Roberts County is at South Dakota's northeastern corner. Its eastern boundary abutsMinnesota (across theBois de Sioux River), and its northern boundary abutsNorth Dakota. The Cottonwood Slough flows southward, draining the upper portion of the county into the River. The terrain consists of rolling hills, devoted to agriculture.[5] The terrain slopes to the east; its highest point is on its upper western boundary line, at 2,047 ft (624 m) ASL.[6]
According to theUnited States Census Bureau, the county has a total area of 1,135.777 square miles (2,941.65 km2), of which 1,101.055 square miles (2,851.72 km2) is land and 34.722 square miles (89.93 km2) (3.1%) is water.[7] It is the 26th largest county in South Dakota by total area. TheTraverse Gap is in eastern Roberts County along theMinnesota border. TheLake Traverse Indian Reservation covers most of the county.
As of the2020 census, there were 10,280 people, 3,844 households, and 2,568 families residing in the county.[14] Thepopulation density was 9.3 inhabitants per square mile (3.6/km2). There were 4,788 housing units.
As of the2010 census, there were 10,149 people, 3,823 households, and 2,655 families residing in the county. The population density was 9.2 inhabitants per square mile (3.6/km2). There were 4,905 housing units at an average density of 4.5 units per square mile (1.7 units/km2). The racial makeup of the county was 61.7% white, 34.5% American Indian, 0.2% Asian, 0.1% black or African American, 0.4% from other races, and 3.0% from two or more races. Those of Hispanic or Latino origin made up 1.2% of the population. In terms of ancestry, 31.3% wereGerman, 19.2% wereNorwegian, 6.3% wereIrish, and 3.8% wereAmerican.
Of the 3,823 households, 34.4% had children under the age of 18 living with them, 49.1% were married couples living together, 13.4% had a female householder with no husband present, 30.6% were non-families, and 27.3% of all households were made up of individuals. The average household size was 2.58 and the average family size was 3.11. The median age was 39.5 years.
The median income for a household in the county was $37,708 and the median income for a family was $46,146. Males had a median income of $34,080 versus $28,423 for females. The per capita income for the county was $19,825. About 14.3% of families and 20.0% of the population were below thepoverty line, including 33.9% of those under age 18 and 11.0% of those age 65 or over.