The average annual return adds up each year’s percentage return and divides by the number of years. The compound annual growth rate (CAGR) is the single steady yearly rate that would turn your starting value into your ending value. When returns vary from year to year, the average is always higher than CAGR, and CAGR is the one that matches what actually happened to your money. Five years of returns of +20%, −10%, +15%, −5% and +25% average 9.0%, but the money only grew at a CAGR of 8.08%.
The two formulas
The arithmetic average (mean) of yearly returns:
The compound annual growth rate, from values or from returns:
The second CAGR form is the geometric mean of the growth factors, minus one. You can compute the simple mean with the mean calculator and the CAGR with the CAGR calculator.
Worked example: five volatile years
Start with $10,000:
| Year | Return | Balance at year end |
|---|---|---|
| 1 | +20% | $12,000.00 |
| 2 | −10% | $10,800.00 |
| 3 | +15% | $12,420.00 |
| 4 | −5% | $11,799.00 |
| 5 | +25% | $14,748.75 |
- Average return: (20 − 10 + 15 − 5 + 25) ÷ 5 = 9.00%
- Growth factor: 1.20 × 0.90 × 1.15 × 0.95 × 1.25 = 1.474875
- CAGR: 1.4748751/5 − 1 = 8.08%
Check: $10,000 × 1.08085 ≈ $14,749, which matches the real ending balance. If you had projected with the 9% average, you would have expected $10,000 × 1.095 = $15,386, overstating the result by about $637.
The extreme case: +50%, then −50%
| Year 1 | Year 2 | |
|---|---|---|
| Return | +50% | −50% |
| Balance (from $100) | $150 | $75 |
The average return is (50 − 50) ÷ 2 = 0%, yet you lost a quarter of your money. CAGR = (75 ÷ 100)1/2 − 1 = −13.40%. This is the clearest illustration of why a loss needs a bigger gain to recover: after −50% you need +100% to break even.
Volatility drag
The gap between the two numbers grows with volatility. A useful approximation:
where σ is the standard deviation of the yearly returns. In the five-year example, σ is about 13.9%, so σ² ÷ 2 ≈ 0.97 percentage points, and the estimate is 9.00% − 0.97% = 8.03%, close to the true 8.08%. Two portfolios with the same average return can end with very different balances if one swings more widely. That is the mathematical case for reducing volatility through diversification.
| Pattern of returns | Average | CAGR | $10,000 after 2 years |
|---|---|---|---|
| +10%, +10% | 10% | 10.00% | $12,100 |
| +20%, 0% | 10% | 9.54% | $12,000 |
| +30%, −10% | 10% | 8.17% | $11,700 |
| +40%, −20% | 10% | 5.83% | $11,200 |
Which number should you use?
Use CAGR when you want to:
- Describe how an investment actually performed over several years
- Compare investments held for the same period
- Project a future balance from a historical rate, as in the investment calculator
- Apply rules of thumb like the Rule of 72 (at 8.08%, money doubles in about 72 ÷ 8.08 ≈ 8.9 years)
Use the arithmetic average when you want to:
- Estimate the expected return for a single upcoming year
- Feed statistical models that work with the distribution of yearly returns
When someone quotes a long-term “average return” for stocks, ask which kind it is. The difference between the arithmetic and geometric averages of historical US stock returns is typically around 1.5 to 2 percentage points, which compounds into a large gap over decades.
What fund reports show
US mutual fund prospectuses report “average annual total return” for 1, 5 and 10 years using an SEC-prescribed formula that is a compounded rate, conceptually the same as CAGR, and that assumes reinvested dividends. So a fund’s 10-year “average annual return” of 8% means its value grew as though it earned 8% every year. Marketing materials, blog posts and casual conversation are where simple averages tend to creep in.
Calculating both in a spreadsheet
If your yearly returns are in cells A2:A6 as decimals (0.20, −0.10 and so on):
| Measure | Excel or Google Sheets formula | Result for the example |
|---|---|---|
| Average return | =AVERAGE(A2:A6) |
9.00% |
| CAGR from returns | =PRODUCT(1+A2:A6)^(1/ROWS(A2:A6))-1 |
8.08% |
| CAGR from values | =(14748.75/10000)^(1/5)-1 |
8.08% |
| CAGR with a built-in | =RRI(5, 10000, 14748.75) |
8.08% |
In older versions of Excel, the PRODUCT formula must be entered as an array formula. GEOMEAN(1+A2:A6)-1 gives the same answer.
Adjusting CAGR for inflation
A nominal CAGR tells you how many dollars you gained, not how much more you can buy. To convert to a real (inflation-adjusted) rate:
With an 8.08% nominal CAGR and 3% average inflation, the real rate is 1.0808 ÷ 1.03 − 1 = 4.93%. Subtracting 3 from 8.08 gives a close estimate of 5.08%, but the division is exact.
When CAGR is not enough
- Contributions and withdrawals. CAGR looks only at the start and end values. If you add $500 a month, the ending balance rises for reasons that have nothing to do with returns. Use a money-weighted return (internal rate of return) for your personal results, or a time-weighted return to judge the investment itself.
- Partial years. Use the exact time in years, such as 1,000 days ÷ 365.25 = 2.74 years, in the exponent.
- Smoothing hides risk. A steady-looking 8% CAGR could hide a −30% year along the way. Look at the year-by-year path too.
For a simpler one-period measure of gain, see how to calculate ROI, and for the mechanics of growth on growth, how compound interest works.
This guide explains return measurement for education only. It is not investment advice, and historical returns do not predict future performance.
Frequently asked questions
Why is CAGR lower than the average return?
Because losses hurt more than equal gains help. A 50% gain followed by a 50% loss averages 0%, but $100 becomes $150 and then $75, a compound annual growth rate of about −13.4%. Whenever yearly returns vary, the compound rate is lower than the simple average.
How do I calculate CAGR?
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1. For $10,000 growing to $18,000 in 6 years, CAGR = 1.8^(1/6) − 1 = 10.29% a year.
Is the average annual return in a mutual fund report a simple average?
No. Under SEC rules for fund prospectuses, the 'average annual total return' for 1, 5 and 10 years is a compounded rate, the same idea as CAGR. Simple averages of yearly returns are more common in marketing and casual comparisons.
When is the arithmetic average return the right number?
It is the better estimate of what to expect in any single future year, and it is used in some statistical and risk calculations. For describing how an investment actually grew over several years, or for projecting a long-term balance, use the compound rate.
Can CAGR handle deposits and withdrawals?
No. CAGR uses only a starting and ending value, so money added or removed along the way distorts it. For accounts with regular contributions, use a money-weighted return such as the internal rate of return.