What is the approximate gain of a half-wave dipole in free space relative to an isotropic radiator?

An isotropic radiator is a theoretical point source that radiates equally in every direction, serving as an absolute baseline (0 dBi) for measuring antenna performance. Unlike this theoretical model, a real-world half-wave dipole focuses its radiated energy perpendicular to the wire. Because the dipole concentrates energy in specific directions rather than radiating spherically, it exhibits a gain over the isotropic model. This inherent focusing effect results in a mathematical gain of approximately 2.15 dB, which is typically rounded to 2.1 dB. Other options like 3.0 dB represent a standard doubling of power, a common number in radio mathematics, but this is entirely incorrect for representing the relationship between a dipole and an isotropic radiator.