Both the city and the county were named for David Gouverneur Burnet, the first (provisional) president of the Republic of Texas. He also served as Vice President during the administration of Mirabeau B. Lamar. The name is pronounced as "BURN-it" rather than "bur-NET" because that is the way David Burnet pronounced his name. In fact, there is an expression known pretty much throughout the hill country of Texas that goes "It's Burnet, durn it, can't you learn it?", where "Burnet", "durn it", and "learn it" all rhyme.
As of the census of 2000, there were 4,735 people, 1,661 households, and 1,114 families residing in the city. The population density was 693.1 people per square mile (267.7/km). There were 1,813 housing units at an average density of 265.4/sq mi (102.5/km). The racial makeup of the city was 83.80% White, 5.32% African American, 1.20% Native American, 0.49% Asian, 0.04% Pacific Islander, 7.77% from other races, and 1.37% from two or more races. Hispanic or Latino of any race were 18.97% of the population.
There were 1,661 households out of which 31.7% had children under the age of 18 living with them, 49.3% were married couples living together, 14.1% had a female householder with no husband present, and 32.9% were non-families. 28.8% of all households were made up of individuals and 16.4% had someone living alone who was 65 years of age or older. The average household size was 2.46 and the average family size was 3.00.
In the city the population was spread out with 23.9% under the age of 18, 9.5% from 18 to 24, 29.9% from 25 to 44, 17.8% from 45 to 64, and 18.8% who were 65 years of age or older. The median age was 37 years.
The median income for a household in the city was $27,093, and the median income for a family was $37,604. Males had a median income of $25,663 versus $17,163 for females. The per capita income for the city was $13,749. About 11.8% of families and 14.7% of the population were below the poverty line, including 18.1% of those under age 18 and 15.2% of those age 65 or over.
Burnet is served by two primary highways:
Rail service is provided by the Hill Country Flyer steam train from Cedar Park. The Hill Country Flyer is operated every Saturday in January and February, most Saturdays and Sundays March-May, and most Saturdays in October and November
Burnet Municipal Airport, Kate Craddock Field (ICAO Code KBMQ) is a general aviation airport located approximately one mile south of State Highway 29 on U.S. Highway 281. It has a 5,000 foot lighted runway with a full length taxiway, which can accommodate aircraft with up to 34,000 pounds per wheel. The airport is home to the Highland Lakes Squadron of the Commemorative Air Force