Question

How to calculate half power beamwidth from radiation pattern of monopole?

Answer 1

You’re asking the wrong question. You don’t ‘calculate’ the half-power beam width of a half wave dipole antenna; you just know it’s 78 degrees, or 1.36 radians. It’s a constant, and doesn’t change no matter what the size or frequency of your antenna is (as long as the length stays much greater than the diameter) because you’ve established the relationship between the two as ‘half wave’. In all cases your antenna length is one half of the wavelength λ for whatever frequency you’re using. This ratio in essence sets the half power beamwidth.

Instead, what you might be interested in is deriving this value.