The calculator gives the equivalent power flux density in dBW/m² and the power an isotropic source would need to radiate (EIRP) to produce the provided field strength at the provided distance.
The default values here are equal to FCC part 15 limits for an unintentional radiator above 960 MHz. Notably, the FCC limits take into account the fact that at 3m you can easily be experiencing near field effects. The 10m limit is 300 µV/m which comes out to a 6dB higher EIRP from an isotropic radiator. Unsurprisingly, this calculator is not going to accurately predict EIRP based on field strength in the near field.
In free space, the power flux density \(S\) (W/m²) is related to the electric field strength \(E\) (V/m) by the impedance of free space \(Z_0 = 120\pi\,\Omega=376.73\Omega\):
\[S = \frac{E^2}{Z_0} \quad (1)\]Where:
In dB form, with field strength in dBµV/m (i.e. \(20\log_{10}(E_{\mu\text{V/m}})\)), power flux density in dBW/m² is:
\[S_{\text{dBW/m}^2} = E_{\text{dB}\mu\text{V/m}} - 10\log_{10}(Z_0) - 120 \quad (2)\]The factor of 120 comes from 20*log10(1e6) for the conversion from µV/m to V/m.
For an isotropic source, the power flux density at distance \(d\) is:
\[S = \frac{\text{EIRP}}{4\pi d^2} \quad (3)\]Where:
So the equivalent isotropic power that would produce your given field strength at distance \(d\) is: \(\text{EIRP} = S \cdot 4\pi d^2\). In dBW:
\[\text{EIRP}_{\text{dBW}} = S_{\text{dBW/m}^2} + 10\log_{10}(4\pi d^2) \quad (4)\]This relationship is independent of frequency and depends only on field strength and distance. If you consider an isotropic receiver in this field, the power it receives would varry with frequency since its effective area is a function of frequency, but the electric field strength and power flux density at this location is not a function of frequency.