How to Calculate CAGR: Formula and Worked Examples

When you want to compare two investments that grew over several years, the raw percentage gain rarely tells the full story. What you really want is the steady yearly rate that connects where you started to where you ended. That single figure is the compound annual growth rate, and it is one of the most useful numbers in investing.

What CAGR Means

CAGR stands for Compound Annual Growth Rate. It answers a clean question: if your investment had grown at one constant rate every year, what would that rate be to take it from its beginning value to its ending value over the given period.

Real investments rarely grow in a smooth line. They surge one year and slump the next. CAGR strips out that noise and gives you the equivalent steady rate, which makes it far easier to compare options that took very different paths to their results.

Why a Simple Average Falls Short

It is tempting to just average the yearly returns, but that can badly mislead you. Suppose an investment gains 50 percent one year and loses 50 percent the next. The simple average is zero, suggesting you broke even. In reality, 100 growing by 50 percent becomes 150, and then losing 50 percent leaves 75. You actually lost a quarter of your money.

CAGR captures this correctly because it is built on compounding and looks only at the true start and end values. That is why analysts reach for CAGR rather than a plain average when judging performance.

The CAGR Formula Explained

The formula is compact. CAGR equals the ending value divided by the beginning value, raised to the power of one divided by the number of years, then you subtract one. Multiply the result by 100 to read it as a percentage.

The components are:

• Beginning value, the amount you started with.
• Ending value, the amount you finished with.
• Number of years, the length of the holding period.

Raising the ratio to one over the number of years is the step that converts the total growth into a per-year rate, undoing the compounding to reveal the constant annual figure.

A Worked Example

Imagine you invested 10,000 and after 5 years it grew to 16,000.

First, divide the ending value by the beginning value: 16,000 divided by 10,000 is 1.6. Next, raise 1.6 to the power of one divided by 5, which is the same as the fifth root of 1.6. That works out to about 1.0986. Subtract 1 to get 0.0986, then multiply by 100 for a CAGR of roughly 9.86 percent.

So your investment grew at an equivalent steady rate of about 9.86 percent per year, even though the actual yearly returns probably bounced around quite a bit. That smoothed figure is exactly what you would use to compare this investment against another over a different period.

How to Use the CAGR Calculator

Taking roots by hand is awkward, so the CAGR Calculator handles it instantly. The steps are simple:

1. Enter the beginning value of your investment.
2. Enter the ending value.
3. Set the number of years between the two.
4. Read the CAGR as a clean annual percentage.

Because the CAGR Calculator updates as you type, you can quickly compare several investments by running each one and lining up the rates. A higher CAGR over the same period generally signals stronger compounded performance.

When CAGR Is and Is Not the Right Tool

CAGR is excellent for comparing the overall growth of investments, but it has blind spots worth respecting:

• It smooths volatility, so it hides how bumpy the ride actually was.
• It assumes a single lump sum, so it does not account for money added or withdrawn along the way.
• It is backward looking, describing what happened rather than predicting the future.

Use CAGR to judge and compare historical performance, and pair it with a look at the year-to-year swings if risk matters to your decision. For projecting future growth from regular contributions, the related calculators are a better fit.

It also helps to keep the time period in mind when you read a CAGR figure. A high growth rate over just one or two years can be down to luck or a single good run, while the same rate sustained across many years is far more meaningful. Whenever you compare two investments, make sure you are measuring each over a comparable number of years, otherwise the rates are not telling you the same kind of story. Comparing a three year CAGR against a ten year CAGR can flatter the shorter, more volatile track record.

Conclusion

CAGR turns messy, uneven returns into a single steady annual rate, which is why it is the go-to metric for comparing investments over time. The formula needs only three inputs, and the worked example shows how a jump from 10,000 to 16,000 over five years translates to about 9.86 percent a year. Run your own figures through the CAGR Calculator, then explore the rest of the free all tools for more financial calculators.