Newtown is a town in Richland Township, Fountain County, Indiana, United States.

According to the 2010 census, Newtown has a total area of 0.5 square miles (1.29 km2), all land.

23.7% of all households were made up of individuals, and 9.7% had someone living alone who was 65 years of age or older.

The racial makeup of the town was 95.68% White, 1.85% Native American, and 2.47% from two or more races.

29.5% of all households were made up of individuals, and 14.8% had someone living alone who was 65 years of age or older.

About 2.3% of families and 8.0% of the population were below the poverty line, including 23.3% of those under the age of eighteen and none of those 65 or over.