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Annualized Rate of Return Calculator

Q: What is the annualized return formula?

The formula is ARR = (EV / BV)^(1/n) - 1, where EV is ending value, BV is beginning value, and n is the number of years.

Use this Annualized Rate of Return Calculator to convert an investment’s total growth into an average yearly growth rate. Enter the beginning value, ending value, and time period to calculate the annualized return, also commonly called CAGR. The calculator shows the formula, total return, investment multiple, absolute gain or loss.

Annualized returnFind $ \left(\frac{EV}{BV}\right)^{1/n}-1 $.

Total returnCompare ending value with beginning value.

Flexible time inputUse years directly or calculate years from dates.

Enter investment values

Use beginning value, ending value, and years Use beginning value, ending value, and dates Use beginning value, total return, and years

Years mode selected.
Enter $BV$, $EV$, and $n$. The calculator uses $ARR=\left(\frac{EV}{BV}\right)^{1/n}-1$.

Beginning value $BV$

Ending value $EV$

Investment period $n$, in years

Rounding

Currency symbol

This calculator assumes one beginning value and one ending value. If there are deposits, withdrawals, dividends reinvested at different times, or irregular cash flows, use a money-weighted return or IRR method instead.

Results

Enter values and calculate.

Annualized rate of return

$8.45\%$

Total return

$50.00\%$

Investment multiple

$1.50\times$

Gain or loss

$5,000.00

Annualized rate of return formula

The annualized rate of return shows the average yearly growth rate of an investment over a period longer or shorter than one year. It converts total growth into a yearly compounded rate, making it easier to compare investments with different holding periods. The standard formula is:

\[ ARR=\left(\frac{EV}{BV}\right)^{\frac{1}{n}}-1 \]

Where:

$ARR$ = annualized rate of return
$BV$ = beginning value of the investment
$EV$ = ending value of the investment
$n$ = number of years the investment was held

When expressed as a percentage, multiply the decimal result by $100$:

\[ ARR\%=\left[\left(\frac{EV}{BV}\right)^{\frac{1}{n}}-1\right]\times100 \]

This formula is also commonly called the compound annual growth rate formula, or CAGR formula. In many investment contexts, annualized return and CAGR are used in a very similar way when there is one beginning value, one ending value, and no interim cash flows.

How to use the Annualized Rate of Return Calculator

Choose the input mode. Use years mode if you already know the investment period. Use dates mode if you want the calculator to estimate the number of years between two dates. Use total-return mode if you know the total percentage gain instead of the ending value.
Enter the beginning value. This is the initial amount invested or the starting portfolio value.
Enter the ending value or total return. The ending value is the final portfolio value. Total return is the percentage change over the full period.
Enter the time period. The annualized rate depends heavily on $n$, so use the correct number of years.
Click Calculate Annualized Return. The calculator will show the annualized return, total return, investment multiple, gain or loss, and calculation steps.
Read the interpretation. The annualized return is not the exact return earned every year. It is the constant yearly rate that would produce the same beginning-to-ending result.

This calculator is useful for stocks, funds, real estate, business growth, savings accounts, education examples, portfolio summaries, and any situation where you need to compare growth across different time periods.

What is annualized rate of return?

The annualized rate of return is the average compounded yearly return that would turn the beginning value into the ending value over the investment period. It does not say the investment earned exactly that rate in every year. Instead, it smooths the full investment performance into one yearly rate.

For example, an investment may rise $30\%$ in one year, fall $10\%$ the next year, and rise again later. The actual yearly returns may be uneven, but the annualized return gives one rate that summarizes the entire period. This makes it easier to compare two investments with different time lengths.

Suppose investment A grows from $10{,}000$ to $15{,}000$ in five years. Investment B grows from $10{,}000$ to $15{,}000$ in ten years. Both have the same total return of $50\%$, but investment A grew faster because it reached the same ending value in less time. Annualized return captures that difference.

