Finance • Compound Growth • CAGR • Investment Return

CAGR Calculator

Q: What is the CAGR formula?

The formula is CAGR = (FV / PV)^(1/t) - 1, where FV is future value, PV is beginning value, and t is time in years.

Use this CAGR Calculator to calculate compound annual growth rate from a beginning value, ending value, and number of years. You can also solve for future value, beginning value, or time using the same compound growth relationship. The calculator shows total return, investment multiple, gain or loss.

Find CAGRUse $CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1$.

Find future valueUse $FV=PV(1+CAGR)^t$.

Compare growthSee total return, multiple, and gain/loss.

Enter CAGR details

Calculate CAGR from beginning value, ending value, and years Calculate future value from beginning value, CAGR, and years Calculate beginning value from future value, CAGR, and years Calculate years needed from beginning value, future value, and CAGR

CAGR mode selected.
Enter $PV$, $FV$, and $t$. The calculator uses $CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1$.

Beginning value $PV$

Ending / future value $FV$

CAGR (%)

Time $t$, in years

Rounding

Currency symbol

CAGR is a smoothed annual growth rate. It assumes steady compounding between the beginning and ending values, even if the real yearly path was uneven.

Results

Enter values and calculate.

Main result

$8.45\%$

Total return

$50.00\%$

Growth multiple

$1.50\times$

Gain or loss

$5,000.00

CAGR formula

CAGR stands for compound annual growth rate. It measures the constant yearly growth rate that would turn a beginning value into an ending value over a specific number of years. The standard CAGR formula is:

\[ CAGR=\left(\frac{FV}{PV}\right)^{\frac{1}{t}}-1 \]

Where:

$CAGR$ is the compound annual growth rate.
$PV$ is the present value, beginning value, or initial value.
$FV$ is the future value, ending value, or final value.
$t$ is the number of years.

To express CAGR as a percentage, multiply the decimal result by $100$:

\[ CAGR\%=\left[\left(\frac{FV}{PV}\right)^{\frac{1}{t}}-1\right]\times100 \]

This calculator uses that formula when solving for CAGR. It also rearranges the same compound growth relationship to solve for future value, beginning value, and years. The core relationship behind all modes is:

\[ FV=PV(1+CAGR)^t \]

How to use the CAGR Calculator

Choose what you want to calculate. Select CAGR, future value, beginning value, or years needed.
Enter the known values. For CAGR, enter beginning value, ending value, and years. For future value, enter beginning value, CAGR, and years.
Choose rounding and currency. Select how many decimals to display and choose the currency symbol that fits your example.
Click Calculate CAGR. The calculator shows the main result, total return, growth multiple, gain or loss, and step-by-step work.
Review the formula steps. Each result includes the formula used, substituted values, and interpretation.
Use the result carefully. CAGR smooths growth into one annual rate. It does not show volatility, risk, timing of cash flows, fees, taxes, or inflation.

This CAGR calculator is useful for investment growth, business revenue growth, website traffic growth, property value growth, startup metrics, portfolio performance, sales growth, and finance education.

What is CAGR?

CAGR is the annualized growth rate that links a beginning value to an ending value over a period of time. It is not the same as a simple average return. CAGR assumes the value grows at a constant compounded rate each year, even if the actual path was uneven.

For example, an investment may rise sharply in one year, fall the next year, and recover later. The actual yearly returns could be very different, but CAGR gives one clean annual growth rate that summarizes the start-to-end performance.

Suppose an investment grows from $10{,}000$ to $15{,}000$ over $5$ years. The total growth is $50\%$, but the CAGR is not $50\%\div5=10\%$. Because growth compounds, the correct CAGR is:

\[ CAGR=\left(\frac{15{,}000}{10{,}000}\right)^{1/5}-1\approx8.45\% \]

This means growing at about $8.45\%$ per year, compounded, would turn $10{,}000$ into $15{,}000$ over $5$ years.

