The range equation calculates the attenuation of an RF signal in free space, taking into account the wavelength and the speed of light.

The page below explains how this equation can be expressed in logarithmic terms, to aid in a back-of-the-envelope distance calculation for RF links and repeaters.

Simply stated, the attenuation in free space can be calculated as:

32.44 + 20\log_{10}\left [ f\left ( GHz \right ) \right ] + 20\log_{10} \left [ d \left ( m \right ) \right ]

Where f is the frequency in GHz, and d is the distance in metres. For example, if a transmitter has a power output of +50 dBm, to calculate the receive power at a distance of 50 Km on 902.9 MHz, would be:

32.44 + 20 \log_{10}\left (0.9029\right ) + 20\log_{10}\left ( 50000 \right )

or: 50 – [ 32.44 + (-.88) + (93.97) ], the result of which is -10.6dBm. A strong signal!

The derivation of this formula is here:-