The power Pr returning to the receiving antenna is given by the equation:
- Pt = transmitter power
- Gt = gain of the transmitting antenna
- Ar = effective aperture (area) of the receiving antenna; this can also be expressed as , where
- = transmitted wavelength
- Gr = gain of receiving antenna
- σ = radar cross section, or scattering coefficient, of the target
- F = pattern propagation factor
- Rt = distance from the transmitter to the target
- Rr = distance from the target to the receiver.
In the common case where the transmitter and the receiver are at the same location, Rt = Rr and the term Rt² Rr² can be replaced by R4, where R is the range. This yields:
This shows that the received power declines as the fourth power of the range, which means that the received power from distant targets is relatively very small.