The Average Return Calculator finds the single smoothed annual growth rate that explains how a beginning value became an ending value over a stated number of years. Enter the beginning value, the ending value and the number of years, and the calculator returns the compound average annual return, expressed as a percentage.
People often say "average return" when what they actually want is the one steady annual rate that, compounded year after year, would carry a starting balance to its final balance. That is not the same as averaging a list of yearly percentage changes, and the difference between the two methods can be surprisingly large once returns bounce around from year to year.
*These results are estimates for information only, not investment advice.*
Understand what "average return" really means here
When an investment's value moves from a beginning amount to an ending amount over several years, there are two common ways to describe its "average" yearly performance. The first is a simple average: add up each year's percentage return and divide by the number of years.
The second is a compound average, sometimes called a geometric average, which finds the single constant rate that would have produced the same ending value if applied every year without interruption.
The Average Return Calculator uses the compound method, since it is the one that actually reconciles with the real beginning and ending numbers. A simple average of yearly percentages can overstate true performance whenever returns are volatile, because losses and gains of the same percentage size do not cancel out evenly (a 50% loss followed by a 50% gain does not return you to even; it leaves you down 25%). The compound average return avoids that distortion entirely by working backward from the two actual dollar figures.
Work through the formula and a worked example
The formula is Average Return = (Ending Value / Beginning Value)^(1/Years) - 1. This single equation finds the constant annual rate that, compounded across the stated number of years, exactly bridges the beginning value to the ending value.
Take a beginning value of $10,000 that grew to $16,289 over 10 years. Dividing 16,289 by 10,000 gives 1.6289. Raising that to the power of 1 divided by 10 (the tenth root) gives approximately 1.05, and subtracting 1 leaves a compound average annual return of about 5.00%. The Average Return Calculator performs this calculation directly from the two dollar figures and the number of years, without needing a year-by-year breakdown of returns at all.
See why this differs from a simple year-by-year average
Because the compound average return is derived purely from the beginning value, the ending value and the elapsed time, it automatically accounts for every bit of volatility that happened along the way, even if the calculator never sees the individual yearly numbers.
Two investments with wildly different year-to-year paths, one smooth and one erratic, will show different simple averages of their yearly returns but can show the exact same compound average return if they started and ended at the same values over the same span of years.
This is precisely why the compound average return, often called CAGR when used for investments, is the standard way to summarize multi-year investment performance in fund reporting and academic finance, rather than a plain average of annual percentage changes, which tends to make volatile investments look better than they actually performed.
Use this to compare investments over different time spans
Because the average return figure is expressed as an annual rate rather than a total percentage gain, it puts investments held for different lengths of time on the same footing.
An investment that gained 30% total over 3 years and one that gained 60% total over 8 years cannot be compared directly by their total gains alone, but converting each to a compound average annual return makes the comparison meaningful.
The Average Return Calculator handles that conversion by taking whatever beginning value, ending value and number of years describe each investment and reducing them to one comparable annual percentage, regardless of how long each investment was actually held.
Know what this calculation assumes
This calculation assumes the beginning and ending values are known exactly, and it treats the entire period as a single, unbroken holding, without accounting for additional deposits, withdrawals, dividends reinvested at different times, taxes or fees unless those effects are already reflected in the two dollar figures entered.
If money was added or removed partway through the period, the resulting return figure will not accurately represent the investment's true underlying performance, since the formula assumes only the original amount grew, undisturbed, into the final amount.
For a portfolio with cash flows during the period, a dollar-weighted or money-weighted return calculation would be more appropriate. The Average Return Calculator is built for the simpler, and very common, case of a single lump sum observed at two points in time.
Frequently asked questions
What is the formula for average return?
The formula for average return, using the compound method, is (Ending Value / Beginning Value)^(1/Years) - 1. This finds the single constant annual rate that would carry the beginning value to the ending value over the stated number of years.
Why isn't average return just the average of yearly percentage changes?
Average return is not simply the average of yearly percentage changes because that simple method can distort results when returns are volatile. A 50% loss followed by a 50% gain averages to 0% using the simple method but actually leaves an investor down 25%, which the compound method correctly reflects.
What does a $10,000 to $16,289 growth over 10 years work out to?
Growth from $10,000 to $16,289 over 10 years works out to a compound average annual return of about 5.00%, found by taking the tenth root of 1.6289 and subtracting 1.
Is average return the same thing as CAGR?
Yes, "average return" calculated this way is the same concept as the compound annual growth rate, commonly abbreviated CAGR. Both describe the single smoothed annual rate that reconciles a beginning value with an ending value over a period of years.
Does this calculation account for deposits or withdrawals during the period?
No, this calculation assumes a single amount grew, without interruption, from the beginning value to the ending value. Additional deposits or withdrawals during the period would require a different, cash-flow-aware return calculation to be accurate.
Summary
The Average Return Calculator finds the compound annual growth rate that bridges a beginning value to an ending value over a stated number of years, using Average Return = (Ending Value / Beginning Value)^(1/Years) - 1. A $10,000 balance that grew to $16,289 over 10 years shows an average annual return of about 5.00%.
This compound method is more accurate than averaging yearly percentage changes, especially when returns are volatile, and it assumes no deposits or withdrawals occurred between the beginning and ending values. Figures are estimates for informational use only, not investment advice.