Worked example: calculate CAGR

Suppose an investment starts at $10{,}000$, ends at $15{,}000$, and is held for $5$ years. First identify the values:

\[ PV=10{,}000,\qquad FV=15{,}000,\qquad t=5 \]

Use the CAGR formula:

\[ CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1 \]

Substitute:

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

Simplify the growth multiple:

\[ CAGR=(1.5)^{1/5}-1 \]

Calculate:

\[ CAGR\approx0.08447 \]

Convert to a percentage:

\[ CAGR\approx8.45\% \]

The investment’s compound annual growth rate is about $8.45\%$.

Future value formula using CAGR

If you know the beginning value, CAGR, and time, you can calculate the future value. The formula is:

\[ FV=PV(1+CAGR)^t \]

For example, suppose $PV=20{,}000$, $CAGR=7\%=0.07$, and $t=10$. Then:

\[ FV=20{,}000(1+0.07)^{10} \]

So:

\[ FV=20{,}000(1.07)^{10} \]

The future value is approximately:

\[ FV\approx39{,}343 \]

This means that if the value grows at a compound annual growth rate of $7\%$, $20{,}000$ becomes about $39{,}343$ after $10$ years.

Beginning value formula

If you know the future value, CAGR, and number of years, you can solve for the beginning value. Start with:

\[ FV=PV(1+CAGR)^t \]

Divide both sides by $ (1+CAGR)^t $:

\[ PV=\frac{FV}{(1+CAGR)^t} \]

For example, if a future value is $50{,}000$, the CAGR is $6\%$, and the time period is $8$ years, then:

\[ PV=\frac{50{,}000}{(1.06)^8} \]

The estimated beginning value is:

\[ PV\approx31{,}370 \]

This means a value of about $31{,}370$ growing at $6\%$ per year for $8$ years would reach $50{,}000$.

Years needed formula

If you know the beginning value, future value, and CAGR, you can solve for the number of years. Start again with:

\[ FV=PV(1+CAGR)^t \]

Divide by $PV$:

\[ \frac{FV}{PV}=(1+CAGR)^t \]

Use logarithms to solve for $t$:

\[ t=\frac{\ln(FV/PV)}{\ln(1+CAGR)} \]

For example, if $PV=10{,}000$, $FV=20{,}000$, and $CAGR=8\%=0.08$, then:

\[ t=\frac{\ln(20{,}000/10{,}000)}{\ln(1.08)} \]

So:

\[ t=\frac{\ln(2)}{\ln(1.08)}\approx9.01 \]

It would take about $9.01$ years to double the value at an $8\%$ CAGR.

CAGR versus total return

Total return measures the full change from beginning value to ending value. CAGR converts that full change into a compounded annual rate. The total return formula is:

\[ \text{Total Return}=\frac{FV-PV}{PV}\times100 \]

If $PV=10{,}000$ and $FV=15{,}000$, the total return is:

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

The CAGR over $5$ years is about $8.45\%$. Both numbers are useful, but they answer different questions. Total return asks, “How much did the value change overall?” CAGR asks, “What constant annual compound rate would create the same overall change?”

This distinction matters when comparing investments or business metrics over different time periods. A $50\%$ total return over $2$ years is much stronger than a $50\%$ total return over $10$ years. CAGR adjusts for the time period.

CAGR versus simple average growth

A simple average growth rate adds yearly growth rates and divides by the number of years. CAGR does not do that. CAGR uses beginning value, ending value, and time. It captures compounding, which is why it is usually better for multi-year growth analysis.

Consider a value that changes from $100$ to $150$ in year one, then from $150$ to $75$ in year two. The yearly returns are $+50\%$ and $-50\%$. The simple average is:

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

But the value did not end at $100$. It ended at $75$. The CAGR is:

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

The CAGR correctly shows that the value declined on a compounded annual basis. This is why CAGR is preferred when the path includes compounding or uneven yearly changes.

