What is the CAGR formula?

CAGR = (Ending Value / Beginning Value)^(1/n) − 1, where n is the number of years. The result is the constant annual growth rate that would take you from the starting value to the ending value in exactly n years. Multiply by 100 to express it as a percentage.

Why is CAGR better than a simple average return?

A simple average ignores compounding and order. If an investment drops 50% one year then gains 50% the next, the simple average is 0% — but you are actually down 25%. CAGR always gives the true smoothed annual rate that accounts for compounding. For multi-year returns it is the only accurate measure.

Can CAGR be negative?

Yes. If the ending value is less than the beginning value, CAGR will be negative. A $10,000 investment that drops to $7,500 over 5 years has a CAGR of about −5.6%. It shows the annualized rate of decline, which is just as useful as the annualized rate of growth.

What is the difference between CAGR and IRR?

CAGR assumes a single lump sum with no cash flows in between — one investment at the start, one payout at the end. IRR handles irregular cash flows (contributions and withdrawals along the way) and solves for the rate that makes the net present value zero. For simple start-to-finish growth with no intermediate transactions, CAGR is faster and simpler.

How do I calculate CAGR on a financial calculator?

Use the TVM keys. Enter N (number of years), PV (beginning value as a negative number), FV (ending value as a positive number), and PMT = 0. Solve for I/Y and the result is your CAGR. For example: N = 8, PV = −10000, FV = 25000, PMT = 0, solve for I/Y gives about 12.13%.

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How to Calculate Compound Annual Growth Rate (CAGR)

CAGR is the investment industry's go-to number for summarizing multi-year performance. It answers one question: if this investment had grown at a steady, constant rate instead of bouncing around, what would that rate be? Here's the formula in plain English, a real worked example, why it beats a simple average, and the mistake everyone makes at least once.

Last updated: August 2, 2026.

The formula, unpacked

The compound annual growth rate formula is:

CAGR = (Ending Value / Beginning Value)^1/n − 1

Only three inputs:

Ending Value — what the investment is worth at the end of the period.
Beginning Value — what you started with.
n — the number of years between those two points.

The result is the annualized growth rate, expressed as a decimal. Multiply by 100 to turn it into a percentage. That's it — one equation, no intermediate steps or year-by-year returns needed. You only care about the start, the end, and how much time passed.

A real example: $10,000 to $25,000 over 8 years

Say you bought $10,000 of an S&P 500 index fund in January 2018. By January 2026 it's worth $25,000. The market didn't go straight up — there was a pandemic crash, a tech rally, a bear market, a recovery — but all you care about is the smoothed annual rate. Plug in the numbers:

CAGR = (25,000 / 10,000)^1/8 − 1

CAGR = (2.5)^0.125 − 1

CAGR = 1.1213 − 1 = 0.1213, or about 12.13%

That means if the account had compounded at a constant 12.13% every single year with no volatility, you'd land at the same $25,000. In reality it jumped around — maybe +28% one year, −18% the next, +22% after that — but the effective annual growth rate was 12.13%.

Why CAGR beats a simple average

The simple average of a set of annual returns is almost always wrong for multi-year performance. Here's why: suppose your portfolio does +50% in year 1 and −50% in year 2. The simple average is (50 − 50) / 2 = 0%, which sounds like you broke even. But you didn't.

Start with $10,000. Up 50% takes you to $15,000. Down 50% from there takes you to $7,500. You lost 25%, not zero. The simple average ignores compounding and the order of returns. CAGR captures both:

CAGR = (7,500 / 10,000)^1/2 − 1 = (0.75)^0.5 − 1 ≈ −0.1340, or −13.4%

That's the true annualized rate of decline. Use CAGR for anything that compounds over multiple periods — investment returns, revenue growth, population growth, user counts. Use a simple average for things that don't compound, like test scores or temperatures.

The thing most people get wrong: partial years

If your holding period is not exactly a whole number of years, n needs to be precise. From March 15, 2020, to September 30, 2024, is not 4 years — it's about 4.54 years. Use the exact number of days divided by 365.25, or count the fraction carefully. Getting n wrong by even half a year can shift CAGR by a couple percentage points on a high-growth asset.

Most financial software does this automatically. If you're doing it by hand, count the months and express as a decimal: 4 years 6 months is 4.5, 7 years 3 months is 7.25, and so on.

