An expression is derived for noise in the tank circuit of a superconducting quantum flux detector run at a radiofrequency. This noise is limited by the sensing element of the device, the superconducting ring with a weak link, and is therefore intimately related to the thermal fluctuations in the ring. Not considering external noise, the superconducting ring and the tank circuit together with the preamplifier should exhaust the important sources of noise in the flux detector.