System-level simulations for ad hoc networks require the mean power that is received by an arbitrary unit of the piconet as an input parameter. Since the radio channel in piconets depends strongly on the environment in which two communicating units are located, easily applicable models for the mean received power must be determined by a few relevant, explicitly geometrical quantities. Starting from a very general description of the stochastic radio channel by an integral equation, it is shown that these quantities are the surface area and the volume of the domain in which the transmitter and the receiver can move. On the basis of an exponential path loss model with path loss exponent q, a lower and an upper bound for the mean received power are derived. The resulting analytical expressions are highly flexible and allow a quick calculation of bounds for the mean received power in many practically relevant cases.