Worked example: annualized return from beginning and ending values

Suppose an investment starts at $10{,}000$, grows to $15{,}000$, and is held for $5$ years. The beginning value is:

\[ BV=10{,}000 \]

The ending value is:

\[ EV=15{,}000 \]

The time period is:

\[ n=5 \]

Substitute into the annualized return formula:

\[ ARR=\left(\frac{15{,}000}{10{,}000}\right)^{\frac{1}{5}}-1 \]

Simplify the investment multiple:

\[ ARR=(1.5)^{\frac{1}{5}}-1 \]

Calculate:

\[ ARR\approx0.08447 \]

Convert to a percentage:

\[ ARR\approx8.45\% \]

This means the investment grew at an average compounded rate of about $8.45\%$ per year.

Total return versus annualized return

Total return and annualized return are related, but they answer different questions. Total return measures the full percentage change over the entire investment period. Annualized return converts that full-period return into a yearly compounded rate.

\[ \text{Total Return}=\frac{EV-BV}{BV} \]

As a percentage:

\[ \text{Total Return}\%=\frac{EV-BV}{BV}\times100 \]

If $BV=10{,}000$ and $EV=15{,}000$, the total return is:

\[ \frac{15{,}000-10{,}000}{10{,}000}\times100=50\% \]

The annualized return over five years is about $8.45\%$. Both numbers are correct, but they describe different things. Total return says the investment grew $50\%$ overall. Annualized return says that this is equivalent to growing at about $8.45\%$ per year, compounded annually, over five years.

Annualized return versus simple average return

A simple average return adds yearly returns and divides by the number of years. Annualized return, however, accounts for compounding. This distinction is important because investment growth compounds multiplicatively, not additively.

Suppose an investment returns $+50\%$ in year one and $-50\%$ in year two. The simple average is:

\[ \frac{50\%+(-50\%)}{2}=0\% \]

But the investment does not end where it started. If $100$ grows by $50\%$, it becomes $150$. If $150$ then falls by $50\%$, it becomes $75$. The total return is $-25\%$, not $0\%$. Annualized return reflects the compounded path from beginning value to ending value:

\[ ARR=\left(\frac{75}{100}\right)^{\frac{1}{2}}-1\approx-13.40\% \]

This is why annualized return is usually more meaningful than a simple average when evaluating multi-year investment performance.

Annualized return and CAGR

CAGR stands for compound annual growth rate. It is the constant annual growth rate that would take a beginning value to an ending value over a specified number of years. In the common beginning-value and ending-value setup, CAGR and annualized rate of return use the same formula:

\[ CAGR=\left(\frac{EV}{BV}\right)^{\frac{1}{n}}-1 \]

For this reason, many people use the phrases “annualized return” and “CAGR” interchangeably. The main idea is compounding. If an investment has a CAGR of $8\%$, it means that growing at $8\%$ per year, compounded, would produce the same ending value.

However, CAGR is a smoothed number. It hides volatility. An investment with a $10\%$ CAGR may have had very uneven yearly returns. It may have dropped sharply in one year and recovered later. CAGR is excellent for comparing start-to-end growth, but it does not show risk, volatility, or the timing of gains and losses.

Investment multiple

The investment multiple compares the ending value with the beginning value. It is calculated as:

\[ \text{Investment Multiple}=\frac{EV}{BV} \]

If $BV=10{,}000$ and $EV=15{,}000$, then:

\[ \frac{15{,}000}{10{,}000}=1.5 \]

This means the ending value is $1.5\times$ the beginning value. A multiple above $1$ indicates growth. A multiple below $1$ indicates loss. A multiple equal to $1$ means the ending value equals the beginning value.

The annualized return formula uses this multiple directly. It asks: “What yearly compounded rate would turn $1$ unit of beginning value into this multiple over $n$ years?” That is why the formula raises the multiple to the power $ \frac{1}{n} $.

