How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator?

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A lossless half-wave dipole in free space already has 2.15 dB of gain over an isotropic radiator, so the dBd figure is always 2.15 dB smaller than the dBi figure for the same antenna. Here 6 dBi − 2.15 dB = 3.85 dBd.