Savanna is located at 34°49'42" North, 95°50'36" West (34.828611, -95.843611).
According to the United States Census Bureau, the town has a total area of 1.41 mi2 (3.65 km2). 1.40 mi2 (3.63 km2) of it is land and 0.01 mi2 (0.02 km2) of it is covered by water. The total area is 0.65% water.
Savanna is located in the Central Standard Time (CST) timezone, GMT-06:00. It observes Daylight Saving Time (DST).