CAGR Calculator

The Compound annual growth rate (CAGR) is a single constant growth rate that would increase an investment from its beginning value to its ending value over a given period of time. Actual returns are not uniform; some years may see increases and others decreases. Therefore, the CAGR is used to smooth out the annual numbers which makes it useful for quoting and comparing.

This calculator allows bidirectional calculations. You can enter the starting value, ending value, and number of years to calculate the CAGR. Alternatively, you can leave one of the four fields blank and the tool will calculate the corresponding value.

What is CAGR?

The CAGR is the average annual growth rate of an investment assuming that it grows at a steady pace every year and all earnings are reinvested during this time. As it is a geometric mean rather than an arithmetic one, it reflects the compounding effect. Even if a fund's total return over five years was 90%, for example, this does not necessarily mean that the fund grew by 18% each year. The actual average growth rate will usually be lower as annual growth builds on the previous year's result. Applying the CAGR figure over five years would give exactly the final value.

The CAGR is particularly useful for comparing investments with different holding periods and initial values because it represents growth as a single, clear rate. It's difficult to compare funds based on their total return if they were held over three years versus seven years. However, the CAGR allows you to make a comparison based on a common annual scale.

The formula for CAGR is:

The Compound annual growth rate is calculated by dividing the final value by the starting value, taking the reciprocal of the number of years and then subtracting one.

Here, EV is the ending value, BV is the starting value and n is the number of years. If you multiply the result by 100, then it will be a percentage.

Example of a calculation:

Suppose an investment has risen from $10,000 to $19,000 in five years. Divide the ending value by the starting value, take the fifth root and then subtract 1.

Thus the Compound annual growth rate (CAGR) is about 13.70%. The total return on this investment would be 90%, which is nearly double but after five years of compound interest growth, it equates to an annualized return of 13.70%. At that pace, capital doubles in approximately 5.4 years. This also aligns with the rule of 72 (roughly 5.3 when you divide 72 by 13.7).

Calculating CAGR backwards:

Often you will know the growth rate and want to solve for another value. For example, if you have a target growth rate and want to determine what your investment needs to be worth or how long it will take to reach that goal. You leave the desired element blank and enter the other three values, then the calculator adjusts the formula accordingly. There are three ways to work backwards:

The last formula answers the question of how long it takes to go from $10,000 to $25,000 assuming a steady annual growth rate of 8%.

Calculate compound annual growth rate (CAGR) monthly, quarterly or for any time period.

Since CAGR is an annualized rate, the easiest input is a whole number of years. For shorter time periods please enter the number of years as a decimal. 18 months would be 1.5 years, 8 months would be about 0.67 (the value of 8 divided by 12), and a quarter would be 0.25 years. The formula will automatically convert growth to an annualized rate and show the Compound annual growth rate for that time period.

Interpreting results for very short periods should be done with caution. A good performance over two months, when converted to an annual rate, can suggest a very high Compound annual growth rate even though that level is unlikely to be sustained in the long term. So CAGR is most meaningful for periods of one year or longer.

Comparison of CAGR and simple average return.

The most common mistake is to average the returns each year instead of compounding them. The simple average ignores the order of the returns and the effect of compound interest, so it often gives a better-looking performance than actually exists because it will always be equal or higher than CAGR. With more volatile swings this difference becomes larger. For example, if an investment goes up 50% in year one and down 50% in year two.

The simple average return is zero but the capital actually reduces to 750 resulting in a real loss. The CAGR reflects reality. The two year growth rate is about -13.4% per annum. When there are fluctuations in returns, you should rely on the CAGR rather than the arithmetic average.

CAGR vs. IRR Comparison

Both the compound annual growth rate (CAGR) and internal rate of return (IRR) provide a measure of growth as an annualized rate but answer different questions. The CAGR focuses only on the beginning and ending values and assumes no cash inflows or outflows, which makes it suitable for one-time investments that are simply meant to grow. IRR is a more flexible metric. It can account for multiple deposits and withdrawals at various dates and condense those cash flows into a single rate. Use IRR if you're making or withdrawing money during the period. If you make a lump sum deposit and withdraw later, then CAGR is the appropriate tool.

How to Interpret the Results

The CAGR only becomes meaningful when combined with a benchmark. The long term return of large U.S. stocks has been about 10% per year, not counting inflation. Since the average rate of inflation is about 3%, your real return is that portion of your CAGR that exceeds this amount. A CAGR of 13.70% is good compared to these benchmarks. A CAGR of 2% will barely keep up with price increases. If you activate a benchmark in this calculator, you can compare your rate against any benchmark and see the resulting dollar difference.

Limitations of the CAGR

The smoothing that makes the CAGR useful also hides some information. Because the investment process is not explained, an investment that has steadily risen and one that has experienced both booms and busts with large swings can have the same CAGR. The latter will be much riskier. The CAGR depends entirely on two endpoints, so temporary highs or lows at either the start or end date can give a skewed result. It is also calculated under the assumption of investing a lump sum, not additional deposits or withdrawals during the period. Finally, past CAGRs are historical observations and not predictions. Just because something has grown steadily in the past does not necessarily mean it will continue to do so in the future. Treat the CAGR as one perspective among many, rather than the only all-encompassing indicator.

Can the CAGR be negative?

Yes. If the ending value is below the starting value then this indicates that the investment has shrunk and the CAGR will be a negative number, i.e. a constant annual rate of decline. For example if an investment falls from 10,000 to 8,000 over three years, the CAGR would be about -7.2% per year. This calculator also supports negative results. Since shrinking investments never double, the time to double is simply not shown.

Calculating CAGR in Excel or Google Sheets

You can calculate the CAGR directly in a spreadsheet. If you have your starting value in cell B1, ending value in cell B2 and number of years in cell B3, one of the following formulas will give you the same result:

If you format the cell as a percentage or multiply by 100, then you can read the result just like this calculator.