Why CAGR is useful

CAGR is useful because it gives a clean way to compare growth across different time periods. If one investment grows $60\%$ over $6$ years and another grows $40\%$ over $3$ years, total return alone does not make the comparison easy. CAGR converts each result into an annual compounded rate.

CAGR is also useful for business metrics. A company may use CAGR to describe revenue growth, customer growth, profit growth, market size growth, or website traffic growth. For example, if revenue grows from $2$ million to $5$ million over $4$ years, CAGR summarizes the annualized growth rate:

\[ CAGR=\left(\frac{5}{2}\right)^{1/4}-1 \]

This produces a yearly compound growth estimate. It helps investors, managers, and analysts understand how quickly the metric grew over the full period.

CAGR in investments

In investing, CAGR is commonly used to summarize portfolio performance, stock growth, fund returns, real estate appreciation, or long-term asset growth. If a portfolio grows from $25{,}000$ to $40{,}000$ over $6$ years, CAGR tells the annual compound rate that produced that start-to-end result.

However, CAGR should not be treated as a complete investment analysis. It does not show volatility, drawdowns, risk, income timing, or cash-flow timing. Two investments can have the same CAGR but very different risk profiles. One may grow smoothly, while another may crash and recover. CAGR only shows the smoothed rate between two endpoints.

For complete investment evaluation, CAGR is often considered alongside volatility, maximum drawdown, fees, taxes, inflation, dividends, cash flows, and risk-adjusted returns.

CAGR in business growth

Businesses use CAGR to measure long-term growth in revenue, users, subscribers, customers, profit, market share, or production volume. For example, if a company grows revenue from $1{,}000{,}000$ to $1{,}800{,}000$ over $3$ years, the CAGR is:

\[ CAGR=\left(\frac{1{,}800{,}000}{1{,}000{,}000}\right)^{1/3}-1 \]

That simplifies to:

\[ CAGR=(1.8)^{1/3}-1 \]

CAGR helps show the pace of business growth in a standardized way. A company with $20\%$ revenue CAGR over several years is generally growing quickly. But CAGR should still be interpreted with context. Growth quality, profit margins, customer retention, and cash flow matter too.

CAGR and investment multiple

The investment multiple is the ratio of ending value to beginning value:

\[ \text{Growth Multiple}=\frac{FV}{PV} \]

If an investment grows from $10{,}000$ to $15{,}000$, the multiple is:

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

This means the ending value is $1.5\times$ the beginning value. CAGR annualizes that multiple. In formula form:

\[ CAGR=(\text{Growth Multiple})^{1/t}-1 \]

When the growth multiple is greater than $1$, CAGR is positive. When it is less than $1$, CAGR is negative. When it equals $1$, CAGR is $0\%$.

Negative CAGR

CAGR can be negative when the ending value is lower than the beginning value. For example, suppose an investment falls from $20{,}000$ to $12{,}000$ over $4$ years. The CAGR is:

\[ CAGR=\left(\frac{12{,}000}{20{,}000}\right)^{1/4}-1 \]

Simplify:

\[ CAGR=(0.6)^{1/4}-1 \]

Calculate:

\[ CAGR\approx-11.99\% \]

This means the value declined at an average compounded rate of about $11.99\%$ per year. A negative CAGR is useful because it expresses a total decline as a yearly compounded loss rate.

Limitations of CAGR

CAGR is simple and powerful, but it has important limitations. First, CAGR smooths the growth path. If an investment moves up and down dramatically, CAGR hides that volatility. It only uses beginning value, ending value, and time.

Second, CAGR does not handle interim cash flows well. If you added money, withdrew money, received dividends, or made irregular contributions during the period, a simple CAGR calculation may not reflect your actual investor experience. For irregular cash flows, a money-weighted return or internal rate of return may be more appropriate.

Third, CAGR does not automatically adjust for taxes, fees, inflation, or risk. If your ending value is before fees or taxes, the CAGR is also before those costs. If inflation was high, nominal CAGR may look good while real purchasing-power growth is lower.

