According to the United States Census Bureau, the city has a total area of 1.5 square miles (3.8 km²), all of it land. Carrington's zip code is 58421. The area code is 701 area code. Carrington has 5 local phone codes. 307, 649, 650, 652, and 653.
As of the census of 2000, there were 2,268 people, 961 households, and 594 families residing in the city. The population density was 1,531.9 people per square mile (591.7/km²). There were 1,057 housing units at an average density of 713.9/sq mi (275.8/km²). The racial makeup of the city was 98.81% White, 0.18% African American, 0.49% Native American, 0.09% from other races, and 0.44% from two or more races. Hispanic or Latino of any race were 0.22% of the population.
There were 961 households out of which 31.0% had children under the age of 18 living with them, 50.8% were married couples living together, 8.4% had a female householder with no husband present, and 38.1% were non-families. 35.6% of all households were made up of individuals and 18.3% had someone living alone who was 65 years of age or older. The average household size was 2.27 and the average family size was 2.97.
In the city the population was spread out with 25.4% under the age of 18, 6.0% from 18 to 24, 26.8% from 25 to 44, 18.7% from 45 to 64, and 23.1% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 90.6 males. For every 100 females age 18 and over, there were 87.3 males.
The median income for a household in the city was $31,197, and the median income for a family was $41,654. Males had a median income of $31,250 versus $19,722 for females. The per capita income for the city was $19,012. About 7.0% of families and 8.9% of the population were below the poverty line, including 10.8% of those under age 18 and 11.0% of those age 65 or over.
