 According to the United States Census Bureau, the township has a total area of , of which is land and (2.74%) is water.It surrounds the borough of Addison, which is located in the southwestern section of the township.Addison Township is bordered by Elk Lick Township to the east, Black Township to the northeast, Upper Turkeyfoot & Lower Turkeyfoot Townships to the northwest, the Youghiogheny River Lake to the west, and the state of Maryland to the south.