Allegany is located at 42°5'24" North, 78°29'39" West (42.090000, -78.494444).
According to the United States Census Bureau, the village has a total area of 0.71 mi2 (1.83 km2). 0.70 mi2 (1.81 km2) of it is land and 0.01 mi2 (0.02 km2) of it is covered by water. The total area is 1.14% water.
Allegany is located in the Eastern Standard Time (EST) timezone, GMT-05:00. It observes Daylight Saving Time (DST).