Independence was originally Center, and under the latter name was laid out in 1830
According to the United States Census Bureau, the city has a total area of 9.64 square miles (24.97 km2), of which 9.54 square miles (24.71 km2) is land and 0.10 square miles (0.26 km2) is water.
Much of the land area in Independence is used by the intersection of I-480 and I-77. The I-77/I-480 interchange is a four-level stack interchange, but locals often refer to as the cloverleaf, as it largely replaced a nearby interchange of that type. The larger interchange opened in 1940, but construction of the Willow Freeway, which became I-77, was stalled by World War II and was not completed until the 1950s. In the late 1970s, I-480 connected into I-77. The original 1939 cloverleaf is still in existence on Granger and Brecksville Roads. It is still in use today, generally for local traffic.