# Dipole antenna radiation field equation

Can anybody provide me with an idealised formula that describes the radiation pattern of an omnidirectional dipole antenna?

In particular I am interested in the formula that creates a plot similar to the following:

Note: I am looking for a simplified closed-form equation, not a full field simulation.

• The polar pattern in the OP reports 10.46 dBi "gain," which is much higher than the 2.15 dBi directivity of a center-fed, 1/2-wave dipole in free space. – Richard Fry Oct 24 '18 at 23:14

According to Antennas by John Kraus, the far E-field for a center-fed $$\lambda/2$$ dipole in free space is:
$$E = \frac{\cos\left({\pi\over 2}\cos\theta\right)}{\sin\theta}$$
In the case of a vertically mounted antenna, $$\theta$$=0 at the horizon of the plot.