How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator?
Why Antenna gain can be referenced either to an isotropic radiator (dBi) or to a half-wave dipole (dBd). A half-wave dipole itself has 2.15 dB of gain over an isotropic radiator, so dBd = dBi - 2.15. Here 6.0 dBi - 2.15 dB = 3.85 dBd.
Watch out The choice that says 8.15 dB comes from adding 2.15 instead of subtracting it, which is the conversion the other direction (dBd to dBi). The choice that says 6.0 dB ignores the reference change entirely.
Remember 2.15: dBi minus 2.15 equals dBd. The dipole already beats isotropic, so the dBd number is always smaller.
The dipole catches the 2:15 train ahead of isotropic. Measured from the dipole, 6 dBi is only 3.85 dBd.