The energy intercepted by the target will be:

(1)

where s is the back scattering cross section of the target. NOTE: s is not necessarily equal to the geometrical cross section.

The amount of energy which gets back to the antenna is:

(2)

The amount of power that is collected by the antenna is:

(3)

where [P_{r}] = watts

A_{e} = effective area of the
antenna

What are typical values of these quantities?

P_{t} ~ 10^{5} W

r ~ 100 km

G ~ 40 dB

s ~ 1 m^{2}

Inserting these numbers into the above equation gives

The gain can be express in terms of the effective area of the antenna and the wavelength of the radar by:

or (4)

so substituting (4) into (3) gives:

This is the radar equation for a point target.