An antenna is said to have a gain of 4.1 dBi. How much gain is this over a half-wave dipole antenna?

To convert gain measured against an isotropic radiator (dBi) to gain measured against a half-wave dipole (dBd), you must subtract 2.1 dB. This is because a standard half-wave dipole inherently has 2.1 dB of gain over a theoretical isotropic radiator. Therefore, to find the gain over a dipole for an antenna with 4.1 dBi, the math is simply 4.1 dBi - 2.1 dB = 2.0 dB. The other options result from either not knowing the 2.1 dB conversion factor or adding it instead of subtracting.