According to my calculations (based on the the fact that 150,000 or a quarter of the civilian population of Okinawa was killed during the invasion there in addition to the 12,000 allied and 110,000 Japanese military deaths) the atomic bombings (which caused a combined total of 246,000 Japanese deaths) saved 18.75 million Japanese lives and perhaps 150,000 allied lives, assuming that the fighting matched the intensity of the Okinawa campaign.
And don’t forget that the quick end to war also saved the lives of many hundreds of thousands of people living and working in Japanese slave labor camps or living under Japanese occupation. I understand several studies suggest that deaths of people in the camps or under occupation was somewhere between 10,000-20,000 per month.
I think the estimate for Allied deaths in a full-scale invasion of Japan would’ve been at minimum a million or more.