According to the United States Census Bureau, the city has a total area of 0.99 square miles (2.56 km2), all land.

[4] In the spring of 1871, the Arapahoe Town Company was formed in Plattsmouth, Nebraska, under the leadership of Captain E. B. Murphy, for the purpose of establishing a settlement in the Republican River valley.

[6][7] It was named for the Arapaho tribe of Native Americans who occupied this area.

In 1882, the Arapahoe Public Mirror was established to support the Democratic Party in the county.

In 1978, it acquired the Elwood Bulletin, which it continues to publish under that name.

There were 515 housing units at an average density of 520.2 per square mile (200.9/km2).

40.9% of all households were made up of individuals, and 23.7% had someone living alone who was 65 years of age or older.

36.8% of all households were made up of individuals, and 25.7% had someone living alone who was 65 years of age or older.