Antenna gain ($G(\hat{\mathbf{r}})=4\pi r^2{S}_r/P_{\mathrm{in}}$)

Antenna gain compares the far-field energy flux in a specified direction with the flux that an isotropic radiator would produce using the same input power. Thus $S_r=G{P}_{\mathrm{in}}/(4\pi r^2)$. Gain includes radiation efficiency; it must be distinguished from a voltage or current amplifier gain and from directivity when losses matter.

The fraction of accepted input power radiated by an antenna. With consistent feed definitions, antenna gain is radiation efficiency times antenna directivity. Ohmic losses reduce the efficiency, while feed mismatch is usually tracked separately.