A discharge module is configured to determine a change in capacity of the battery between: (i) a measurement of a first open circuit voltage (OCV) of a battery of a vehicle; and (ii) a measurement of a second OCV of the battery. A lookup table is stored in memory and includes reference states of charge (SOCs) indexed by reference OCVs and reference capacities. A relationship module is configured to: from the lookup table, identify a first set of the reference SOCs associated with the first OCV and the reference capacities, respectively; from the lookup table, identify a second set of the reference SOCs associated with the second OCV and the reference capacities, respectively; determine changes in SOC associated with the reference capacities; determine changes in capacity; and determine an equation that relates changes in capacity to capacity based on the changes in capacity and the reference capacities, respectively.