According to the U.S. Census Bureau, the county has a total area of 1,866 km² (720 mi²). 1,855 km² (716 mi²) of it is land and 10 km² (4 mi²) of it is water. The total area is 0.55% water.
As of the census2 of 2000, there are 5,835 people, 2,557 households, and 1,685 families residing in the county. The population density is 3/km² (8/mi²). There are 3,113 housing units at an average density of 2/km² (4/mi²). The racial makeup of the county is 98.56% White, 0.26% Black or African American, 0.21% Native American, 0.19% Asian, 0.00% Pacific Islander, 0.33% from other races, and 0.46% from two or more races. 0.94% of the population are Hispanic or Latino of any race.
There are 2,557 households out of which 25.60% have children under the age of 18 living with them, 58.80% are married couples living together, 4.80% have a female householder with no husband present, and 34.10% are non-families. 31.80% of all households are made up of individuals and 18.00% have someone living alone who is 65 years of age or older. The average household size is 2.23 and the average family size is 2.80.
In the county the population is spread out with 22.30% under the age of 18, 4.50% from 18 to 24, 22.10% from 25 to 44, 25.00% from 45 to 64, and 26.10% who are 65 years of age or older. The median age is 46 years. For every 100 females there are 93.20 males. For every 100 females age 18 and over, there are 90.80 males.
The median income for a household in the county is $30,494, and the median income for a family is $39,215. Males have a median income of $25,260 versus $17,274 for females. The per capita income for the county is $17,433. 9.10% of the population and 6.00% of families are below the poverty line. Out of the total people living in poverty, 12.40% are under the age of 18 and 8.90% are 65 or older.
Republic County was first settled around 1860 by Daniel and Conrad Myers. The territory was principally inhabited by Pawnees, Iowas, and Otoes who greeted the incoming settlers - mostly farmers - peaceably. By 1868, Republic County was holding elections.