The power flow density in the space can be obtained by the Poynting vector.
The average Poynting vector is given by
The filed which contribute to the power flow are essentially the radiation fields. The average Poynting vector therefore is
The total power radiated by the antenna can be calculated by integrating the Poynting vector over a sphere of any radius enclosing the antenna. The total power radiated by the antenna is
After substituting for and doing some manipulations, and noting that the intrinsic impedance of the medium = , we get the total radiated power as
The total radiated power of the Hertz dipole is proportional to the square of the normalized length (normalized with respect to the wavelength) of the dipole.
Longer the length more will be the radiated power for a given excitation current. Note however, that for increasing the radiated power, the length can not be increased arbitrarily. For the Hertz dipole we should have .
Radiation Resistance
If the Hertz dipole is seen from its terminal, it appears like a resistance which consumes power. This resistance is directly related to the power radiated by the dipole.
A hypothetical resistance which will absorb same power as that radiated by the Hertz dipole when excited with the same peak current , is called the Radiation Resistance of the antenna.
The radiation resistance of the Hertz dipole is
For a Hertz dipole of length , the radiation resistance is about 8 ohms.
and doing some manipulations, and noting that the intrinsic impedance of the medium = 
, we get the total radiated power as 
. 
, is called the Radiation Resistance of the antenna. 
, the radiation resistance is about 8 ohms. 
