Unity is drained by the Little Sugar River.
Colonization eventually resulted in the establishment of the Province of New Hampshire. Within that province, the area known as modern-day Unity was part of a territory chartered in 1753 and named "Buckingham" after John Hobart, 1st Earl of Buckinghamshire. Grants in the area were given by both the early Massachusetts government and by Governor Benning Wentworth, which led to disputes. The town was incorporated as "Unity" in 1764 after amicable resolutions of the disputes were reached.
In the 1790 census, the town had 538 residents. Unity was on the Second New Hampshire Turnpike, an important trade route chartered in 1799 that connected Amherst, Massachusetts to Claremont, New Hampshire. By 1810, the town had 1,044 inhabitants, with two grain mills, five sawmills, a clothing mill and a distillery. Sheep farming was a principal business.
There were 504 households, out of which 30.4% had children under the age of 18 living with them. 66.5% were married couples living together, 4.2% had a female householder with no husband present, and 23.6% were non-families. 17.1% of all households were made up of individuals, and 4.4% had someone living alone who was 65 years of age or older. The average household size was 2.59, and the average family size was 2.89.
In the town, the population was spread out, with 20.0% under the age of 18, 5.9% from 18 to 24, 27.5% from 25 to 44, 26.1% from 45 to 64, and 20.6% who were 65 years of age or older. The median age was 43 years. For every 100 females, there were 101.8 males. For every 100 females age 18 and over, there were 97.7 males.
The median income for a household in the town was $41,594, and the median income for a family was $47,045. Males had a median income of $31,199 versus $24,833 for females. The per capita income for the town was $17,908. About 6.8% of families and 8.1% of the population were below the poverty line, including 15.4% of those under age 18 and 1.4% of those age 65 or over.