As of the census of 2000, there were 772 people, 277 households, and 219 families residing in the town. By population, Leyden ranked 22nd out of the 26 towns in Franklin County, and 333rd out of 351 cities and towns in Massachusetts. The population density was 42.9 people per square mile (16.6/km2), which ranked 18th in the county and 316th in the Commonwealth. There were 306 housing units at an average density of 17.0 per square mile (6.6/km2). The racial makeup of the town was 98.45% White, 0.39% African American, 0.26% Native American, 0.13% Asian, and 0.78% from two or more races. Hispanic or Latino of any race were 0.26% of the population.