WASHINGTON — Some of the nation’s largest food companies have cut calories in their products by more than 6.4 trillion, according to a new study.

The study sponsored by the Robert Wood Johnson Foundation found between 2007 and 2012 the companies reduced their products’ calories by the equivalent of around 78 calories per person per day. The total is more than four times the amount those companies had pledged to cut by next year.

Seventy-eight calories would be about the same as an average cookie or a medium apple, and the federal government estimates an average daily diet at around 2,000 calories. The study said the calories cut averaged out to 78 calories per day for the entire U.S. population.

The 2010 pledge taken by 16 companies — including General Mills Inc., Campbell Soup Co., ConAgra Foods Inc., Kraft Foods Inc., Kellogg Co., Coca-Cola Co., PepsiCo Inc. and Hershey Co. — was to cut 1 trillion calories by 2012 and 1.5 trillion calories by 2015.

The Robert Wood Johnson Foundation signed on to hold the companies accountable, and that group hired researchers at the University of North Carolina at Chapel Hill to painstakingly count the calories in almost every single packaged item in the grocery store. To do that, the UNC researchers used the store-based scanner data of hundreds of thousands of foods, commercial databases and nutrition facts panels to calculate exactly how many calories the companies were selling.

The researchers aren’t yet releasing the entire study, but they said Thursday that the companies have exceeded their own goals by a wide margin.

Dr. James Marks, director of the Health Group at the Robert Wood Johnson Foundation, said the group is pleased with the results but the companies “must sustain that reduction, as they’ve pledged to do, and other food companies should follow their lead.”

The Robert Wood Johnson Foundation is a nonpartisan philanthropic and research organization that works to improve the nation’s health.

Even though the companies that made the commitment represent most of the nation’s most well-known food companies, they sold only around a third of all packaged foods and beverages at the beginning of the study. Missing are many off-label brands sold under the names of retailers, and it’s unknown whether those products have changed.

It is also unclear how the reduction in calories translates into consumers’ diets. When the companies made the pledge in 2010, they said one way they would try to reduce calories would be to change portion sizes in an attempt to persuade consumers to eat less. The companies also said they would develop new lower-calorie options and change existing products so they have fewer calories.