"tools […] that can show the location of bad blocks" – Bad blocks are ones that are about to be reallocated maybe. If they are known, SMART counts them as
Current_Pending_Sector. The question explicitly talks about "the number of reallocated sectors", so this is Reallocated_Sector_Ct, sectors that have been reallocated. "Pending" and "reallocated" are two different stages of managing a faulty sector. Are you sure the tool you're recommending can show reallocated and not just pending sectors? If it cannot then this shall be stated clearly because it does not answer the question.