Editing Effective radiated power (section)

== Relation to signal strength ==
If the signal path is in free space ([[line-of-sight propagation]] with no [[multipath propagation|multipath]]) the signal strength ([[irradiance|power flux density]] in watts per square meter) <math>\ S\ </math> of the radio signal on the main lobe axis at any particular distance <math>r</math> from the antenna can be calculated from the EIRP or ERP. Since an isotropic antenna radiates equal power flux density over a sphere centered on the antenna, and the area of a sphere with radius <math>\ r\ </math> is <math>\ A = 4\pi\ r^2\ </math> then
<math display="block">\ S(r) = \frac{\ \mathsf{EIRP}\ }{\ 4\pi\ r^2\ } ~.</math>
Since <math>\ \mathrm{EIRP} = \mathrm{ERP} \times 1.64\ ,</math>
<math display="block">\ S(r) = \frac{\ 0.410 \times \mathsf{ERP}\ }{\ \pi\ r^2\ } ~.</math>
After dividing out the factor of <math>\ \pi\ ,</math> we get:
<math display="block">\ S(r) = \frac{\ 0.131 \times \mathsf{ERP}\ }{\ r^2\ } ~.</math>

However, if the radio waves travel by [[ground wave]] as is typical for medium or longwave broadcasting, [[skywave]], or indirect paths play a part in transmission, the waves will suffer additional attenuation which depends on the terrain between the antennas, so these formulas are not valid.