Plenty of factors can contribute to your financial well-being, from earning enough to afford the lifestyle you want to being on track with your retirement savings.

But having at least $2,000 saved for emergencies may have the biggest impact on how you feel about money, a recent study from investment management company Vanguard shows.

Respondents with at least that much in emergency savings reported a level of financial well-being 21% higher than those who don't have any emergency savings, Vanguard found. The firm used the Consumer Financial Protection Bureau's questionnaire to measure respondents' well-being.

"People with emergency savings have a higher level of financial well-being, spend less time thinking about and dealing with their finances, and are less distracted at work," Paulo Costa, senior behavioral economist at Vanguard and co-author of the study, said in a press release.

The firm surveyed over 12,400 of its investors to gauge how they feel about money and which factors may be contributing to those emotions. Bigger incomes and more assets were also positively correlated with higher levels of well-being, but having at least $2,000 saved for a rainy day delivered the largest boost.

Less stress, more time

Having a healthy emergency fund not only brings more peace of mind, but can also help you reclaim some of your time, the study found.

Overall, Vanguard investors report spending an average of 4.3 hours a week thinking about and dealing with their finances, the study found. But investors without any emergency savings spend significantly more time on these matters, at an average of 7.3 hours a week. That figure drops to just 3.7 hours a week among respondents with at least $2,000 in emergency savings.

"Emergency savings buy peace of mind and provide a buffer in case anything goes wrong," said Malena de la Fuente, a behavioral scientist and economist at Vanguard and another of the study's co-authors.

Further, 51% of investors with no emergency savings reported an increase in financial stress year-over-year. Just 15% of those with at least $2,000 saved reported the same.

How much you need saved for emergencies

Money experts have long advised aiming to put away three to six months' worth of expenses for emergencies. In fact, having enough in savings to cover a full three to six months' worth of expenses delivers a 13% increase to financial well-being, Vanguard found.

But that can be a lofty goal to reach, especially for those living paycheck-to-paycheck. Still, many experts also say that something is better than nothing when it comes to your rainy day fund.

You need to consider your personal situation when deciding how much to sock away, Will Kellar, a certified financial planner and partner and lead advisor at Human Investing, previously told CNBC Make It. "While the conventional wisdom endorses three to six months of living expenses, I persistently advocate that any amount is superior to none," he said.

The average cost of an emergency hit $1,700 in 2023, according to LendingClub, so the $2,000 benchmark may be sufficient in many situations. But if you own your home, have children or deal with chronic medical problems, for example, you may want more of a cushion.

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