Greenback is located at 35°39'38" North, 84°10'19" West (35.660833, -84.172222).
According to the United States Census Bureau, the town has a total area of 7.21 mi2 (18.67 km2). 7.08 mi2 (18.34 km2) of it is land and 0.13 mi2 (0.33 km2) of it is covered by water. The total area is 1.76% water.
Greenback is located in the Eastern Standard Time (EST) timezone, GMT-05:00. It observes Daylight Saving Time (DST).