We give an exact enumeration of the unlabeled disconnected posets according to the number of connected components of the posets. This result establishes that the enumeration of unlabeled posets belonging to a class that is closed under the direct sum depends mainly on the enumeration of unlabeled connected posets contained in the class. We also give an algorithm to determine the parameters involved in the enumeration formula, and finally, find the number of unlabeled disconnected posets with a certain number of elements. We show that the enumeration algorithm runs in polynomial time.