Arapahoe is located at 42°57'43" North, 108°29'20" West (42.962222, -108.488889).
According to the United States Census Bureau, the city has a total area of 31.58 mi2 (81.79 km2). 31.35 mi2 (81.20 km2) of it is land and 0.23 mi2 (0.59 km2) of it is covered by water. The total area is 0.72% water.
Arapahoe is located in the Mountain Standard Time (MST) timezone, GMT-07:00. It observes Daylight Saving Time (DST).