CAGR calculator

What is a CAGR calculator?

A CAGR calculator is a free online tool that works out the compound annual growth rate of an investment — the constant yearly rate at which a starting amount would have to grow to reach its ending amount over a given number of years. Because real returns are uneven from year to year, the CAGR smooths them into a single, steady percentage that is easy to compare across investments and time periods.

Why CAGR matters

Two investments can end at the same value yet take very different paths to get there, and they may also run for different lengths of time. CAGR removes that noise by expressing growth as one annualised rate, so a three-year result and a ten-year result can be placed side by side fairly. It is widely used to compare stocks, funds, business revenue, and savings, because it answers a simple question: on average, how fast did this grow each year?

How does the CAGR calculator work?

You provide three pieces of information:

• The beginning value (what the investment was worth at the start).
• The ending value (what it is worth at the end).
• The number of years between the two values.

The calculator divides the ending value by the beginning value to get the total growth factor, raises it to the power of one divided by the number of years, subtracts one, and expresses the result as a percentage. It also shows the total growth over the whole period for context.

CAGR versus total growth

Total growth tells you how much the investment changed in total, while CAGR tells you the equivalent steady rate per year. Over a one-year period the two are identical. Over longer periods they diverge: a 90% total gain spread across five years is only about 13.7% per year, because each year’s growth compounds on top of the previous year’s.

Formula

The compound annual growth rate is calculated as:

$CAGR = \left(\frac{V_{end}}{V_{begin}}\right)^{\frac{1}{n}} - 1$

Where:

• $CAGR$ is the compound annual growth rate (as a decimal; multiply by 100 for a percentage).
• $V_{end}$ is the ending value of the investment.
• $V_{begin}$ is the beginning value of the investment.
• $n$ is the number of years.

Examples of use

1. An investment that grows from $10,000 to $19,000 over 5 years:

   • Beginning value $V_{begin}$ = 10000
   • Ending value $V_{end}$ = 19000
   • Years $n$ = 5

   Calculation: $CAGR = \left(\frac{19000}{10000}\right)^{\frac{1}{5}} - 1 \approx 0.136974 = 13.6974\%$

2. An investment that doubles from $1,000 to $2,000 over 10 years:

   • Beginning value $V_{begin}$ = 1000
   • Ending value $V_{end}$ = 2000
   • Years $n$ = 10

   Calculation: $CAGR = \left(\frac{2000}{1000}\right)^{\frac{1}{10}} - 1 \approx 0.071773 = 7.1773\%$

3. An investment that falls from $10,000 to $8,000 over 3 years has a negative CAGR of about -7.1682%, even though the total change over the period is -20%.

Notes

CAGR assumes a single starting point and a single ending point, so it ignores any contributions or withdrawals made along the way and any volatility in between. It is a backward-looking, smoothed measure rather than a guarantee of future returns. For interest that compounds within a year, or to project a balance forward, other tools are a better fit.

Compare related tools such as the compound interest calculator and the APY calculator to model growth in more detail.

FAQs

What is the difference between CAGR and average annual return?

A simple average of yearly returns ignores compounding and can overstate growth. CAGR accounts for compounding by working from the start and end values, so it reflects the rate that actually links them.

Can CAGR be negative?

Yes. If the ending value is lower than the beginning value, the CAGR is negative, showing the steady yearly rate of decline over the period.

Does CAGR account for deposits or withdrawals?

No. CAGR only uses the beginning value, the ending value, and the number of years. If money was added or removed during the period, the result will not reflect those cash flows.