A battery capacity estimation apparatus includes one or more hardware processors that: calculate a current integrated value by integrating electric currents of a secondary battery system whose capacity is to be estimated; calculate an SOC estimate value in a stabilization state where a change in SOC of a secondary battery per unit time is comparatively small; perform a regression analysis in which the current integrated value is defined as a dependent variable and the SOC estimate value is defined as an independent variable, the regression analysis being performed while correcting the current integrated value based on a value of a coefficient of determination so that a result of the regression analysis has predetermined accuracy; and estimate a capacity of the secondary battery system based on the result of the regression analysis.