A method for managing an electrochemical accumulator or a storage battery includes determining an estimated value of a state of deterioration of the accumulator from the accumulator's history of voltage values, intensity of current flow, and temperature. The estimated value is a barycentric value of the state of deterioration calculated as a barycenter of at least two values. The at least two values include a first value indicative of the state of deterioration of the accumulator calculated by a first method and a second value indicative of the state of deterioration of the accumulator calculated by a second method different from the first method. From an initial commissioning state of the accumulator, barycentric coefficients are varied at least once to calculate the next barycentric value when a previous value of the state of deterioration of the accumulator, calculated according to the first method, has passed a first threshold.