Will you have enough money for health care when you retire?

For many Americans, the idea of a secure retirement free from financial anxiety has become increasingly out of reach. One report showed last year that more than one-third of all working-age adult Americans have no retirement savings.

People are also fretting about another key issue that everyone eventually faces in retirement: health care.

AARP quotes data from Fidelity Investments, which estimated a 65-year-old couple retiring in 2013 would need $240,000 to cover their future medical costs, including deductibles, copayments, hearing aids, eyeglasses and other expenses not covered by Medicare.

Meanwhile, according to a new survey by personal finance site Bankrate.com of more than 1,000 adults, 28 percent of respondents say high medical expenses are their largest financial worry as they think about retirement.

The group most worried about running up medical costs in retirement isn't low-income households, but rather those earning at least $75,000 per year. Millennials, or people ages 18 to 29, also express concern, according to Bankrate.

One source of that anxiety: Working Americans aren't expecting much help from Social Security once they reach their golden years. Only 13 percent of those surveyed expect Social Security to make up all or most of their retirement income, compared to another 14 percent who are hoping it will account for about half of that income. Around 1 in 4 working Americans think they won't get anything from Social Security once they retire.

"The average Social Security payout is only around $15,000 per year, so people are realistic to think they'll need to supplement that income," Sheyna Steiner, senior investing analyst at Bankrate, said in a statement.