What Is CAGR? Compound Annual Growth Rate Explained
Compound annual growth rate (CAGR) is the single steady yearly rate that would take an investment from its starting value to its ending value. A fund that gains 40% one year and loses 20% the next grew 12% in total, which is a CAGR of about 5.8% a year, not the 10% a simple average suggests.
What Is CAGR?
CAGR is the constant annual rate at which an investment would have grown if it compounded at the same speed every year over a given period.
The key word is compound. Each year's growth builds on the previous year's total, not just the original principal. This is the same engine behind compound interest, which is why CAGR is so closely tied to the way real investments accumulate value over time.
CAGR is the standard way to describe multi-year growth of stocks, funds, revenue or website traffic. It does not claim the investment grew by the same amount each year; it reports the equivalent smooth rate.
The CAGR Formula
The formula is compact and only needs three inputs: your beginning value, your ending value, and the number of years between them.
CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1
Reading it from the inside out: you divide the ending value by the beginning value to get the total growth multiple, raise that multiple to the power of one over the number of years to find the per-year multiple, and then subtract one to convert it back into a percentage rate.
The exponent is what makes this a compound rate rather than a simple division. Taking the nth root effectively reverses compounding, isolating the single annual rate that, applied repeatedly, reproduces your total return.
A Fully Worked Example
Suppose you invested $10,000 in an index fund, and after 5 years your account is worth $16,105. Your total gain is 61%, but what was the annual growth rate?
Plug the numbers into the formula:
CAGR = ($16,105 ÷ $10,000)^(1 ÷ 5) − 1
First, the growth multiple: $16,105 ÷ $10,000 = 1.6105.
Next, the fifth root: 1.6105^(1 ÷ 5) = 1.6105^0.2 = 1.10.
Finally, subtract one: 1.10 − 1 = 0.10, or 10% per year.
So your investment grew at a compound annual growth rate of 10%. Check it by compounding forward: $10,000 × 1.10 = $11,000 after year one, then $12,100, $13,310, $14,641, and $16,105 after year five.
Why CAGR Smooths Out Volatility
The most common alternative is the simple average annual return, and it can mislead badly. Imagine an investment that gains 50% in year one and loses 50% in year two. The simple average is (50% − 50%) ÷ 2 = 0%, suggesting you broke even.
But you didn't. A $1,000 investment grows to $1,500 after the 50% gain, then falls to $750 after the 50% loss—a real loss of 25%. The CAGR tells the true story: ($750 ÷ $1,000)^(1 ÷ 2) − 1 = −13.4% per year. That negative figure reflects what actually happened to your money, while the 0% simple average ignores the effect of compounding on a smaller base after a loss.
This gap between simple averages and CAGR widens as volatility increases. The more an investment swings up and down, the more the arithmetic average overstates the real growth. CAGR is sometimes called the geometric mean for this reason—it respects the order and compounding of returns, where the simple arithmetic mean does not.
Using CAGR to Compare Investments
CAGR is most useful for comparing options measured over different time spans or starting amounts: a 3-year bond and a 7-year stock holding become comparable.
Say Investment A turned $5,000 into $8,000 over 4 years, while Investment B turned $20,000 into $40,000 over 9 years. Investment B doubled your money, which sounds impressive, but its CAGR is about 8.0% per year. Investment A's CAGR is about 12.5% per year—it grew faster despite the smaller absolute gain. Without annualizing, you'd likely pick the wrong one.
A CAGR calculator takes the beginning value, ending value, and number of years and saves you the fractional exponents. For a share position, the stock return calculator gives the same figure: with dividends set to zero, the purchase price, current price, number of shares and holding period give the CAGR.
The Limitations of CAGR
CAGR is a summary, and summaries hide detail.
First, CAGR ignores interim volatility. Two investments can share an identical 10% CAGR while one climbed steadily and the other went through deep crashes and recoveries. The smooth rate says nothing about the ride, so it understates risk for anyone who might need to sell at a bad moment.
Second, CAGR ignores cash flows. The basic formula assumes a single deposit at the start and a single value at the end. If you added money mid-period, withdrew funds, or reinvested dividends along the way, plain CAGR won't capture that. For those situations you need a money-weighted return such as the internal rate of return (IRR).
Third, CAGR is backward-looking. It describes what happened, not what will happen. A spectacular historical CAGR is no guarantee of future performance, and past results say nothing about the conditions that produced them. Treat any CAGR figure as a summary for comparison, not as investment advice.