Directivity of antennas is a measure of the concentration of radiation in the direction of theaximum:

directivity =  = (1)

Directivity and gain differ only by the efficiency, but directivity is easily estimatedfrom patterns. Gain—directivity times efficiency—must be measured.

The average radiation intensity can be found from a surface integral over theradiation sphere of the radiation intensity divided by 4π, the area of the sphere insteradians:

average radiation intensity =  (2)

This is the radiated power divided by the area of a unit sphere. The radiation intensityU(θ,φ) separates into a sum of co- and cross-polarization components:

U₀ =  (3)

Both co- and cross-polarization directivities can be defined:

directivity_C= directivity_× = (4)

Directivity can also be defined for an arbitrary direction D(θ, φ) as radiation intensitydivided by the average radiation intensity, but when the coordinate angles are notspecified, we calculate directivity at U_max.