Electromagnetic Wave Speed Calculator (Maxwell)
Speed of an electromagnetic wave in a material, its velocity factor, refractive index, wavelength and wave impedance from εr and µr.
Results
The dashed line marks the value you entered.
What this tool does
Maxwell's equations predict waves whose speed is set by two properties of the material, its permittivity and its permeability: v = 1/√(με). Put in the values for empty space and out comes 299 792 458 m/s — which is how, in 1865, light was recognised as an electromagnetic wave. In a cable or a circuit board the same formula gives the velocity factor: about 66 % in solid polyethylene, roughly half the speed of light in FR-4. Beware that εr depends on frequency: water is around 80 at radio frequencies but behaves like 1.33² ≈ 1.8 for visible light.
Formula
v = 1 ÷ √(μ ε) = c ÷ √(μᵣ εᵣ) · n = √(μᵣ εᵣ) · Z = Z₀ √(μᵣ ÷ εᵣ), Z₀ = μ₀ c ≈ 376.73 Ω
Variables
| Symbol | Meaning | Unit |
|---|---|---|
er | Relative permittivity εr | — |
mr | Relative permeability µr | — |
f | Frequency | MHz |
V | Wave speed | m/s |
VF | Velocity factor | % |
N | Refractive index n | — |
WL | Wavelength in the material | m |
W0 | Wavelength in vacuum | m |
Z | Wave impedance | Ω |
DL | Delay per metre | ns/m |
Worked example
- Relative permittivity εr2.25
- Relative permeability µr1
- Frequency100 MHz
- Wave speed199,861,639 m/s
- Velocity factor66.67 %
- Refractive index n1.5000
- Wavelength in the material1.99862 m
- Wavelength in vacuum2.99792 m
- Wave impedance251.15 Ω
- Delay per metre5.003 ns/m
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.