Why did the US use the atomic bombs?

The United States was faced with the daunting prospect of invading Japan in order to force a close to World War 2. The Japanese had already shown a willingness to go to incredible lengths to continue the war and to cause destruction to their enemies. The fierce fighting for islands near the Japanese mainland (Iwo Jima and Okinawa) resulted in a staggering loss of 19,800 American dead and 58,000 wounded. Leaders knew that the losses in undertaking any invasion of the home islands would result in many, many more casualties. Some estimated that American casualties would reach 750,000 in invading Japan. Japanese civilian casualties were not a tremendous concern for American leaders at that time, but they were aware of the huge wave of suicides on Okinawa and of the 100,000+ death toll from the bombing and fires in Tokyo. In this method of calculating, the atomic bombs (if they worked as planned) would actually save lives: hundreds of thousands of American soldiers and sailors, and likely more than a million fewer Japanese civilian deaths.

Another viewpoint is that the use of the bomb to shorten the war was essential economically. Four years of war had seriously strained America's finances. The government was not able to borrow any more money. The Treasury was in a panic. If the bomb was able to end the war, the risk of federal bankruptcy would be averted. The economic crisis was suppressed during the war and easy to ignore in history, but was very real at the time.