Using dates to annualize a return

When the investment period is not a whole number of years, you can estimate $n$ from dates. A common approximation is:

\[ n=\frac{\text{number of days held}}{365.25} \]

The value $365.25$ accounts roughly for leap years. For example, if an investment is held for $913$ days, then:

\[ n=\frac{913}{365.25}\approx2.50 \]

The annualized formula then becomes:

\[ ARR=\left(\frac{EV}{BV}\right)^{\frac{1}{2.50}}-1 \]

Date-based annualization is useful when comparing investments held for different numbers of months or days. However, it is still a simplified measure and assumes the beginning and ending values are the only relevant cash flow points.

Interpreting a positive annualized return

A positive annualized return means the ending value is greater than the beginning value. For example, an annualized return of $8\%$ means the investment’s start-to-end performance is equivalent to compounding at $8\%$ per year over the given period.

If the beginning value is $10{,}000$, an annualized return of $8\%$ for five years would produce:

\[ EV=10{,}000(1+0.08)^5 \]

Simplify:

\[ EV=10{,}000(1.08)^5\approx14{,}693.28 \]

This is why annualized return can be used both backward and forward. Backward, it summarizes historical performance. Forward, it can model hypothetical growth. However, a historical annualized return does not guarantee future returns.

Interpreting a negative annualized return

A negative annualized return means the ending value is less than the beginning value. For example, if an investment falls from $10{,}000$ to $8{,}000$ over four years, the formula is:

\[ ARR=\left(\frac{8{,}000}{10{,}000}\right)^{\frac{1}{4}}-1 \]

Simplify:

\[ ARR=(0.8)^{\frac{1}{4}}-1\approx-5.43\% \]

This means the investment’s total loss is equivalent to losing about $5.43\%$ per year, compounded, for four years. Negative annualized returns are important because they show how losses compound over time. A small annualized loss over a long period can still create a large total decline.

Annualized return with total return input

If you already know total return, you can calculate annualized return without entering an ending value. First convert the total return percentage into a growth multiple:

\[ \text{Multiple}=1+\frac{\text{Total Return}\%}{100} \]

Then annualize the multiple:

\[ ARR=\left(1+\frac{\text{Total Return}\%}{100}\right)^{\frac{1}{n}}-1 \]

For example, if total return is $50\%$ over $5$ years, then:

\[ ARR=\left(1+\frac{50}{100}\right)^{\frac{1}{5}}-1 \]

So:

\[ ARR=(1.5)^{\frac{1}{5}}-1\approx8.45\% \]

This is the same answer as using $BV=10{,}000$ and $EV=15{,}000$, because those values also represent a $50\%$ total return.

When annualized return is useful

Annualized return is useful when comparing investments held for different time periods. A $20\%$ return in one year is very different from a $20\%$ return over ten years. Total return alone does not reveal the speed of growth. Annualized return adjusts for time.

For example, suppose investment A earns $40\%$ over two years and investment B earns $60\%$ over six years. At first, $60\%$ looks larger. But annualized return may show that investment A grew faster each year. This makes annualized return a better comparison tool than total return when time periods differ.

Annualized return is commonly used for stocks, mutual funds, ETFs, index performance, private investments, real estate, business revenue growth, and long-term savings growth. It is also used in education to teach exponential growth and compounding.

Limitations of annualized return

Annualized return is powerful, but it has limitations. First, it smooths performance. If an investment had large ups and downs, the annualized return will not show that volatility. Two investments can have the same annualized return but very different risk levels.

Second, the formula assumes there are no interim cash flows. If money was added or withdrawn during the period, the beginning-to-ending formula may be misleading. In that case, a money-weighted return, internal rate of return, or time-weighted return may be more appropriate.

Third, annualized return does not include taxes, fees, inflation, or risk unless the input values already reflect them. A nominal annualized return may look attractive, but the real return after inflation could be much lower. Always interpret the result in context.

