Electromagnetic Wave Solver Calculator

How to use

Solve one wave variable in one declared medium

1. Select frequency, wavelength, or relative permittivity as the unknown; the corresponding field is disabled.
2. Enter frequency in MHz or wavelength in meters for the same phase-wave state.
3. Enter positive real relative permittivity and permeability for a homogeneous lossless medium.
4. Read the solved quantity together with phase speed and intrinsic impedance; they are coupled by the constitutive assumptions.
5. Inspect period and phase constant before transferring the result into antenna, material, or propagation work.
6. Use the f lambda residual to verify the wave relation before copying or exporting the current solution.

Plane-wave fundamentals

Five ideas behind the medium solution

Source frequency

The temporal oscillation rate, which remains continuous across a stationary material interface.

Phase wavelength

The distance between equal carrier phases in the declared medium, equal to phase speed divided by frequency.

Relative permittivity

The positive real electric constitutive ratio used by this ideal lossless model.

Relative permeability

The corresponding magnetic constitutive ratio, retained explicitly even when near unity.

Intrinsic impedance

The E/H ratio of a uniform traveling plane wave, not a device terminal impedance.

Calculation method

Close the constitutive and kinematic equations together

The medium first sets v_p = c0/sqrt(epsilon_r mu_r). The selected unknown is then solved from v_p = f lambda, or relative permittivity is inferred from measured frequency and phase wavelength. Period and phase constant follow from the solved state.

Intrinsic impedance is calculated independently as eta0 sqrt(mu_r/epsilon_r). The final residual compares f lambda with the constitutive phase speed so unit or input wiring errors cannot hide behind a plausible wavelength.

Evidence to retain

Keep the material state with the solved wave

Record specimen identity, lot and orientation, temperature, moisture, frequency, measurement fixture and calibration, extracted complex permittivity and permeability when available, uncertainty, sample thickness, interface assumptions, and whether the reported wavelength is measured phase wavelength or inferred from nominal material data.

Scope and limitations

Where the lossless plane-wave model stops

• No conductivity, dielectric loss tangent, magnetic loss, attenuation constant, or complex impedance
• No dispersion, anisotropy, nonlinearity, plasma, negative-index, or resonant constitutive behavior
• No interface reflection, refraction, polarization conversion, or multilayer interference
• No waveguide cutoff, cable modes, antenna near field, or cavity boundaries
• No field amplitude, Poynting power, photon energy, or exposure limit calculation
• No material certification from a single inferred relative-permittivity value

The solver describes a uniform plane wave in a linear, homogeneous, isotropic, lossless, nondispersive medium with positive real relative permittivity and permeability. It does not model conductivity, complex material parameters, waveguides, plasma cutoffs, interfaces, or group delay.

Key terminology

Electromagnetic-wave glossary

Plane wave

An ideal field with constant phase over planes transverse to propagation.

Phase speed

The speed at which a fixed phase point travels through the medium.

Phase constant

The phase change in radians per meter, equal to 2 pi divided by wavelength.

Constitutive parameter

A material property linking electric or magnetic flux density to its corresponding field.

Intrinsic impedance

The field ratio E/H for a traveling plane wave in the bulk medium.

Dispersion

Frequency dependence of propagation parameters that can separate phase and group velocities.

Practical cases

Two solutions with different engineering consequences