According to the U.S. Census Bureau, the county has a total area of 2,111 square miles (5,470 km2), of which 2,084 square miles (5,400 km2) is land and 27 square miles (70 km2) (1.3%) is water. It is the third-smallest county in Wyoming by area.
There were 3,625 households out of which 30.00% had children under the age of 18 living with them, 58.90% were married couples living together, 6.80% had a female householder with no husband present, and 31.20% were non-families. 27.30% of all households were made up of individuals and 13.20% had someone living alone who was 65 years of age or older. The average household size was 2.40 and the average family size was 2.92.
In the county the population was spread out with 25.40% under the age of 18, 6.60% from 18 to 24, 24.30% from 25 to 44, 27.30% from 45 to 64, and 16.60% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 97.40 males. For every 100 females age 18 and over, there were 96.50 males.
The median income for a household in the county was $33,866, and the median income for a family was $41,449. Males had a median income of $31,484 versus $19,635 for females. The per capita income for the county was $17,530. About 8.50% of families and 11.70% of the population were below the poverty line, including 15.90% of those under age 18 and 12.20% of those age 65 or over.