# Effective Area

Gain and directivity of an antenna in transmitter or receiver operation are equal (reciprocity).

The received power ${P}_{r}$ is obtained from power density $S$ (electromagnetic field).

Effective area of an antenna ${A}_{e}$ is defined according to:

$${\mathrm{P}}_{r}={A}_{e}\cdot S$$

Isotropic antenna:

$${A}_{ei}=\frac{{\lambda}^{2}}{4\pi}$$

Real antenna with directivity, $D$ :

$${A}_{e}=D\cdot {A}_{ei}$$