Republic is located at 48°38'53" North, 118°44'11" West (48.648333, -118.736389).
According to the United States Census Bureau, the town has a total area of 1.59 mi2 (4.12 km2). 1.58 mi2 (4.10 km2) of it is land and 0.01 mi2 (0.02 km2) of it is covered by water. The total area is 0.47% water.
Republic is located in the Pacific Standard Time (PST) timezone, GMT-08:00. It observes Daylight Saving Time (DST).