[4] It was named from its position near the geographical center of Clay County.

[5] The first post office was established in Clay Center on July 3, 1862.

[7] According to the United States Census Bureau, the city has a total area of 3.08 square miles (7.98 km2), all land.

[9] The climate in this area is characterized by hot, humid summers and generally mild to cool winters.

[10] The 2020 United States census counted 4,199 people, 1,809 households, and 1,116 families in Clay Center.

There were 2,103 housing units at an average density of 659.0 per square mile (254.5/km2).

34.8% of households consisted of individuals and 18.9% had someone living alone who was 65 years of age or older.

There were 2,158 housing units at an average density of 700.6 per square mile (270.5/km2).

35.0% of all households were made up of individuals, and 20.1% had someone living alone who was 65 years of age or older.

33.4% of all households were made up of individuals, and 19.7% had someone living alone who was 65 years of age or older.

[25] The Clay Center government consists of a mayor and eight council members, which meets twice a month.