In her apartment just north of Washington Square Park, Edith Windsor ran down a few pieces of simple arithmetic on Wednesday afternoon to explain why she had gone to the trouble of suing the government in what surely are the late seasons of her life.

Ms. Windsor, 83, is a widow, but by act of Congress, signed into law by former President Bill Clinton at the height of the 1996 campaign, she has paid more than $500,000 in inheritance taxes because her spouse, Thea Spyer, was a woman. “If Thea was a Theo, I wouldn’t have had to pay,” Ms. Windsor said. “One letter.”

This week, a federal judge in Manhattan ruled in her case that the law, the Defense of Marriage Act, was unconstitutional. Across the country, legal conveyor belts are carrying other cases that challenge the law toward the Supreme Court. Few of them can provide an exact dollar amount on the cost of the unequal treatment of same-sex marriages, but Ms. Windsor can.

The estate tax bill from the federal government was $363,053. New York State took an additional $200,000.