Plymouth is a town in Box Elder County, Utah, United States. The population was 414 at the 2010 census.According to the United States Census Bureau, the town has a total area of 0.5 square miles, all of it land.As of the census of 2000, there were 328 people, 105 households, and 89 families residing in the town. The population density was 607.0 people per square mile. There were 114 housing units at an average density of 211.0 per square mile. The racial makeup of the town was 99.09% White, 0.30% Native American, and 0.61% from two or more races. Hispanic or Latino of any race were 1.52% of the population.There were 105 households out of which 51.4% had children under the age of 18 living with them, 70.5% were married couples living together, 10.5% had a female householder with no husband present, and 15.2% were non-families. 15.2% of all households were made up of individuals and 7.6% had someone living alone who was 65 years of age or older. The average household size was 3.