[4] Breckenridge was laid out in 1856, and named for Vice President John C.

According to the United States Census Bureau, the city has a total area of 0.55 square miles (1.42 km2), all land.

[7] As of the census[9] of 2010, there were 383 people, 160 households, and 97 families residing in the city.

There were 205 housing units at an average density of 372.7 per square mile (143.9/km2).

33.8% of all households were made up of individuals, and 11.2% had someone living alone who was 65 years of age or older.

There were 230 housing units at an average density of 416.5 per square mile (160.8/km2).

31.4% of all households were made up of individuals, and 12.0% had someone living alone who was 65 years of age or older.