Average Return Calculator
Compare the simple average of yearly returns with the steady rate that matches what you actually earned.
- Geometric average (what you actually earned a year)
- 5.42%
- Arithmetic average
- 5.6%
The simple average is 5.6%, but the steady yearly rate that gives the same final result is 5.42%. The geometric average is the better measure of growth.
How it is calculated
Arithmetic average = sum ÷ count; geometric average = (product of (1 + return)) ^ (1 ÷ count) − 1
Example: returns of 10%, −5%, 12%, 8% and 3% average 5.60% simply, but grow your money at 5.42% a year.
Assumptions and limitations
- Enter returns for consecutive years, in order.
- Past returns do not predict future returns.
- Fees and taxes are not included unless they are already in the returns entered.
What this calculator tells you
Investment returns are often reported as a simple average of yearly figures. This calculator shows two averages side by side: the arithmetic mean, which is the simple average, and the geometric mean, which is the steady yearly rate that would have produced the same final result. The geometric mean is the more useful measure of how an investment actually grew.
The two numbers differ whenever returns vary from year to year. The gap is largest when returns are volatile, which is why a simple average can look flattering next to what an investor actually earned.
How the two averages are calculated
The arithmetic average is the sum of the yearly returns divided by the number of years. The geometric average multiplies together one plus each yearly return, takes the root equal to the number of years, and subtracts one. Written as a formula, it is (product of (1 + return)) raised to the power 1 ÷ n, minus 1.
A worked example
Take returns of 10%, minus 5%, 12%, 8% and 3% over five years. The simple average is 5.60%. But an investment of 100 grows to about 130.20 over those five years, and the steady rate that produces this is about 5.42% a year. The gap of about 0.18 percentage points comes from the early loss, which reduces the base for later growth.
Why losses hurt more than averages suggest
A fall of 50% needs a rise of 100% to recover. Because of this asymmetry, a volatile sequence of returns grows more slowly than its arithmetic average implies. The geometric average captures this effect, and it is the number to use when comparing how two investments have grown over the same period.
How to use the result
Enter the yearly returns in order, one per year, as percentages. The calculator needs at least one year, and it rejects a return of minus 100% or lower because that would mean losing everything in a single year, which the formula cannot handle.
Compare the geometric average with the rate you expect on future investments. If the geometric average is much lower than the arithmetic one, the investment has been volatile, and you should expect the same pattern to reduce compound growth in future.
What the calculator does not do
Past returns are not a forecast. The calculator does not adjust for inflation, fees, taxes, or contributions and withdrawals made during the period. A period of five years is short, and a longer record is more informative. The returns you enter should be total returns that include dividends and any distributions, otherwise the figures understate growth.
Use the calculator to understand past performance and to compare investments on the same basis. Do not treat either average as a guarantee that the same pattern will continue.
Using the result in a review
When you review an investment, state the period, the starting and ending values and the number of years used. Without these, a figure cannot be checked or compared. Use the geometric average for the growth you actually received, and the simple average only as a rough guide to the typical yearly result. Comparing both over the same years, and against a broad market measure for the same dates, shows whether the investment did better or worse than the market as a whole.
Remember that past averages describe what happened, not what will happen. A strong record over a particular decade may reflect the conditions of that decade, so treat any average as one input to a longer decision rather than a forecast.
Frequently asked questions
Which average should I use to judge an investment?
The geometric average is the better measure of growth, because it reflects compounding. The arithmetic average is useful for a rough sense of typical yearly returns, but it overstates growth when returns are volatile.
Why is the geometric average lower?
Losses reduce the base on which later returns are earned. The more the returns vary, the bigger the gap between the simple average and the steady rate that gives the same result.
Should I include dividends in the returns?
Yes, if you want to measure total return. Enter returns that include dividends and interest; otherwise you measure only the price change and understate what you earned.
Can I enter returns for more or fewer than five years?
The calculator accepts a list of yearly returns of any length. Its layout shows five years, but the same method applies to any number of years you can enter by changing the form fields.
Does a good average return mean an investment is safe?
No. An average says nothing about how much the value fell in its worst year. Look at the range of yearly returns, the maximum fall, and how much risk you were prepared to take.