Disclosed is a system and methods for measuring electrochemical state of rechargeable batteries such as state of charge (SoC) and state of health (SoH). In various aspects, the system may include an inductive coil attached to the battery and a battery current sensor. Alternating current with a fixed frequency is applied to the coil to generate magnetic fields, and the magnetic fields induce losses including Eddy current loss and a loss related to battery currents. The system compensates for the effect of the loss related to battery currents for battery electrochemical state estimation. In another aspect, the system uses both coil-based measurement and ampere hour counting (AHC) measurement for SoC measurement. The system conducts coil-based SoC measurement only occasionally to reset the accumulated error of AHC-based SoC measurement. In yet another aspect, the system combines coil-based measurement with other measurements.