Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Arithmetic average return and geometric average return answer genuinely different questions about the identical set of annual returns, and the gap between the two widens with volatility. Geometric return reflects what actually happened to a compounding balance, while arithmetic average can overstate real performance whenever returns swing meaningfully year to year.
Before you rely on it
What to check
Use geometric return, not arithmetic average, when the question is about actual compounded wealth growth over the period.
The common error
Where people go wrong with average investment return calculator
Quoting arithmetic average return as if it described actual compounded growth. A volatile series of returns can post a respectable arithmetic average while the actual compounded outcome, geometric return, comes in noticeably lower.
Sensitivity evidence
How year 1 return changes the geometric average return
| Year 1 return | Geometric average return | Arithmetic average return | Five-year cumulative return |
|---|---|---|---|
| 8.0% | 5.7% | 6.0% | 32.0% |
| 10.0% | 6.1% | 6.4% | 34.5% |
| 12.0%worked example | 6.5% | 6.8% | 36.9% |
| 14.0% | 6.9% | 7.2% | 39.4% |
| 16.0% | 7.2% | 7.6% | 41.8% |
Every input, tested
Which input moves the geometric average return most
| Input | Tested from | To | Geometric average return at each end | Swing |
|---|---|---|---|---|
| Year 5 return | 7.0% | 11.0% | 6.1% to 6.9% | 0.782% (12%) |
| Year 1 return | 10.0% | 14.0% | 6.1% to 6.9% | 0.761% (12%) |
| Year 3 return | 13.0% | 17.0% | 6.1% to 6.9% | 0.741% (11%) |
| Year 4 return | 5.0% | 7.0% | 6.3% to 6.7% | 0.402% (6.2%) |
Two variables at once
Geometric average return by year 1 return and year 3 return
| Year 1 return \ Year 3 return | 11.0% | 15.0% | 19.0% |
|---|---|---|---|
| 8.0% | 5.0% | 5.7% | 6.4% |
| 10.0% | 5.4% | 6.1% | 6.8% |
| 12.0% | 5.7% | 6.5% | 7.2% |
| 14.0% | 6.1% | 6.9% | 7.6% |
| 16.0% | 6.5% | 7.2% | 8.0% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Year 1 return | 12.0% |
| Year 2 return | -8.0% |
| Year 3 return | 15.0% |
| Year 4 return | 6.0% |
| Year 5 return | 9.0% |
| Geometric average return | 6.5% |
| Arithmetic average return | 6.8% |
| Five-year cumulative return | 36.9% |
Where the inputs come from
Enter each year's return as a percentage, using negative numbers for losing years. Use total returns including dividends for the same account or fund, and check that the years are consecutive. The calculator takes five years; for a longer history, work in blocks or use the CAGR calculator with the start and end values. Calendar-year returns from a fund fact sheet are the usual source.
Using the geometric average return in a real decision
Use the geometric figure to judge what happened and the arithmetic one only to estimate a typical future year.
When the result stops applying
Five years is a short window, and a single strong or weak year can dominate it. The averages assume you invested one lump sum at the start and made no deposits, so they do not describe a personal account. They also ignore taxes and fees unless the returns entered are already net of them.
What to compare it with
Convert the geometric average into an ending value with the future value calculator, and check volatility with the investment volatility calculator. The CAGR page gives the same geometric figure from beginning and ending values. Compare against an index's average over the same five years to see whether the fund earned its fee.
People also ask
Frequently asked questions
Which average return should I use?
The geometric average shows the growth you actually got. The arithmetic average is higher and is used to estimate a typical single year going forward.
Why is the arithmetic average higher?
Because gains and losses compound unevenly. A 50% gain followed by a 50% loss averages to zero but leaves you 25% down.
Should negative years be entered as negatives?
Yes. Enter an 8% loss as -8, because the calculator needs the sign to compute both the arithmetic and the geometric averages correctly.