The city is probably named after the Danish city of Viborg, as the US city was founded by Danish-Americans.
Viborg is located at (43.172664, -97.080757).
According to the United States Census Bureau, the city has a total area of 0.4 square miles (1.0 km²), all of it land.
Viborg has been assigned the ZIP code 57070 and the FIPS place code 67020.
There were 366 households out of which 22.7% had children under the age of 18 living with them, 48.9% were married couples living together, 6.0% had a female householder with no husband present, and 42.1% were non-families. 39.6% of all households were made up of individuals and 24.3% had someone living alone who was 65 years of age or older. The average household size was 2.11 and the average family size was 2.85.
In the city the population was spread out with 20.0% under the age of 18, 6.6% from 18 to 24, 20.3% from 25 to 44, 18.4% from 45 to 64, and 34.7% who were 65 years of age or older. The median age was 47 years. For every 100 females there were 79.3 males. For every 100 females age 18 and over, there were 76.2 males.
The median income for a household in the city was $29,231, and the median income for a family was $39,327. Males had a median income of $27,337 versus $20,625 for females. The per capita income for the city was $17,738. About 5.2% of families and 6.4% of the population were below the poverty line, including 3.2% of those under age 18 and 10.5% of those age 65 or over.