Average Return Calculator
Calculate the arithmetic mean and geometric mean (CAGR) of annual investment returns, plus best and worst year performance.
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How to use this calculator
Arithmetic mean simply averages the returns. Geometric mean accounts for compounding and reflects the true growth rate — always lower or equal to arithmetic mean.
- 1
Enter annual return percentages for each year — use negative values for loss years.
- 2
Leave trailing year fields at 0 if you have fewer than 8 data points.
- 3
The calculator shows both arithmetic and geometric (CAGR) means, plus best and worst years.
- 4
The geometric mean is the more accurate representation of compound growth — use it for "what did I actually earn?" questions.
Frequently asked questions
What formulas does this tool use?
This tool uses Arithmetic Mean = (r₁ + r₂ + … + rₙ) ÷ n and Geometric Mean = [(1 + r₁)(1 + r₂)…(1 + rₙ)]^(1 ÷ n) − 1, with each return converted from percent to a decimal first. It also reports the best and worst year, the cumulative return (the product minus 1) and what 1,000 would grow to.
How does it decide how many years I entered?
The form has eight year fields and cannot tell an unused field from a real 0%, so any run of zeros at the end is treated as unused. Five returns followed by three zeros counts as five years. A genuine 0% year in the middle is kept, but a 0% year in the last position is dropped.
Are returns entered as percentages?
Yes, 12 means 12% and −5 means a 5% loss. A return of −100% means everything was lost, which drives the geometric mean to −100%. Anything below −100% is impossible for an investment held without borrowing, so the tool shows n/a.
Why can the two averages disagree so much?
The arithmetic mean ignores that each year’s gain or loss applies to a changed balance. Returns of +50% and −50% average 0.00%, yet 1,000 becomes 750.00 and the geometric mean is −13.40% a year. Equal returns, such as 10% three times, give the same figure for both averages: 10.00%.
Does the order of the returns matter?
Not for either average, because multiplication and addition do not depend on order. Five returns give the same arithmetic mean, geometric mean and final value in any sequence. Order matters once money is added or withdrawn between years, and this tool does not model that.
What does the Growth of 1,000 line show?
It multiplies a base of 1,000 by every (1 + return), so 12, −5, 18, 7 and 22 turn 1,000 into 1,638.96, a cumulative 63.90%. The 1,000 is a figure built into the tool for illustration and does not come from your portfolio.
What is not included?
Deposits, withdrawals, fees, taxes, dividends beyond what is in your return figures, and inflation. Each yearly figure is treated as the complete return for that year. The result is an illustration from your inputs, not a forecast or advice.
Arithmetic and geometric average returns compared
Two ways to average the same years
The arithmetic mean adds the yearly returns and divides by the count. The geometric mean multiplies the growth factors, takes the root matching the number of years, and subtracts 1. The first answers “what was a typical year?” and the second answers “what constant rate would have produced the same final balance?” The calculator reports both next to the best and worst year.
Worked example: five uneven years
Returns of 12%, −5%, 18%, 7% and 22% average 10.80% arithmetically but 10.39% geometrically. Cumulative growth is 63.90%, so 1,000 becomes $1,638.96. The 0.41-point gap is the cost of the one losing year and the spread between the others. The five-year row below uses these same numbers, and the opposite extreme appears in the +50% and −50% row.
| Yearly returns (%) | Arithmetic | Geometric | 1,000 becomes |
|---|---|---|---|
| 12, −5, 18, 7, 22 | 10.80% | 10.39% | $1,638.96 |
| 50, −50 | 0.00% | −13.40% | $750.00 |
| 10, 10, 10 | 10.00% | 10.00% | $1,331.00 |
| −10, 20, 5, 0.5, 3, 8, −2, 4 | 3.56% | 3.26% | $1,292.11 |
| −30, then 10 for seven years | 5.00% | 3.96% | $1,364.10 |
Why a loss weighs more than its size
A fall of 30% needs a rise of about 43% just to recover, so volatility reduces the geometric mean below the arithmetic one. In the last table row, a −30% year followed by seven years of +10% averages 5.00% arithmetically yet compounds at 3.96%. The more the returns scatter, the wider the gap; identical returns close it completely.
Which figure answers which question
Use the geometric mean when asking what an amount invested at the start would have become, since it reproduces the ending value. The arithmetic mean is the better summary of a single typical year but overstates compound growth whenever returns vary. When a source quotes an “average return” without saying which, the two can differ by several points over a volatile run.
Limits of the inputs
Eight years is the maximum, and the tool takes each year’s return as a finished number, so it cannot see deposits, withdrawals, fees or tax. The output describes the series you typed, not the one that will happen next, and past figures from any source say nothing definite about future ones. Because trailing zeros are read as unused years, place a genuine 0% year before the last entry, or use a tiny figure such as 0.01 to keep it counted. Results update as you type, so you can change one year and watch both averages move.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →