Washington, D.C. is 3.6 times larger than Providence, Rhode Island.
Area: 49 km2 calculated
Providence is the capital and most populous city in Rhode Island. Founded in 1636, it is one of the oldest cities in the United States. It is located in Providence County, and is the third-largest city in the New England region after Boston and Worcester. Wikipedia
Area: 178 km2 calculated
Washington, D.C., formally the District of Columbia and commonly referred to as Washington, "the District", or simply D.C., is the capital of the United States. Wikipedia