What is CAGR, the compound annual growth rate?

CAGR, short for compound annual growth rate, is the single yearly rate that would carry a starting value to an ending value over a given number of years if growth compounded at exactly that rate every year. It is a summary, not a record: an investment with a 10% CAGR may never have returned 10% in any one year. Analysts use it to put growth over spans of different lengths on the same footing, whether the series is a stock index, a company's sales or the price level. The stocks hub covers the investments it is most often quoted for.

How do you calculate CAGR?

Divide the ending value by the starting value, raise the result to the power of one over the number of years, then subtract 1.

The number of years does not have to be whole: for a period counted in days, divide the days by 365.25. Run the formula backward and it gives the ending value, starting value × (1 + CAGR) ^ years, which is the compounding arithmetic set out in how compound interest works. FINRA's investor page on evaluating performance gives the same calculation under the name annualized return, (1 + return) ^ (1 ÷ years) − 1, where return is the cumulative gain written as a decimal. In a spreadsheet, type =(end/start)^(1/years)-1, or use Excel's RRI function, RRI(nper, pv, fv), which Microsoft describes as the equivalent interest rate for the growth of an investment.

Two conditions limit the formula. The starting value must be above zero, so CAGR cannot describe a company moving from a loss to a profit. And it reads only the two end points, so nothing that happened in between enters the result.

What was the S&P 500's CAGR over the last 10 years?

On price alone, the S&P 500 compounded at about 13.8% a year from October 31, 2016 to October 28, 2026, the decade of daily data FRED publishes.

These levels come from the S&P 500 series that S&P Dow Jones Indices supplies to the St. Louis Fed's FRED database, which is a price index and leaves dividends out. A fund that reinvested its dividends compounded faster, and that gap is what total return measures. The same series feeds our bitcoin vs S&P 500 study, which reports 3-year and 5-year rates to the same end date of 23.4% and 11.0% a year: one index and one end date give three quite different CAGRs, depending only on where the window starts. What is the S&P 500 covers what the index holds.

Why is CAGR lower than the average annual return?

A loss shrinks the base that the next gain works on, so the simple average of yearly returns runs ahead of the rate at which money actually compounded.

The average says the index earned 2.39% a year; the money says it went almost nowhere. The gap widens with the size of the swings. Using the rounded calendar-year figures in the same study, bitcoin lost 64.2% in 2022 and gained 155.7% in 2023, an average of +45.8% a year, yet $10,000 would have dropped to $3,580 and recovered only to about $9,154, a CAGR of roughly −4.3%. Calmer stretches show a smaller gap: the S&P 500's nine calendar-year returns from 2017 through 2025 average 14.41%, while its CAGR over those years, from 2,238.83 to 6,845.50, is 13.22%.

A rule of thumb connects the two: CAGR ≈ average return − variance ÷ 2, where variance is the square of the standard deviation of the yearly returns. From 2017 to 2025 that standard deviation was 15.44 points, so the drag is about 0.1544 × 0.1544 ÷ 2 = 1.19 points, and 14.41 − 1.19 = 13.22. The shortcut fails for swings as large as bitcoin's, where only the full formula works.

Where do you see CAGR?

You meet it in fund prospectuses and fact sheets, in company presentations, in economic statistics and in any multi-year return quoted per year.

• Fund documents. SEC Form N-1A tells a mutual fund to report its average annual total return for 1, 5 and 10 years by solving P(1 + T)^n = ERV, where P is a hypothetical $1,000 payment, T the return, n the number of years and ERV the ending redeemable value. The instructions deduct the maximum sales load, reinvest every distribution and state the result to the nearest hundredth of a percent. Despite the word "average", T is a compound rate: a CAGR of total return after fund costs. Index funds explained shows where those tables appear.
• Company reports. Investor presentations often quote revenue or earnings per share growth as a five- or ten-year CAGR. Check the base year, because a weak starting point inflates the rate.
• Economic data. The Bureau of Labor Statistics CPI-U index rose from 241.428 in September 2016 to 336.940 in September 2026, 39.6% in all, which is 3.39% a year compounded.
• Savings rates. An APY is the one-year compound growth of a deposit, so it plays the same role for a bank account; APY vs APR explains the conversion.
• Calculators and shortcuts. The compound interest calculator runs the formula forward from a rate you choose, and the rule of 72 turns a CAGR into a doubling time: 72 ÷ 13.8 ≈ 5.2 years.

How does CAGR compare with other return measures?

CAGR is a compound, time-weighted rate for one lump sum; cumulative return, the average annual return and the money-weighted return each answer a different question.

The last row matters to anyone who adds money over time. In a 2023 rule filing, FINRA described the average annual total returns that mutual funds advertise as time-weighted returns, which ignore the size and timing of cash flows, while an internal rate of return measures how a specific portfolio performed. Two people in the same fund over the same decade see the same CAGR, but the one who put most of the money in just before a fall earns less. That is why regular investing is judged with money-weighted figures, as in lump sum vs dollar-cost averaging and the DCA calculator.

What are the limits of CAGR?

CAGR hides the ride, depends on the dates chosen, and leaves out cash flows, the dividends missing from price data and inflation unless you add them back.

• It hides volatility. The S&P 500's 13.8% decade included a fall from 3,386.15 on February 19, 2020 to 2,237.40 on March 23, 2020, a drawdown of 33.9%. A smooth rate says nothing about whether an investor could have sat through that.
• It depends on the end points. Starting a window at a market low or at a company's weakest year raises the result, and starting at a peak lowers it. Compare CAGRs only over identical dates.
• It ignores deposits and withdrawals. Dividing a balance that includes new savings by the opening balance overstates growth; a money-weighted return handles the cash flows.
• Price-only data understate it. Index levels exclude dividends while fund figures include them after costs, so check which one you are reading before comparing.
• It is nominal unless adjusted. Prices rose 3.39% a year over the decade to September 2026, so a 13.8% nominal CAGR was roughly 10.1% after inflation (1.138 ÷ 1.0339 − 1), with the caveat that the two windows end a month apart. Real returns and inflation walks through the adjustment.
• Short periods annualize badly. A 5% gain in one quarter compounds to 21.6% a year on paper, which assumes the same pace for three more quarters.
• It looks backward. A past CAGR describes history only, and past performance does not predict future results.