Norwich is a village in Muskingum County, Ohio, United States.

[4] According to the United States Census Bureau, the village has a total area of 0.10 square miles (0.26 km2), all land.

There were 56 housing units at an average density of 560.0 per square mile (216.2/km2).

26.5% of all households were made up of individuals, and 16.3% had someone living alone who was 65 years of age or older.

17.5% of all households were made up of individuals, and 2.5% had someone living alone who was 65 years of age or older.

There were 21.4% of families and 36.2% of the population living below the poverty line, including 61.5% of under eighteens and none of those over 64.