Want to retire with $1 million? Here's what researchers say is the ideal age to start saving.

Americans say they'll need about $1.8 million to retire comfortably, a pie-in-the-sky figure for most households given that the average retirement fund holds just over $113,000. But a nest egg of that size isn't out of reach — as long as you start saving at the ideal age, according to new research. 

The optimal age to start socking away money for your golden years is 25 years old or younger, according to a new report from the Milken Institute, an economic think tank. And there's a very simple mathematical reason for that number. Due to the power of compounding, starting a retirement savings while in one's early 20s — or even younger, can help ensure your assets grow to at least $1 million by age 65. 

"The message of early investing needs to be conveyed in ways that resonate with Americans across the board," the report noted.