According to the U.S. Census Bureau, Sylvania has a total area of 8.6 square miles (22.2 km2), of which 8.5 square miles (21.9 km2) is land and 0.1 square miles (0.3 km2), or 1.16%, is water.
As of the census of 2000, there were 1,186 people, 485 households, and 354 families residing in the town. The population density was 161.9 people per square mile (62.5/km²). There were 517 housing units at an average density of 70.6 per square mile (27.2/km²). The racial makeup of the town was 96.37% White, 0.08% Black or African American, 1.18% Native American, 0.08% Asian, 0.51% from other races, and 1.77% from two or more races. 0.67% of the population were Hispanic or Latino of any race.
There were 485 households out of which 34.0% had children under the age of 18 living with them, 59.2% were married couples living together, 10.5% had a female householder with no husband present, and 27.0% were non-families. 25.2% of all households were made up of individuals and 11.8% had someone living alone who was 65 years of age or older. The average household size was 2.45 and the average family size was 2.89.
In the town, the population was spread out with 24.3% under the age of 18, 9.8% from 18 to 24, 27.5% from 25 to 44, 25.3% from 45 to 64, and 13.2% who were 65 years of age or older. The median age was 38 years. For every 100 females, there were 91.6 males. For every 100 females age 18 and over, there were 88.7 males.