An object is to improve the characteristics of a power storage device such as a charging and discharging rate or a charge and discharge capacity. The grain size of particles of a positive electrode active material is nano-sized so that a surface area per unit mass of the active material is increased. Specifically, the grain size is set to greater than or equal to 10 nm and less than or equal to 100 nm, preferably greater than or equal to 20 nm and less than or equal to 60 nm. Alternatively, the surface area per unit mass is set to 10 m2/g or more, preferably 20 m2/g or more. Further, the crystallinity of the active material is increased by setting an XRD half width to greater than or equal to 0.12° and less than 0.17°, preferably greater than or equal to 0.13° and less than 0.16°.