A drilling system used with drilling fluid for drilling a wellbore has at least one choke in adjustable communication with flow from the wellbore. A programmable control device determines a flow coefficient value of the choke from a measured position value and a stored characteristic of the choke. The device then calculates a first value of the flow of the drilling fluid from the wellbore through the choke based on the flow coefficient value and a pressure differential measured across the choke. The device adjusts operation of the drilling system at least partially based on the calculated flow value. To adjust operation, the device can set the choke (or another choke) to a set flow value relative to the calculated first flow value. Density of the flow can also be determined so the device can adjust operation based on mass flow rate.