How to Calculate CAGR: The Formula, an Example, and Why Most People Get It Wrong

If you have ever read that the stock market "returns 10% per year on average" and assumed your portfolio will reliably compound at 10% annually, you have already fallen into the trap that confuses millions of investors. The number you actually need is CAGR — compound annual growth rate — and it is almost always lower, and far more honest, than the "average return" headline you see in the news. This article explains exactly how to calculate CAGR, walks through a real example you can verify yourself in our portfolio simulator, and shows why the simpler "average return" number can mislead you by thousands of dollars.

What is CAGR and why does it matter?

CAGR stands for compound annual growth rate. It is the single, constant annual return that would have taken your starting value to your ending value over a specific number of years, assuming reinvestment of all gains along the way.

In plain English: if your portfolio started at $10,000 and ended at $20,000 after 10 years, the CAGR is the steady yearly rate that, if you earned it every single year with no volatility, would produce exactly that same ending value. Markets do not actually deliver steady returns, of course — some years are +30%, others are -20% — but CAGR smooths all of that out into one honest comparison number.

This matters because CAGR is the only fair way to compare two investments that ran for different lengths of time or had very different volatility paths. Total return is useless for comparison if one investment ran for 3 years and the other for 15. Arithmetic average return is useless because it treats a -50% year and a +50% year as cancelling out, which they absolutely do not.

The CAGR formula

The formula is simple once you see it:

CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1

Or in spreadsheet notation: =(Ending / Beginning)^(1/Years) - 1

That is it. No advanced math. The "^(1/Years)" part is just taking the n-th root, which reverses the compounding effect so you get the equivalent per-year rate. If you prefer to think in percentages, multiply the result by 100.

A worked example

Let us say you invested $10,000 in an S&P 500 index fund on 1 January 2014. On 1 January 2024, it was worth $37,000. What is the CAGR?

• Beginning Value = $10,000
• Ending Value = $37,000
• Number of Years = 10

CAGR = ($37,000 / $10,000)^(1/10) - 1 = 3.7^0.1 - 1 = 1.1397 - 1 = 0.1397, or roughly 13.97%

So the S&P 500 "behaved as if" it returned about 14% every single year for a decade, even though the actual yearly returns bounced between roughly +30% and -20%. You can run this exact scenario yourself in our simulator: what if I invested in VOO 10 years ago.

Why arithmetic average return is not CAGR (and why it lies)

Here is the mistake almost every beginner makes, and even some financial journalists: they add up the yearly returns and divide by the number of years. That is the arithmetic mean, and it is the wrong number for growth.

Imagine a two-year investment:

• Year 1: +50%
• Year 2: -50%

Arithmetic average = (+50% + (-50%)) / 2 = 0%. Sounds like you broke even.

But in reality: $10,000 × 1.50 = $15,000. Then $15,000 × 0.50 = $7,500. You lost 25%.

The CAGR over those two years is actually -13.4% per year. The arithmetic mean said 0%. The CAGR says -13.4%. Only one of those is true, and it is not the one that looks nicer.

The bigger the volatility, the bigger the gap between arithmetic average and CAGR. For the S&P 500 over long periods, the arithmetic average is usually about 1.5 to 2 percentage points higher than the CAGR. That gap is not a rounding error. Over 30 years, 2% per year compounds into a difference of tens of thousands of dollars.

When to use CAGR vs total return

Use CAGR when:

• Comparing two investments that ran for different lengths of time.
• Reporting the "annualised" performance of a single investment.
• Evaluating whether a strategy beat a simple benchmark like the S&P 500.

Use total return when:

• You just want to know "how many dollars did I end up with?"
• You are comparing two investments over the exact same window and you only care about the end result.

Our portfolio simulator reports both on every backtest, because both matter in different contexts. If you are reading a stat bar and only looking at total return, you are missing the most useful comparison number. For a deeper dive on running a clean backtest, see our guide on how to backtest a portfolio.

Common mistakes when calculating CAGR

1. Using the wrong time period. If you measure from the bottom of a crash to the top of a bubble, your CAGR will look incredible and mean almost nothing. Always check whether the window includes at least one full market cycle.

2. Ignoring contributions or withdrawals. The simple CAGR formula assumes a single starting and ending value. If you added money along the way, the formula no longer applies — you need an internal rate of return (IRR) or money-weighted return instead. Our simulator handles this automatically when you add recurring contributions.

3. Confusing CAGR with the geometric mean of yearly returns. They are mathematically related, but geometric mean of yearly returns is not the same as CAGR unless you are measuring from a single starting lump sum. With contributions, the distinction matters.

4. Forgetting inflation. A 10% CAGR during a 3% inflation period is really a 7% real return. For long-term planning, you should care about real CAGR, not nominal CAGR.

CAGR in context: a reality check

Once you know how to calculate CAGR, the next step is calibrating your expectations. Here are some rough historical CAGRs for major asset classes over the last 20-30 years, measured in USD:

• US large-cap stocks (S&P 500): roughly 9-11%
• Global stocks (MSCI World): roughly 7-9%
• US bonds (Bloomberg Aggregate): roughly 3-5%
• Gold: roughly 5-7%, but with very long flat periods
• Cash / short-term treasuries: roughly 1-3%, often below inflation

If someone shows you a strategy with a 25% CAGR over 10 years, the honest response is not "amazing" — it is "what risk did they take, and what would the CAGR look like if I extended the window by five more years?" Most strategies that produce 20%+ CAGR over a decade either took extreme concentration risk, used leverage, or happened to start at a lucky moment.

A short checklist

Before you quote or compare any annual return figure:

• Is it CAGR or arithmetic average? If it is not CAGR, convert it. ✓
• Does the window include at least one bear market? ✓
• Does it account for fees, taxes and inflation (or at least acknowledge them)? ✓
• If contributions were made, is the return money-weighted or time-weighted? ✓

If you cannot answer those four questions, the number is a headline, not a fact.

FAQ

Is CAGR the same as annualised return?

Yes, in most contexts. "Annualised return," "CAGR," and "geometric mean return" are often used interchangeably when talking about a single lump-sum investment. The only subtle difference is that "annualised return" can sometimes be calculated with more complex formulas when contributions are involved, whereas "CAGR" usually implies the simple start-to-end formula.

Can CAGR be negative?

Absolutely. If your ending value is lower than your beginning value, the CAGR will be negative. A -5% CAGR over 5 years means your portfolio lost value at an equivalent rate of 5% per year.

Why do fund websites show average return instead of CAGR?

Because the arithmetic average is almost always higher, and higher numbers sell better. This is not universal — many professional platforms now lead with CAGR — but you should still check which number you are looking at before comparing funds.

How do I calculate CAGR with monthly contributions?

The simple CAGR formula no longer works because there is no single "beginning value" anymore. You need a money-weighted return, which is essentially an internal rate of return (IRR). The easiest way is to use our portfolio simulator — add your monthly contribution amount, set your assets, and the stats bar will calculate the correct annualised return for you.

Is a 7% CAGR good?

It depends entirely on what you compare it to. A 7% CAGR from a globally diversified stock portfolio is perfectly respectable and roughly in line with long-term historical returns. A 7% CAGR from a leveraged, concentrated crypto strategy would be disappointing. Always compare like for like: same asset class, same time period, same risk profile.

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Ready to see CAGR in action? Open the simulator, pick any asset and any time window, and compare the total return to the CAGR. The gap between what happened and what "feels like" it happened is usually the most educational part. New to the basics? Start with what an investment portfolio is.