No, there is not any single formula that I've ever seen, but it could be created.
Each component of loss has to be addressed individually because each is determined by different factors. Conduction loss is relatively straight forward but ON resistance is influenced by gate-source voltage and has a moderately large positive temperature coefficient. Switching loss depends on the transition times, which in turn depend at least in part on gate drive, and the nature of the load. Turn on may be faster than turn off and/or the "load" may be entirely different at turn-on than turn off (e.g. an inductive load in discontinuous current mode forces the current to be zero at start of turn-on, but the "opposite" at turn-off, and both cases differ from a resistive load. In certain applications the reverse recovery losses of the FETs own intrinsic body diode or that of another diode must be considered. In some applications the intrinsic body diode is allowed to avalanche.
There is no reason one grand formula could not be produced that included terms for all possible losses, some of which would be zero in many cases. This sort of thing is convenient (?!) for calculations but useless from a design point of view. In design it is useful to evaluate each loss term so that the possibility of minimizing each or trading off one against another can be done.
MOSFET losses is a complex topic. A great deal has been written about it and much is available on the web from several of the large manufacturers of FETs such as Vishay, Nexperia and Infineon (some of the papers will originally have been from International Rectifier, a major pioneer of power MOSFETs).