Memory devices are provided. A memory device includes a voltage generation circuit that includes an offset compensator configured to receive a reference voltage and an offset code and to link the offset code to the reference voltage. The voltage generation circuit includes a comparator configured to compare the reference voltage linked to the offset code with a bit line pre-charge voltage and to output driving control signals. The voltage generation circuit includes a driver configured to output the bit line pre-charge voltage at a target level of the reference voltage in response to the driving control signals. The voltage generation circuit includes a background calibration circuit configured to generate the offset code for performing control so that a target short current flows through an output node of the driver from which the bit line pre-charge voltage is output. Related methods of generating a bit line pre-charge voltage are also provided.