A breathing assistance system configured to determine pressure drop may include a gas delivery system configured to deliver gas toward a patient, one or more sensors configured to measure one or more parameters of gas delivered by the gas delivery system, a calibration module, and a pressure drop calculation module. The calibration module may be configured to perform one or more pressure drop calibration tests, each pressure drop calibration test measuring a pressure drop in gas flowing through a breathing assistance system apparatus at a particular flow rate； and based at least on the results of the one or more pressure drop calibration tests, generating a non-linear equation relating (a) pressure drop in gas flowing through the breathing assistance system apparatus with (b) flow rate of gas flowing through the breathing assistance system apparatus. The pressure drop calculation module may be configured to determine pressure drops in gas flowing through the breathing assistance system apparatus for various flow rates based at least on the non-linear equation.
