Effective radiated power

== 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) = {\mathrm{EIRP} \over 4\pi r^2}</math>
Since <math>\mathrm{EIRP} = \mathrm{ERP} \times 1.64</math>,
<math display="block">S(r) = {\mathrm{0.41 \times ERP} \over \pi 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.