Calculate radiation power of an antenna in respect to a given antenna radiation pattern and a given angle
The parameter I was looking for is the EIRP which gives us the radiated power in direction of the maximum antenna gain in dBm or mW. 



source: http://cdn.everythingrf.com/live/erp_eirp_formula.PNG

The EIRP can also be calculated for any other direction if you take the loss in dB from the radiation pattern. These values are measured in dB and they are relative to the antenna gain. So if you take the picture from Update 1, the antenna gain at 30° would be decreased about 4.5 dB. The directive antenna gain at 30° would be -1.5 dBi (3 bBi which is the max gain of the anetnna - 4.5 dB).
Now you can do the calculation of the EIRP by insert the -1.5 dBi for the variable Ga.