Background current noise is often a significant limitation when using constant-potential amperometry for biosensor application such as amperometric recordings of transmitter release from single cells through exocytosis. In this paper, we fabricated thin-film electrodes of gold and conductive polymers and measured the current noise in physiological buffer solution for a wide range of different electrode areas. The noise measurements could be modeled by an analytical expression, representing the electrochemical cell as a resistor and capacitor in series. The studies revealed three domains; for electrodes with low capacitance, the amplifier noise dominated, for electrodes with large capacitances, the noise from the resistance of the electrochemical cell was dominant, while in the intermediate region, the current noise scaled with electrode capacitance. The experimental results and the model presented here can be used for choosing an electrode material and dimensions and when designing chip-based devices for low-noise current measurements.