The reliability and safety of battery operations necessitate an efficient battery management system (BMS) with accurate battery state of charge (SOC) and capacity estimation techniques. This paper investigates the incremental capacity analysis (ICA) and differential voltage analysis (DVA) methods for onboard battery SOC and capacity estimation. Since the conventional cell terminal voltage based ICA/DVA methods are sensitive to the changed battery resistance and polarization during battery aging processes, the SOC based ICA/DVA methods are proposed to address this problem as so to accurately identify features of interest on incremental capacity (IC) and differential voltage (DV) curves for applications. Three feature points (FPs) that are potential to be easily identified by battery management systems are extracted from the SOC based IC/DV curves, and then the relations between FPs and cell SOCs/capacities are quantified and applied for battery SOC and capacity estimation. The robustness of the proposed approach against various aging levels and erroneous cumulative capacities is evaluated. Promising results with the maximum absolute error of 1.0% and the relative error of 2.0% can be achieved for battery SOC and capacity estimation, respectively. •ICA and DVA methods are developed for onboard battery SOC and capacity estimation.•The SOC based IC/DV curves can reflect the relation between IC/DV values and SOCs.•The relations between feature points and SOCs/capacities are quantified.•The proposed method can perform well even with biased cumulative capacities.