The majority of methods used for lithium-ion (Li-ion) capacity estimation are usually restricted to certain applications. Such methods often are time consuming and inconsistent with actual experimental data as well as depending on complicated battery operating and/or aging conditions. A geometrical approach to Li-ion battery capacity estimation is presented in this work. The proposed method utilizes four geometrical features that are sensitive to slight changes in the performance degradation of a Li-ion battery. The Laplacian Eigenmap method is used to establish an intrinsic manifold, and the geodesic on the manifold is used to estimate battery capacity. Tests are conducted based on data obtained under different operating and aging conditions provided by NASA Prognostics Center of Excellence. The evaluation results suggest that the proposed geometrical approach can be used to estimate Li-ion battery capacity accurately for the conditions given in this article.