Antenna gain and directivity

Directivity (D) is the ratio of maximum radiation intensity to the average radiation intensity: D = 4πU_max/P_rad. It depends only on the pattern shape.

Gain (G) is the same ratio but referred to the input power, so it includes losses: G = 4πU_max/P_in = η·D, where η is the radiation efficiency. Hence G ≤ D. Example: λ/2 dipole D = 1.64; with η = 0.97, G ≈ 1.59 (2.0 dBi).