Use the calculator to estimate effective permittivity in three common cases: (1) two-material mixtures (using several mixing rules), (2) microstrip effective dielectric constant, and (3) stacked dielectric layers. For mixtures, enter relative permittivities (dielectric constants, dimensionless) and a volume fraction; for a two-material mixture the volume fractions should satisfy V1 + V2 = 1.

Effective Permittivity Calculator

Mixtures
Microstrip
Layered
Enter relative permittivities (dimensionless) and volume fraction of Material 1 (0–1). Loss tangent is optional.

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Effective Permittivity Formula (Parallel / Volume-Weighted)

The following formula is the parallel (volume-weighted) mixing rule for a two-material mixture. It is also the Wiener upper bound and applies to idealized cases such as layered dielectrics with the electric field parallel to the layers. In general, effective permittivity depends on geometry/microstructure and field direction, so other models (series/harmonic lower bound, Maxwell–Garnett, Bruggeman, etc.) may be more appropriate.

ε_e = (ε_1 * V_1) + (ε_2 * V_2)

Variables:

  • ε_e is the effective permittivity (often reported as an effective relative permittivity, which is dimensionless)
  • ε_1 is the (relative) permittivity of material 1 (dielectric constant, dimensionless)
  • V_1 is the volume fraction of material 1
  • ε_2 is the (relative) permittivity of material 2 (dielectric constant, dimensionless)
  • V_2 is the volume fraction of material 2 (for a two-material mixture, V_2 = 1 − V_1)

To calculate this parallel/volume-weighted effective permittivity, multiply the permittivity of each material by its respective volume fraction and sum the results.

What is Effective Permittivity?

Effective permittivity is an equivalent (homogenized) permittivity used to model a composite material or electromagnetic structure (for example, a two-phase mixture, a layered stack, or a microstrip line). It is often expressed as an effective relative permittivity (effective dielectric constant), which is dimensionless. By contrast, relative permittivity (dielectric constant) refers to the intrinsic property of a single homogeneous material (εr = ε/ε0).

How to Calculate Effective Permittivity?

The following steps outline how to calculate the Effective Permittivity.

  1. First, determine the (relative) permittivity of material 1 (ε_1).
  2. Next, determine the volume fraction of material 1 (V_1).
  3. Next, determine the (relative) permittivity of material 2 (ε_2).
  4. Next, determine the volume fraction of material 2 (V_2), ensuring V_1 + V_2 = 1 (for two materials, V_2 = 1 − V_1).
  5. Finally, if the parallel/volume-weighted model applies, calculate ε_e = (ε_1 * V_1) + (ε_2 * V_2). Otherwise, use a different mixing model (such as series, Maxwell–Garnett, or Bruggeman) as appropriate for the geometry.
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (using the parallel/volume-weighted rule).

Permittivity of Material 1 (ε_1) = 4.5

Volume Fraction of Material 1 (V_1) = 0.6

Permittivity of Material 2 (ε_2) = 2.3

Volume Fraction of Material 2 (V_2) = 0.4

Effective permittivity (parallel/volume-weighted): ε_e = 4.5(0.6) + 2.3(0.4) = 2.7 + 0.92 = 3.62