# Calculating receive wattage given transmit power, antennae dBi and path loss

I would like to understand how to calculate receive wattage given the following (excluding feeder loss and SWR):

Transmit 50 dBm (100W) => 24 dBi directional antenna => 30 dB path loss => 24 dBi directional antenna (receive) => wattage?

For instance, say we're working at a wavelength of 2 meters. The Friis formula tells us that the path loss will be $$20 \log \left( \frac{4\pi d}{2 m} \right)$$. Setting that equal to 30, we get $$d$$ = 5.03 meters. But a gain of 24 dB for a 2 meter wavelength requires a parabolic dish at least 10 meters in diameter, for which the far field begins (and the Friis equation is valid) only at a distance of at least 100 meters! No matter how you slice it, the laws of physics won't let you do that. So your example numbers don't represent a physically possible system.