Directivity is the ratio of the radiation intensity in a given direction from the antenna in relation to the radiation intensity averaged over all directions.

If the main direction of radiation is known, the directivity D can be calculated for each antenna pattern with the following equation:

D = ( S max S i ) r = c o n s t , P t = c o n s t

S max indicates the maximum radiated power density and S i indicates the power density radiated by the isotropic radiator.

Figure 1. Graphical representation of directivity.

It is also possible to determine D from the directional characteristic with:

D = 4 π φ = 0   2 π ϑ = 0   π C 2 ( ϑ , φ ) sin ( ϑ )   d ϑ   d φ

If the antenna pattern consists of a discrete number of values, the integrals in the equations must be substituted with a summation with increments Δ ϑ and Δ φ :

D = 4 π Δ ϑ Δ φ i = 1 2 π Δ φ j = 1 π Δ ϑ C 2 ( i Δ ϑ , j Δ φ ) sin ( j Δ φ )

Often the directivity of an antenna is given in dB. The logarithmic value D d b in dB can be obtained from the linear value D of the directivity with the following equation:

D d B = 10 log D