A CAGR calculator tells you the steady yearly growth rate that would take a starting value to an ending value over a set number of years. CAGR stands for compound annual growth rate. It is one of the most common ways to describe how an investment, a company’s sales, or an account balance grew over time.
This guide covers what the number means, how to work it out by hand, and why it should be read with care. Each term is explained as it comes up.
What a CAGR calculator measures
Most things do not grow by the same amount each year. A stock might rise 20 percent one year, fall 10 percent the next, and rise 5 percent after that. Describing that path takes a lot of numbers.
CAGR replaces the whole path with one rate. It asks a simple question. If growth had been perfectly steady, what yearly rate would produce the same start and finish? The answer is the CAGR. It is a summary, like an average speed on a long drive.
The formula in words
Divide the ending value by the beginning value. Raise that result to the power of one divided by the number of years. Then subtract one. As a formula, CAGR = (ending value / beginning value)^(1/years) – 1. Multiply by 100 to show it as a percent.
The step with the power is a root. Raising to the power of one-half is a square root. Raising to the power of one-fifth is a fifth root. It finds the single yearly growth factor that, when multiplied by itself for each year, gives the total growth.
A worked example
Suppose an account grew from $10,000 to $16,000 over 5 years.
Step one: divide the ending value by the beginning value. $16,000 / $10,000 = 1.6. Step two: raise 1.6 to the power of 1/5, which is 0.2. That gives about 1.0986. Step three: subtract one to get 0.0986. As a percent, the CAGR is about 9.86 percent.
Now check it by working forward. Start with $10,000 and multiply by 1.0986 five times. After year one you have about $10,986. After year two, about $12,069. After year three, about $13,259. After year four, about $14,566. After year five, about $16,000. The check works, which tells us the answer is right.
Why CAGR smooths out the ups and downs
Here is a short case that shows the smoothing. An account starts at $10,000. In year one it rises 50 percent, to $15,000. In year two it falls 20 percent, to $12,000.
A simple average of the two yearly results is (50 – 20) / 2 = 15 percent. That sounds strong. But the account only went from $10,000 to $12,000, a 20 percent total gain over two years. The CAGR is the square root of 1.2 minus one, which is about 9.54 percent.
So the plain average overstates what happened, and CAGR gives the rate that really connects start to finish. This is the main reason people prefer it to a simple average for growth over time.
Why CAGR also hides risk
The same smoothing that makes CAGR tidy also hides the bumpy ride. Two investments can share the same CAGR and feel completely different to own.
One may climb gently each year. Another may drop by a third, then jump back up. If both start and end at the same values, the CAGR is identical. The calculator cannot tell you which path you would have had to sit through.
This matters because the ride affects real choices. A large drop in the middle can lead people to sell at a bad time, or can shake confidence in a plan. CAGR says nothing about the worst year, the length of a decline, or how much the value moved around.
How to read the result
Read CAGR as a description of the past, not a promise about the future. A 9.86 percent CAGR means the value grew as if it gained that much each year. It does not mean it will continue.
Look at the time span too. A short period can be flattering or harsh depending on the start and end dates. Try the same investment over several windows, such as 3, 5, and 10 years, and see how the rate changes. If the numbers swing a lot, the single figure is hiding something.
CAGR also works for things other than prices. You can use it for revenue, user counts, savings balances, or dividends. The math is identical.
Common mistakes
- Using the wrong number of years. Count the gaps between the dates, not the number of data points.
- Forgetting to subtract one at the end, which leaves a growth factor instead of a rate.
- Using the plain average of yearly returns when a compound figure is needed.
- Ignoring cash added or removed during the period. CAGR assumes none.
- Comparing CAGRs that cover different time windows as if they were equal.
Limits of the tool
A CAGR calculator only needs a start value, an end value, and a time span. Everything between those points is invisible to it. That is its strength and its weakness.
It also ignores deposits, withdrawals, dividends, taxes, and fees unless you build them into the values. If the end value is negative or the start value is zero, the formula does not work. And a rate that looks smooth on paper is never a guarantee of a smooth path.
Common questions
Is CAGR the same as average return?
No. An average return adds yearly returns and divides. CAGR finds the steady rate that links the start and end values. The two usually differ, and CAGR is usually lower when returns swing.
Can CAGR be negative?
Yes. If the ending value is lower than the beginning value, the result is negative. It means the value shrank at that steady yearly pace.
How many years should I use?
Use the real length of the period you want to study. Longer spans tend to give a fuller picture, but they can also blend very different eras into one number.
Does CAGR include dividends?
Only if the values you enter include them. Price-only values leave dividends out. Total-return values include them.
Is a higher CAGR always better?
Not on its own. A higher number may have come with larger drops along the way. It helps to look at risk and the path as well.
Putting it to use
Use the CAGR calculator on this site to try your own numbers. You can also look up unfamiliar terms in the glossary, browse more tools in the calculators section, practice with Stockvert, or test your knowledge with Stock Jeopardy. Run a few examples, then compare them. Used with care, a CAGR calculator gives a clear way to describe past growth, as long as you remember what the single number leaves out.
For free, neutral basics from the government, the SEC runs Investor.gov.
Positive Stocks is for education only. It is not investment advice. Investing involves risk, including loss of money. Do your own research and speak with a licensed professional.