Annualized return, IRR, and time-weighted return

Annualized return from beginning and ending values is simple and useful when there is one starting value and one ending value. But investors sometimes need more advanced return measures. Internal rate of return, or IRR, is often used when there are multiple cash flows at different times. Time-weighted return is often used for portfolio manager performance because it reduces the effect of investor deposits and withdrawals.

Measure	Best used when	Main idea
Annualized return / CAGR	One beginning value, one ending value, and one holding period.	Finds the constant yearly compounded rate.
IRR	There are deposits, withdrawals, or irregular cash flows.	Finds a discount rate that balances cash flows.
Time-weighted return	Evaluating portfolio performance independent of cash-flow timing.	Breaks performance into subperiods and compounds them.
Total return	You only need the full-period gain or loss.	Measures total percentage change from start to finish.

This calculator is designed for the first case: clean beginning-to-ending annualized return. If your investment has cash flows during the period, use the result as a simplified estimate rather than a complete performance measurement.

Common mistakes when calculating annualized return

Using total return as annualized return. A $50\%$ total return over five years is not $50\%$ per year.
Dividing total return by years. $50\%\div5=10\%$ is a simple average, not a compounded annualized return.
Using the wrong time period. Annualized return changes significantly if $n$ is entered incorrectly.
Ignoring cash flows. Additional deposits or withdrawals can make the simple beginning-to-ending formula misleading.
Forgetting to convert percentages. $8.45\%$ is $0.0845$ as a decimal.
Assuming smooth yearly returns. Annualized return is a smoothed result, not the actual return earned each year.
Ignoring inflation, fees, and taxes. The calculator uses the values you enter; it does not automatically adjust for real-world costs.

Annualized return formula summary table

Metric	Formula	What it tells you
Annualized return	$ARR=\left(\frac{EV}{BV}\right)^{1/n}-1$	The average compounded yearly return.
Annualized return percentage	$ARR\%=\left[\left(\frac{EV}{BV}\right)^{1/n}-1\right]\times100$	The annualized return expressed as a percentage.
Total return	$\frac{EV-BV}{BV}\times100$	The full-period percentage gain or loss.
Investment multiple	$\frac{EV}{BV}$	How many times larger the ending value is than the beginning value.
Gain or loss	$EV-BV$	The absolute increase or decrease in value.
Years from days	$n=\frac{\text{days}}{365.25}$	Converts a date range into an annualization period.

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Annualized Rate of Return Calculator FAQs

What is annualized rate of return?

Annualized rate of return is the average compounded yearly return that would turn a beginning value into an ending value over a given number of years.

What is the annualized return formula?

The formula is $ARR=\left(\frac{EV}{BV}\right)^{1/n}-1$, where $EV$ is ending value, $BV$ is beginning value, and $n$ is the number of years.

Is annualized return the same as CAGR?

For a simple beginning-value and ending-value calculation with no interim cash flows, annualized return and CAGR use the same formula.

Is total return the same as annualized return?

No. Total return measures the full gain or loss over the entire period. Annualized return converts that result into an average yearly compounded rate.

Can annualized return be negative?

Yes. If the ending value is lower than the beginning value, the annualized return will be negative.

Does this calculator handle deposits and withdrawals?

No. This calculator assumes one beginning value and one ending value. For irregular deposits or withdrawals, an IRR or money-weighted return calculation is usually more appropriate.

Metric	Formula	What it tells you
Annualized return	\(ARR=\left(\frac{EV}{BV}\right)^{1/n}-1\)	The average compounded yearly return.
Annualized return percentage	\(ARR\%=\left[\left(\frac{EV}{BV}\right)^{1/n}-1\right]\times100\)	The annualized return expressed as a percentage.
Total return	\(\frac{EV-BV}{BV}\times100\)	The full-period percentage gain or loss.
Investment multiple	\(\frac{EV}{BV}\)	How many times larger the ending value is than the beginning value.
Gain or loss	\(EV-BV\)	The absolute increase or decrease in value.
Years from days	\(n=\frac{\text{days}}{365.25}\)	Converts a date range into an annualization period.