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EM Field and Power-Density Converter

Convert E, H, B, and average power density for a free-space far-field plane wave.

FORMULAv1.0.0
INPUT PARAMETERS

Choose one known far-field quantity

Convert E, H, B, and average power density for a free-space far-field plane wave.

Applicability boundaryFree-space far-field plane waves only. The E/H ratio is not fixed in the near field.
CALCULATION RESULT

Calculation result

Calculated locally
∿

Enter the parameters and run the calculation to see results and model assumptions here.

FORMULA & TRACEABILITY

Formulas and applicability

Formulas, variables, and model boundaries are published. References last reviewed on 2026-08-30.

4 formulas · 3 references
CORE EQUATIONS

Core equations

These equations directly produce the primary results and define the tool’s core model.

2
F01

Free-space plane-wave impedance

E / H = Z₀

For a uniform free-space far-field plane wave, the ratio of RMS electric to magnetic field equals vacuum impedance.

E
RMS electric field strengthV/m
H
RMS magnetic field strengthA/m
Z₀
Vacuum characteristic impedance, 376.730 313 412Ω
Applicability
  • Free-space far field
  • Uniform plane wave
  • Not applicable in the reactive or radiating near field
F02

Average power density

S = EH = E²/Z₀ = H²Z₀

Use RMS field strength to calculate time-average Poynting power density.

S
Time-average power densityW/m²
Applicability
  • E and H are RMS amplitudes of the same plane wave
  • Medium approximates free space
DERIVED & CONVERSION

Derived and conversion equations

Derive units, levels, and supporting engineering quantities from the core values.

2
F03

Magnetic field strength and flux density

B = μ₀H

Calculate magnetic flux density from magnetic field strength in vacuum or an air approximation.

B
RMS magnetic flux densityT
μ₀
Vacuum permeability (2022 CODATA)H/m
Applicability
  • Free-space or air approximation
  • Do not use a fixed μ₀ near magnetic materials
F04

Logarithmic levels for field quantities and power density

L_E = 20log₁₀(E/1μV·m⁻¹)；L_S = 10log₁₀(S/1mW·m⁻²)

Use 20 times the logarithm for field quantities and 10 times for power quantities, with each reference stated.

Applicability
  • Electric-field reference is 1 μV/m
  • Power-density reference is 1 mW/m²
REFERENCES

References

01ITU-R · Recommendation P.525-5Calculation of free-space attenuation2024 · Gives free-space propagation and the plane-wave relationships among electric field, magnetic field, and power flux density.
02NIST / CODATA · NIST SP 961 database, 2022 adjustment2022 CODATA recommended values of the fundamental constants2024 web edition · Provides current recommended values for vacuum impedance and permeability.
03NIST · NIST SP 811NIST Guide to the SI, Chapter 8: Logarithmic quantities and units2008 (web edition updated) · Specifies 20 lg for field quantities and 10 lg for power quantities, with explicit references.
Engineering use notice

Results use the models and assumptions shown on this page for design estimates and pre-compliance risk review. Complex structures, dispersion, near-field coupling, and test setup can cause significant deviation.

FAQ

Frequently asked questions

What is the E/H ratio of a free-space plane wave?

In the far-field plane wave, E / H = Z₀ = 376.73 Ω (the vacuum wave impedance). For example, E = 1 V/m corresponds to H ≈ 2.65 mA/m.

How do power density and field strength convert?

S = E² / Z₀, so E = √(S × 376.73); 1 W/m² corresponds to E ≈ 19.4 V/m. Remember: 20·log for field quantities, 10·log for power.

Why do these ratios fail in the near field?

Near-field E/H depends on the source: high-impedance electric sources (e.g., rods) over-weight E, low-impedance magnetic sources (e.g., loops) over-weight H. The ratio is not fixed and wave impedance breaks down.

PRE-COMPLIANCE SUPPORT

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