Calculate field strength or power density from the other using the free-space impedance formula with V/m, V/ft, V/cm and W/m², W/ft², W/cm² conversions.

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Free-space plane-wave model (377 Ω). The peak convention assumes a sinusoid; general near-field measurements need a different model.

Field Strength to Power Density Formula

The following formula gives average power density from the peak electric field of a sinusoidal free-space plane wave. For RMS electric field, use S = E² / Z instead.

S = (E²) / (2 × Z)

Variables:

  • S is the power density (W/m²)
  • E is the sinusoidal peak electric field strength (V/m) in this formula.
  • Z is the impedance of free space (Ω)

For sinusoidal peak field, square the field strength and divide by twice the impedance of free space. For RMS field, divide by the impedance without the factor of two. This conversion does not describe general near-field power flow.

Field Strength to Power Density Conversion Table (Sinusoidal peak, plane-wave, Z0 = 377 Ω)
Field Strength (V/m) Power Density (W/m²)
10.001
20.005
30.012
50.033
100.133
200.531
27.51.003
301.194
38.81.997
503.316
61.45.000
757.462
10013.263
13724.893
15029.841
20053.050
300119.363
400212.202
500331.565
10001326.260
Uses free-space plane-wave relation: S = E² / (2·Z0). With Z0 = 377 Ω, average S is in W/m² when sinusoidal peak E is in V/m.

What is Field Strength?

Field strength, also known as electric field strength, is a measure of the force exerted by an electric field on a charged particle. It is typically measured in volts per meter (V/m). Field strength is an important parameter in electromagnetics and is used to describe the intensity of an electric field at a particular point in space. It plays a crucial role in the transmission and reception of electromagnetic waves, such as radio waves, and is a key factor in determining the power density of the field.

How to Calculate Field Strength to Power Density?

The following steps outline how to calculate the power density from field strength and impedance of free space.

  1. First, determine the sinusoidal peak field strength (E) in volts per meter (V/m).
  2. Next, determine the impedance of free space (Z) in ohms (Ω). The standard value is 377 Ω.
  3. Next, calculate the power density (S) using the formula S = (E²) / (2 * Z).
  4. Finally, calculate the power density.
  5. 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.

Sinusoidal Peak Field Strength (E) = 50 V/m

Impedance of Free Space (Z) = 377 Ω