Carbon County is a county located in the U.S. state of Utah. As of the 2010 census, the population was 21,403. Its county seat and largest city is Price. The county is named for the major coal deposits in the area.The Price, UT Micropolitan Statistical Area includes all of Carbon County.Carbon County is the second largest natural gas producer in Utah (after Uintah County), with 94 billion cubic feet produced in 2008.