The liquids almost always contain the addictive ingredient from the tobacco plant, nicotine, the health department says.
"We knew it was going to be high, but we didn't know it was going to be that high," said Adam Bramwell, media liaison for the department's tobacco-prevention effort.
"Teens are adopting these things left and right," he said. "They are believing the marketing, that these are safe."
About 35,000 students in the three grades are surveyed every other year.
The long-term effects of e-cigarettes have not been studied. But David Patton, executive director of the Utah Health Department, said in a statement that the new data indicate many adults are sustaining their nicotine addiction by using both cigarettes and e-cigarettes.
"And as has been known for decades, the health risks of tobacco use are great," Patton said, "so anything that is furthering that addiction is guilty by association."
The 2013 report, relying on a 2011 survey, said 4.9 percent of teenage girls and 5.5 percent of teenage boys in the same three grades had tried e-cigarettes, less than half as many as two years later.
It's illegal for people under age 19 to buy or possess e-cigarettes, but there is little regulation of sellers, Bramwell noted.
Retailers need licenses to sell cigarettes, but not to sell e-cigarettes or to manufacture the "juice" that refills the e-cigarette devices. Most teenagers say they are buying e-cigarettes from smoke shops, Bramwell said, but the devices are available at most every gas station.
The Davis County Health Department board voted last winter to begin regulating e-cigarettes, and the state's 11 other health departments are preparing their own regulations, Bramwell said. The city of Tooele bans the use of e-cigarettes in public parks and other outdoor areas.
Weber County has by far the highest rates of e-cigarette use among teenagers, according to the new report.
More than 30 percent of the eighth, 10th and 12th-grade students surveyed there had tried e-cigarettes, and more than 20 percent said they regularly use them. Utah County has the lowest rates of teenagers both sampling and regularly using e-cigarettes, at 4.3 percent and 1.7 percent.
The survey results come after years of declining cigarette use among teenagers. Traditional cigarette use among Utah teenagers 3.9 percent in 2013 has dropped more than 63 percent since 1999, according to the latest report.
While the use of hookah declined slightly among teenagers in the latest study, it is being used regularly by 4.4 percent of teenagers and sampled by 11.7 percent, the new study showed.
Hookah is a water pipe that produces a water-filtered tobacco smoke.
The Health Department also found e-cigarette use soaring among adults. Some 4.8 percent of Utah adults reported using e-cigarettes in 2013, more than double the percentage in 2012. Some 10.2 percent of adults regularly smoke cigarettes, a percentage that was essentially unchanged.
Bramwell said the survey indicated that adults, too, are believing the marketing around e-cigarettes: that they're safe, nonaddictive and a good way to wean oneself from smoking cigarettes.
"They think, 'This will be my way out,' " Bramwell said. "And then they end up using both products."
Of those who use e-cigarettes, 60 percent said they also smoke regular cigarettes, according to the report.