Hi.
why you don't use from it's dipole equivalent and convert dipole formula to monopole?
you can find dipole antenna formula on any antenna book,for example balanis,stutzman and ....
In general for a half wave dipole and a quarter wave monopole we have (from balanis):
normalized power pattern = [sin(theta)]^3
Radiation resistance(monopole) = 0.5*Radiation resistance(dipole) = 36.5 ohms
directivity(monopole) = 2*directivity(dipole) = 3.286
input impedance(monopole) = 0.5*input impedance(dipole) = 36.5 + j21.25
in fact,monopole antenna is same as dipole antenna that is radiating in half sapce ( 0<theta<90)
good luck