Livingston is located at 45°39′32"N 110°33′49"W (45.658840, -110.563718), at an altitude of 4.501 feet (1372 m).

According to the United States Census Bureau

United States Census Bureau

The United States Census Bureau is the government agency that is responsible for the United States Census. It also gathers other national demographic and economic data...

, the city has a total area of 2.6 square miles (6.7 km²), of which, 2.6 square miles (6.7 km²) of it is land and 0.38% is waters.
At the 2000 census

Census

A census is the procedure of systematically acquiring and recording information about the members of a given population. It is a regularly occurring and official count of a particular population. The term is used mostly in connection with national population and housing censuses; other common...

, there were 6,851 people, 3,084 households and 1,751 families residing in the city. The population density

Population density

Population density is a measurement of population per unit area or unit volume. It is frequently applied to living organisms, and particularly to humans...

 was 2,601.3 per square mile (1,005.8/km²).