A sensor designed to determine the amount and concentration of analyte in a sample having a volume of less than about 1 μL. The sensor has a working electrode coated with a non-leachable redox mediator. The redox mediator acts as an electron transfer agent between the analyte and the electrode. In addition, a second electron transfer agent, such as an enzyme, can be added to facilitate the electrooxidation or electroreduction of the analyte. The redox mediator is typically a redox compound bound to a polymer. The preferred redox mediators are air-oxidizable.The amount of analyte can be determined by coulometry. One particular coulometric technique includes the measurement of the current between the working electrode and a counter or reference electrode at two or more times. The charge passed by this current to or from the analyte is correlated with the amount of analyte in the sample. Other electrochemical detection methods, such as amperometric, voltammetric, and potentiometric techniques, can also be used.The invention can be used to determine the concentration of a biomolecule, such as glucose or lactate, in a biological fluid, such as blood or serum. An enzyme capable of catalyzing the electrooxidation or electroreduction of the biomolecule is provided as a second electron transfer agent.