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According to the United States Census Bureau, the city has a total area of 4.6 km² (1.8 mi²). 4.5 km² (1.7 mi²) of it is land and 0.1 km² (0.1 mi²) of it is water. The total area is 2.81% water.
The Salmon River passes through Salmon; white water rafters and other people interested in outdoor recreation have brought additional economic activity to Salmon.
As of the census of 2000, there are 3,122 people, 1,369 households, and 829 families residing in the city. The population density is 700.8/km² (1,813.2/mi²). There are 1,576 housing units at an average density of 353.8/km² (915.3/mi²). The racial makeup of the city is 96.76% White, 0.19% African American, 0.54% Native American, 0.29% Asian, 0.00% Pacific Islander, 0.61% from other races, and 1.60% from two or more races. 2.18% of the population are Hispanic or Latino of any race.
There are 1,369 households out of which 28.6% have children under the age of 18 living with them, 46.2% are married couples living together, 11.0% have a female householder with no husband present, and 39.4% are non-families. 34.6% of all households are made up of individuals and 16.5% have someone living alone who is 65 years of age or older. The average household size is 2.26 and the average family size is 2.93.
In the city the population is spread out with 26.4% under the age of 18, 6.8% from 18 to 24, 23.9% from 25 to 44, 25.1% from 45 to 64, and 17.8% who are 65 years of age or older. The median age is 40 years. For every 100 females there are 92.2 males. For every 100 females age 18 and over, there are 89.1 males.
The median income for a household in the city is $26,823, and the median income for a family is $34,844. Males have a median income of $30,417 versus $18,819 for females. The per capita income for the city is $15,749. 19.5% of the population and 15.5% of families are below the poverty line. Out of the total people living in poverty, 28.3% are under the age of 18 and 14.3% are 65 or older.
The Lewis and Clark expedition crossed the continental divide within 30 miles to the southeast of Salmon. Sacagawea was born in the Lemhi Valley near Salmon. The Sacagawea Interpretive Center was opened in Salmon in August of 2003.