This summer millions of Americans could find a check in the mail from an unexpected source: their health-insurance company.

Consumers and businesses will receive about $1.3 billion by this August from insurance plans that failed to meet a new standard in the 2010 health-care law, according to estimates released Thursday by the independent Kaiser Family Foundation. (That’s assuming the law, or at least the portion of it containing the rule, is upheld by the Supreme Court, which is expected to issue its decision in late June.)

The rule requires most insurers to spend at least 80 percent of the premiums they collect from customers on health-care claims or quality improvement efforts — leaving no more than 20 percent for administrative expenses, such as salaries and marketing, and profits for investors.

This “medical loss ratio” requirement took effect on Jan. 1, 2011, so under current law, any plans that exceeded their limits last year must refund customers the difference by Aug. 1.

The amount will vary by state and plan, ranging from about a dollar to more than $500.

Rebates vary by state and plan. (The Washington Post/Kaiser Family Foundation analysis)

Not all rebates will be issued in the form of a check. In some cases, insurers could give consumers and employers discounts on future premiums. Rebates on employer-purchased plans will generally be provided to the employer, which may opt to pass them on to workers.

The official tally won’t be known for weeks, but researchers at Kaiser came up with an initial estimate by analyzing preliminary data that insurers recently submitted to state regulators.

They found that at least 486 plans covering 15.8 million people will have to issue refunds. And the number could be higher because data for California were unavailable.

Some plans last year set their premiums too high because they overestimated the amount of medical care their customers would use, said Larry Levitt, an author of the Kaiser report.

“Since the recession, patients have been going to the doctor less and have been having fewer elective procedures because they don’t feel economically secure,” he said. “And it’s now two years running that insurers expected things to bounce back, and they haven’t.”

Other plans sought to give themselves a cushion, reasoning that it would be better to risk paying rebates than to set premiums too low to cover costs.

People who have purchased plans for themselves are the most likely to get rebates. Nationwide, about one-third of those individuals will receive rebates, while about one-fourth of those covered through small businesses and one-fifth of those covered by large businesses will get rebates.

However, those shares and the average amount of the rebates will differ widely by state — partly due to local market factors and partly because of variation in state rules.

So, while about 92 percent of individual-plan holders in Texas will be getting rebates, in Vermont, Rhode Island and Iowa, less than 1 percent of such individuals can expect them. The average rebate per enrollee in such plans will be highest in Alaska ($304.99) and Maryland ($294), according to Kaiser’s estimate. In New Mexico and Vermont, rebates will average barely more than a dollar.

The medical-loss-ratio rule does not apply to “self-insured” plans, in which an employer collects premiums from workers directly, adds its own contribution and pays for health care out of the pot — often paying an insurance company to simply administer the plan.

Supporters of the rule contend that it helps consumers get better value for their premium dollar. But Robert Laszewski, a health-care industry consultant and former insurance executive, said that rather than sacrificing profits, many insurers have cut administrative costs in ways that could ultimately be passed on to customers.

Perhaps most importantly, he said, the rule does not address the main driver of insurance premiums: Health-care costs continue to grow faster than wages and the rest of the economy.

“This rule doesn’t make health insurance any more affordable,” he said.

Those concerns were echoed by America’s Health Insurance Plans, an industry trade group, which also complained in a statement that the rule would cause coverage disruptions that “are likely to outweigh any benefit these rebates will provide to consumers.”