According to the 2000 U.S. Census, the county has a total area of 506.77 square miles (1,312.5 km2), of which 505.71 square miles (1,309.8 km2) (or 99.79%) is land and 1.07 square miles (2.8 km2) (or 0.21%) is water.
As of the census of 2010, there are 4,131 people in the county, organized into 1,791 households and 1,217 families. The population density is 9 people per square mile (3/km²). There are 2,317 housing units at an average density of 5 per square mile (2/km²). The racial makeup of the county is 98.51% White, 0.09% Black or African American, 0.09% Asian, 0.02% Native American, 0.16% from other races, and 1.12% from two or more races. Approximately 0.60% of the population were Hispanic or Latino of any race.
There are 1,791 households out of which 27.90% have children under the age of 18 living with them, 57.50% are married couples living together, 6.90% have a female householder with no husband present, and 32.00% are non-families. 29.30% of all households are made up of individuals and 16.00% have someone living alone who is 65 years of age or older. The average household size is 2.38 and the average family size is 2.93.
24.90% of the county's population is under the age of 18, 6.20% from 18 to 24, 23.70% from 25 to 44, 23.90% from 45 to 64, and 21.20% who are 65 years of age or older. The median age is 42 years. For every 100 females there are 92.9 males. For every 100 females age 18 and over, there are 91.6 males.
The median income for a household in the county is $27,124, and the median income for a family is $31,741. Males have a median income of $22,636 versus $18,902 for females. The per capita income for the county is $13,075. 18.00% of the population and 12.90% of families are below the poverty line. Out of the total population, 24.10% of those under the age of 18 and 16.50% of those 65 and older are living below the poverty line.
The TFR for Knox County in 2004 was relatively high at 2.64, despite the population being 98% white.