As of the census of 2000, there were 15,260 people, 6,077 households, and 4,405 families residing in the town. The population density was 519.8 people per square mile (200.7/km²). There were 6,474 housing units at an average density of 220.5/sq mi (85.1/km²). The racial makeup of the town was 97.98% White, 0.43% Black or African American, 0.17% Native American, 0.39% Asian, 0.03% Pacific Islander, 0.22% from other races, and 0.79% from two or more races. Hispanic or Latino of any race were 0.68% of the population.
There were 6,077 households out of which 29.6% had children under the age of 18 living with them, 60.2% were married couples living together, 8.8% had a female householder with no husband present, and 27.5% were non-families. 23.1% of all households were made up of individuals and 11.7% had someone living alone who was 65 years of age or older. The average household size was 2.51 and the average family size was 2.95.
The age distribution of the population of Tiverton was 22.1% under the age of 18, 5.9% from 18–24, 29.0% from 25–44, 26.6% from 45-64, and 16.5% 65 years older. The median age was 41 years. For every 100 females there were 94.9 males. For every 100 females age 18 and over, there were 92.6 males aged 18 or more.
The median income for a household in the town was $49,977, and the median income for a family was $58,917. Males had a median income of $41,042 versus $29,217 for females. The per capita income for the town was $22,866. About 2.9% of families and 4.5% of the population were below the poverty line, including 2.7% of those under age 18 and 9.1% of those age 65 or over.