Final answer:
The war department estimated that the invasion of mainland Japan could result in half a million American casualties and kill millions of Japanese civilians.
Step-by-step explanation:
The estimated number of casualties that the war department felt the invasion of mainland Japan would take varied, but some officials believed that it could cost half a million American casualties and result in the death of millions of Japanese civilians. This estimation was based on the high casualties experienced during previous battles in the Pacific, such as Iwo Jima and Okinawa, where U.S. forces suffered significant losses. The Japanese's fierce resistance and the use of tactics like kamikaze attacks further contributed to the expectation of high casualties.