People usually buy life insurance for the peace of mind that their family will be okay in their absence. But a new survey shows that money may not outlive them for quite as long as they expect.

Americans say they want life insurance to cover expenses for at least 14 years after they die - but in reality, the money is usually enough to cover only three years of expenses, according to a poll by New York Life Insurance Company.

The poll, conducted by the Futures Company, a third-party research firm, surveyed more than 1,000 people last year who were at least 25 years old and were either married or had dependents. People were first asked generally how they felt about their life insurance, and about 60 percent said they thought they had enough coverage. Asked specific questions about how they want their life insurance benefit to be used, it turned out only 20 percent had enough coverage to meet those needs.

"If you make $45,000 a year . . . and if someone talks about a $100,000 insurance policy, that sounds like a fortune to you," says Chris Blunt, co-president of the insurance group of New York Life. "But then you start to think about how long will that last you."

The people surveyed had a median of $220,000 in life insurance coverage. They were asked about things such as if they wanted it to cover college expenses for their children or if they wanted it to replace their income as the main breadwinner in the family. Researchers found that people needed much more - a median of $540,000 - in coverage to meet those goals.

That $320,000 coverage gap is bigger than a shortage of about $290,000 found in a 2008 survey. Some families cut back on coverage after the financial crisis, Blunt says.

People who buy life insurance need to ask themselves what they want that money to accomplish, says Antwone Harris, a financial planner with Charles Schwab. Do they hope that the money will pay off the mortgage? If a surviving parent that used to stay home with the children is going to need to return to work, will the money be enough to pay for day care? Or perhaps for long-term care for an aging spouse?

"People don't put much thought into it," Harris says. "They're looking at the absolute number and saying that sounds fine."