 10^{-27}\ \text{J/T}

J/TA neutral particle with a magnetic moment of −1.913 nuclear magnetons — proof on its own that the neutron has charged internal structure.

Magnetic flux quantum exact

Φ0=2.067833848461929×10−15 Wb\Phi_{0} = 2.067833848461929 \times 10^{-15}\ \text{Wb}

WbThe smallest unit of magnetic flux that can thread a superconducting loop, h/2e — exact since the 2019 SI redefinition fixed h and e.

Josephson constant exact

KJ=4.835978484169836×1014 Hz/VK_{\mathrm{J}} = 4.835978484169836 \times 10^{14}\ \text{Hz/V}

Hz/VThe frequency-to-voltage ratio 2e/h of a Josephson junction — 483.6 THz per volt, and the modern practical realisation of the volt.

von Klitzing constant exact

RK=25812.8074593045 ΩR_{\mathrm{K}} = 25812.8074593045\ \text{Ω}

ΩThe quantum Hall resistance h/e² ≈ 25.813 kΩ, exact since 2019 and the reference by which the ohm is now realised worldwide.

Conductance quantum exact

G0=0.00007748091729863649 SG_{0} = 0.00007748091729863649\ \text{S}

SThe conductance 2e²/h of a single ballistic quantum channel, about 77.5 μS — the step size in nanoscale wires and atomic point contacts.

Inverse conductance quantum exact

G0−1=12906.40372965225 ΩG_{0}^{-1} = 12906.40372965225\ \text{Ω}

ΩHalf the von Klitzing constant, h/2e² ≈ 12.906 kΩ — the resistance of one perfect ballistic channel and the floor for any nanoscale wire.

Faraday constant exact

F=96485.33212331001 C/molF = 96485.33212331001\ \text{C/mol}

C/molThe charge carried by one mole of electrons, N_A×e ≈ 96485 coulombs — the bridge between the coulombs you meter and the moles you plate.

Proton gyromagnetic ratio measured

γp=267522187.08 s−1⋅T−1\gamma_{\mathrm{p}} = 267522187.08\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The proton's precession rate per unit magnetic field in angular frequency — the constant that turns a magnet strength into an NMR frequency.

Proton gyromagnetic ratio over 2π measured

γp/2π=42577478.461 Hz/T\gamma_{\mathrm{p}}/2\pi = 42577478.461\ \text{Hz/T}

Hz/TThe proton Larmor frequency per tesla, 42.577 MHz/T — the number every NMR spectroscopist and MRI physicist works in directly.

Electron gyromagnetic ratio measured

γe=1.76085962784×1011 s−1⋅T−1\gamma_{\mathrm{e}} = 1.76085962784 \times 10^{11}\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The electron's spin precession rate per tesla, 658 times the proton's — the basis of electron spin resonance and of spin-qubit control.

Relative permittivity of air measured

εr,air=1.00059 —\varepsilon_{r,\mathrm{air}} = 1.00059\ \text{—}

—Typical dielectric constant of dry air at 0 °C and one atmosphere — so close to vacuum that most capacitor and antenna work ignores the difference.

Relative permittivity of water measured

εr,H2O=80.1 —\varepsilon_{r,\mathrm{H_2O}} = 80.1\ \text{—}

—Typical static dielectric constant of liquid water at 20 °C — an outlier among common liquids and the reason water dissolves salts so well.

Relative permittivity of PTFE measured

εr,PTFE=2.1 —\varepsilon_{r,\mathrm{PTFE}} = 2.1\ \text{—}

—Typical dielectric constant of PTFE (Teflon), about 2.1 and almost flat from DC to tens of gigahertz — the benchmark low-loss RF insulator.

Relative permittivity of FR-4 measured

εr,FR-4=4.4 —\varepsilon_{r,\mathrm{FR\text{-}4}} = 4.4\ \text{—}

—Typical dielectric constant of FR-4 circuit-board laminate near 1 GHz — the number behind every microstrip impedance and trace-delay calculation.

Relative permeability of iron measured

μr,Fe=5000 —\mu_{r,\mathrm{Fe}} = 5000\ \text{—}

—Typical maximum relative permeability of commercial soft iron — a wildly variable figure spanning roughly 200 to 5000 with purity and field level.

Relative permeability of mu-metal measured

μr,μ-metal=80,000 —\mu_{r,\mu\text{-metal}} = 80,000\ \text{—}

—Typical relative permeability of annealed mu-metal in weak fields — the nickel-iron alloy used to shield instruments from stray magnetic fields.

Speed of light in water measured

cH2O=224,900,000 m/sc_{\mathrm{H_2O}} = 224,900,000\ \text{m/s}

m/sLight travels through water at about 225,000 km/s, or c/1.333 — the slowing that bends a straw at the waterline and lets Cherenkov detectors work.

Speed of light in glass measured

cglass=197,230,000 m/sc_{\mathrm{glass}} = 197,230,000\ \text{m/s}

m/sTypical propagation speed in crown glass, c/1.52 or about 197,000 km/s — the delay that makes lenses focus and optical fibres carry data.

Mains frequency (North America) measured

f60=60 Hzf_{60} = 60\ \text{Hz}

HzNominal 60 Hz AC power frequency across North America, held within about ±0.05 Hz by grid operators balancing generation against load.

Mains frequency (Europe and most of the world) measured

f50=50 Hzf_{50} = 50\ \text{Hz}

HzNominal 50 Hz AC power frequency used across Europe, Asia, Africa and Oceania, regulated to roughly ±0.05 Hz in normal grid operation.

Nominal mains voltage (North America) measured

V120=120 VV_{120} = 120\ \text{V}

VNominal 120 V RMS at North American outlets, with ANSI C84.1 allowing roughly 114–126 V at the point of utilisation under normal service.

Nominal mains voltage (Europe) measured

V230=230 VV_{230} = 230\ \text{V}

VNominal 230 V RMS single-phase supply under IEC 60038, the harmonised European figure that replaced the old 220 V and 240 V standards.

Earth's magnetic field strength measured

B⊕=0.00005 TB_{\oplus} = 0.00005\ \text{T}

TTypical magnitude of the geomagnetic field at the surface, near 50 μT but ranging from about 25 μT at the equator to 65 μT near the poles.