The Cramer-Rao bounds for battery state of charge, capacity and resistance estimation are derived in this paper. Independent of any specific form of observers, the bounds explore the quality of the data collected for estimation and indicate the best achievable accuracy of any (unbiased) estimator under measurement noise. The derivation is performed based on an equivalent circuit model. First, the Cramer-Rao bounds for standalone estimation, where only one state/parameter is estimated, is derived. The discussion is then extended to combined estimation where multiple state/parameters are estimated from the same data set. It is found that for current inputs that satisfy certain patterns, loss of accuracy in combined estimation can be avoided. The derived explicit analytic expressions are easy to use for improving the accuracy of both online and offline state/parameter estimation.