The United States Capitol, often called Capitol Hill, is the seat of the United States Congress, the legislative branch of the U.S. federal government.It sits atop Capitol Hill, at the eastern end of the National Mall in Washington, D.C. .hough not at the geographic center of the Federal District, the Capitol forms the origin point for the District's street-numbering system and the District's four quadrants. The original building was completed in the year 1800 and was subsequently expanded, particularly with the addition of the massive dome.