Elkton is located at 38°24'26" North, 78°37'24" West (38.407500, -78.623611).
According to the United States Census Bureau, the town has a total area of 1.40 mi2 (3.62 km2). 1.37 mi2 (3.56 km2) of it is land and 0.02 mi2 (0.06 km2) of it is covered by water. The total area is 1.70% water.
Elkton is located in the Eastern Standard Time (EST) timezone, GMT-05:00. It observes Daylight Saving Time (DST).