An amperometric gas sensor for determining oxygen content in a gas mixture includes a solid-state electrolyte. A first electrode configured as a cathode and a second electrode configured as an anode are disposed on the solid-state electrolyte and exposed to the gas mixture. The cathode is in contact with the gas mixture without any interposed diffusion barrier and has a design such that a flow of oxygen molecules from the gas mixture to a three-phase boundary between the solid-state electrolyte, the cathode and the gas mixture is limited in a defined manner. A voltage source configured to apply a DC voltage between the electrodes. A measuring device is configured to measure a limiting current flowing between the electrodes as a measure of the oxygen content in the gas mixture.