Abstract: Volumetric accuracy in hemodialysis systems is provided by swapping pumps between the replacement fluid side and the output side for a hemofiltration system and between the return fluid side and the sorbent side for a closed-loop, sorbent-based system, such that same quantity of fluid is pumped at each point after the end of an even number of pump swaps. A method for calculating the time interval between swaps is provided based on an allowable difference in amount pumped in the two functions at any given time. A mechanism is provided for compensating for the differences in head pressure presented to the pumps for fluid coming from the replacement-fluid containers or the reservoir and that coming back from the patient through the dialyzer. The pump-swapping system provides an accurate means that can be inexpensively implemented, including using a disposable device.