Newton is located at [show location on an interactive map] 38°59′17″N, 88°9′52″W (38.988119, -88.164390).
According to the United States Census Bureau, the city has a total area of 1.9 square miles (4.8 km²), all of it land.
 
Demographics
As of the census of 2000, there were 3,069 people, 1,329 households, and 810 families residing in the city. The population density was 1,647.3 people per square mile (637.1/km²). There were 1,490 housing units at an average density of 799.8/sq mi (309.3/km²). The racial makeup of the city was 98.99% White, 0.10% African American, 0.20% Asian, 0.23% from other races, and 0.49% from two or more races. Hispanic or Latino of any race were 0.59% of the population.

There were 1,329 households out of which 27.9% had children under the age of 18 living with them, 48.5% were married couples living together, 9.3% had a female householder with no husband present, and 39.0% were non-families. 35.4% of all households were made up of individuals and 19.6% had someone living alone who was 65 years of age or older. The average household size was 2.25 and the average family size was 2.94.

In the city the population was spread out with 23.9% under the age of 18, 9.3% from 18 to 24, 25.4% from 25 to 44, 20.4% from 45 to 64, and 21.1% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 84.9 males. For every 100 females age 18 and over, there were 81.2 males.
The median income for a household in the city was $30,280, and the median income for a family was $42,788. Males had a median income of $31,808 versus $17,877 for females. The per capita income for the city was $16,363. About 8.4% of families and 11.7% of the population were below the poverty line, including 20.7% of those under age 18 and 10.1% of those age 65 or over.