Hyundai and Kia, both of which have chalked up big sales gains over the past three years, will have to adjust their fuel-economy stickers on the vehicles they sell in the United States after the Environmental Protection Agency said they had deliberately  overstated the miles per gallon figures required by the government.
The Environmental Protection Agency uncovered the discrepancy during an audit. The Korean automakers, which share testing and engineering labs both in the U.S. and South Korea, insisted the mathematical mistake that led to the faulty numbers was not done deliberately.
 Nevertheless, they  must retrofit the window stickers on the cars, reducing their fuel economy figures by one-to-six miles per gallon depending on the model, the EPA said. Both companies also face hefty fines.
"Consumers rely on the window sticker to help make informed choices about the cars they buy," said Gina McCarthy, assistant administrator of the EPA's air-quality office. "EPA's investigation will help protect consumers and ensure a level playing field among automakers."
The EPA said its inquiry into the errors is continuing, and the agency would not comment when asked if the companies will be fined or if a criminal investigation is under way. But the EPA said it's the first case in which erroneous test results were uncovered in a large number of vehicles from the same manufacturer. Only two similar errors have been discovered since 2000, and those involved single models.
Hyundai and Kia executives apologized for the errors, insisting they unintentional, and promised to pay the owners of 900,000 cars and SUVs for the difference in mileage. The payments, which will be made annually for as long as people own their cars, could run into the hundreds of millions of dollars for both companies.
 Both Kia and Hyundai have touted fuel economy in their marketing campaigns over the past three yers. Hyundai especially has touted the fact it sell more non-hybrid models that get better than 40 miles per gallon than any other automaker.
The EPA said it received about a dozen complaints from consumers that the mileage of their 2012 Hyundai Elantra compact cars didn't match the numbers on the window stickers. So staffers at the EPA's vehicle and fuel emission laboratory in Ann Arbor, Mich., included the Elantra in an annual audit that focused on cars that lead their market segments in mileage.
The audit turned up discrepancies between agency test results and data turned in by Hyundai and Kia, the EPA said. As a result, the automakers will have to knock one or two miles per gallon off the mileage posted on most of the models' window stickers. Some models will lose three or four miles per gallon, and the Kia Soul, a funky-looking boxy small SUV, will lose six mpg from the highway mileage on its stickers.
Hyundai and Kia, which have a common owner though they operate independently in the U.S. and other parts of the world, blamed the discrepancies on mistakes stemming from procedural differences between their mileage tests and those performed by the EPA.
"We're just extremely sorry about these errors," said John Krafcik, Hyundai's CEO of American operations. "We're driven to make this right."
The changes affect 13 models from the 2011 through 2013 model years, including seven Hyundais and six Kias. Window stickers will have to be changed on some versions of Hyundai's Elantra, Sonata Hybrid, Accent, Azera, Genesis, Tucson, Veloster and Santa Fe models, as well as the Kia Sorrento, Rio, Soul, Sportage and Optima Hybrid.
Michael Sprague, executive vice president of marketing for Kia Motors America, also apologized and said the companies have a program in place to reimburse customers for the difference between the mileage on the window stickers and the numbers from the EPA tests.
In an effort to compensate customers, Kia andHyundai plan to find out how many miles the cars have been driven, find the mileage difference and calculate how much more fuel the customer used based on average regional fuel prices and combined city-highway mileage. Customers will also get a 15 percent  premium for the inconvenience, and the payments would be made with debit cards, Sprague said. The owner of a car in Florida with a one mpg difference who drove 15,000 miles would get would get a debit card for $88.03 that can be refreshed every year as long as the person owns the car, Sprague said.
If all 900,000 owners get cards for $88.03, it would cost the automakers more than $79 million a year.
For information, owners can go to www.hyundaimpginfo.com or www.kiampginfo.com .
Sung Hwan Cho, president of Hyundai's U.S. technical center near Ypsilanti, said the EPA requires a complex series of tests that are very sensitive and can have variations that are open to interpretation. The companies did the tests as they were making a large number of changes in their cars designed to improve mileage. The changes, such as direct fuel injection into the cylinders around the pistons, further complicated the tests, Cho said.
"This is just a procedural error," he said. "It is not intended whatsoever."
Krafcik said the companies have fixed testing procedures and are replacing window stickers on cars in dealer inventories. Owners can be confident in their mileage stickers now, he said, adding that Hyundai will still be among the industry leaders in gas mileage even with the revised window stickers.
The mileage was overstated on about one-third of the Hyundais and Kias sold during the three model years, he said.
Customers can find information about their Hyundai's m.p.g. here. Customers can find information about their Kia's m.p.g. here.  By Joseph Szczesny