Abstract: A breathing system for ventilating a patient has a gas channel enclosing a gas channel volume (V), and a compliance (C). The system has a flow calculation unit operative to determine a gas flow estimate (Fe) at a flow estimate location in the gas channel. The gas flow estimate (Fe) is based on a relationship between a monitored gas flow (Fm) in the gas channel and a compressible gas flow (Fc) which depends on the compliance (C) in the gas channel. The monitored gas flow (Fm) is a gas flow at a monitoring location in the gas channel and the compressible gas flow (Fc) is a flow of gas in the gas channel between the flow estimate location and the monitoring location, and the flow estimate location is remote from the monitoring location.