Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless "isotropic antenna", which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi). An alternative definition compares the received power to the power received by a lossless half-wave dipole antenna, in which case the units are written as "dBd". Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is formula_1. For a given frequency, the antenna's effective area is proportional to the power gain. An antenna's effective length is proportional to the "square root" of the antenna's gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any reciprocal antenna when receiving is equal to its gain when transmitting.