CAGR, IRR, and annualized return

CAGR, annualized return, and IRR are related, but they are not always interchangeable. CAGR is best for a simple start-to-end calculation with no interim cash flows. Annualized return often means the same thing in that simple context. IRR is better when there are multiple cash flows at different times.

Measure	Best used when	Main idea
CAGR	One beginning value, one ending value, and one time period.	Find the smoothed compound annual growth rate.
Annualized return	Simple start-to-end investment comparison.	Often uses the same formula as CAGR.
IRR	There are deposits, withdrawals, or irregular cash flows.	Find a rate that balances multiple timed cash flows.
Total return	You only need the full-period percentage gain or loss.	Measures total percentage change from start to finish.

Use CAGR when the growth story can be fairly represented by a beginning value, ending value, and duration. Use more advanced methods when cash-flow timing matters.

Common mistakes when calculating CAGR

Dividing total return by years. This creates a simple average, not CAGR.
Using percentages directly in formulas. Convert $8\%$ into $0.08$ before using it in compound growth formulas.
Using the wrong number of years. CAGR depends strongly on the time period $t$.
Ignoring cash flows. Contributions, withdrawals, dividends, and partial investments can make simple CAGR misleading.
Assuming CAGR shows risk. CAGR does not show volatility or drawdowns.
Comparing CAGRs without context. A high CAGR may come with high risk, low liquidity, or unusual market timing.
Forgetting inflation. Nominal CAGR may be higher than real CAGR after inflation.

CAGR formula summary table

Calculation	Formula	Use it when
CAGR	$CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1$	You know beginning value, ending value, and years.
Future value	$FV=PV(1+CAGR)^t$	You know beginning value, CAGR, and years.
Beginning value	$PV=\frac{FV}{(1+CAGR)^t}$	You know future value, CAGR, and years.
Years needed	$t=\frac{\ln(FV/PV)}{\ln(1+CAGR)}$	You know beginning value, future value, and CAGR.
Total return	$\frac{FV-PV}{PV}\times100$	You want the full-period percentage gain or loss.
Growth multiple	$\frac{FV}{PV}$	You want to know how many times the value grew.

Related calculators and study tools

CAGR connects naturally to annualized return, compound interest, appreciation, APY, and percentage change. These related tools can help users continue learning finance and growth calculations on NUM8ERS.

Update these internal links if your final NUM8ERS URL structure uses different calculator paths.

CAGR Calculator FAQs

What is CAGR?

CAGR stands for compound annual growth rate. It is the constant annual growth rate that would turn a beginning value into an ending value over a set number of years.

What is the CAGR formula?

The formula is $CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1$, where $FV$ is future value, $PV$ is beginning value, and $t$ is time in years.

Is CAGR the same as annualized return?

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

Can CAGR be negative?

Yes. If the ending value is lower than the beginning value, CAGR is negative.

Does CAGR include deposits or withdrawals?

No. A basic CAGR calculation assumes one beginning value and one ending value. If there are irregular cash flows, IRR may be more appropriate.

Why is CAGR better than simple average growth?

CAGR accounts for compounding. Simple average growth can be misleading when yearly returns are uneven.

Calculation	Formula	Use it when
CAGR	\(CAGR=\left(\frac{FV}{PV}\right)^{1/t}-1\)	You know beginning value, ending value, and years.
Future value	\(FV=PV(1+CAGR)^t\)	You know beginning value, CAGR, and years.
Beginning value	\(PV=\frac{FV}{(1+CAGR)^t}\)	You know future value, CAGR, and years.
Years needed	\(t=\frac{\ln(FV/PV)}{\ln(1+CAGR)}\)	You know beginning value, future value, and CAGR.
Total return	\(\frac{FV-PV}{PV}\times100\)	You want the full-period percentage gain or loss.
Growth multiple	\(\frac{FV}{PV}\)	You want to know how many times the value grew.