Solving it on a financial calculator (TVM keys)

You don't need to compute fractional exponents by hand. The time-value-of-money keys on a financial calculator are built for this. For the $10,000 to $25,000 over 8 years example:

P/Y = 1 (annual compounding)
N = 8
PV = −10,000 (money you put in, so negative)
FV = 25,000 (money you got out, so positive)
PMT = 0 (no intermediate cash flows)
Solve for I/Y → 12.13%

Try it on the financial calculator. The same solver handles any variation — if you know the CAGR and the starting value and want to project the ending value, just plug in I/Y, PV, and N, then solve for FV.

When CAGR hides risk

CAGR is a smoothing metric. It tells you the constant rate that would produce the same result, but it erases all the volatility along the way. Two investments can have identical CAGRs but wildly different risk profiles. One might have climbed steadily at 8% per year; the other might have crashed 40%, rallied 90%, crashed again, then rocketed up. Same CAGR, totally different ride.

That's why CAGR is almost always reported alongside standard deviation, max drawdown, or a Sharpe ratio. The CAGR tells you how much it grew; the risk metrics tell you how painful the path was. Both matter.

CAGR vs. IRR: when to use which

CAGR assumes one lump sum in, one lump sum out, and nothing in between. If you made a single $10,000 investment and cashed out later, CAGR is the right tool. But if you added $500 a month along the way, or pulled money out for living expenses, CAGR doesn't work — it has no way to account for those intermediate cash flows.

That's when you need IRR (internal rate of return). IRR solves for the discount rate that makes the net present value of all cash flows equal zero. It's more complex, but it handles irregular contributions and withdrawals. Most brokerage account performance reports use a variant called money-weighted return, which is conceptually the same as IRR.

Rule of thumb: one buy, one sell, no changes in between? Use CAGR. Recurring contributions, partial withdrawals, or lumpy timing? Use IRR.

Negative CAGR: it works the same way

If the ending value is less than the beginning value, CAGR will be negative. That's not a problem — it just means the investment shrank instead of grew. A $10,000 position that drops to $6,500 over 5 years has a CAGR of:

CAGR = (6,500 / 10,000)^1/5 − 1 = (0.65)^0.2 − 1 ≈ −0.0846, or −8.46%

That's the annualized rate of decline. It's the same math, just pointed the other direction. Some people call this CAGD (compound annual growth decline), but it's the same formula.

Real-world quirks and adjustments

CAGR assumes all dividends and interest are reinvested. If you took cash dividends and spent them, the ending value doesn't include that income, and the CAGR will look artificially low. For a fair comparison, either reinvest everything or compute total return CAGR, which adds back all distributions to the ending value.

CAGR also ignores taxes and fees. A 12% CAGR in a taxable account with annual rebalancing might net out closer to 9.5% after taxes and transaction costs. A 12% CAGR in a Roth IRA keeps the full 12%. Context matters.

Frequently asked questions

Can I use CAGR for something that compounds more often than annually?

Yes, but you need to adjust. If you're measuring monthly growth, use the number of months for n, and the result will be a monthly CAGR. To annualize it, use (1 + monthly CAGR)^12 − 1. Same idea for quarterly or daily — just match the compounding period to your time unit.

What is a good CAGR for an investment?

Depends entirely on the asset class and the time period. US large-cap stocks have averaged about 10–11% CAGR over the long run. High-yield bonds might do 5–7%. Crypto has delivered 50%+ CAGRs over some periods and −30% over others. Compare apples to apples — a stock portfolio to a stock index, a real-estate fund to a REIT benchmark, and so on.

Is CAGR the same as annualized return?

Usually yes, but "annualized return" is sometimes reported as a simple average of yearly returns rather than a compounded rate. If someone says "10% annualized return," ask if they mean CAGR or arithmetic mean. CAGR is the geometrically correct measure for multi-year performance; the arithmetic mean will almost always be higher and is misleading for compounding assets.

Why does Excel's RATE function give a different answer than the CAGR formula?

Excel's =RATE() function is for TVM problems with regular periodic payments (like a loan or annuity). For CAGR with no intermediate cash flows, use =(ending/beginning)^(1/years) − 1 or the simpler =RRI(years, beginning, ending) function, which is built specifically for CAGR.

Try it yourself

Pull up your brokerage statement and find a position you've held for a few years. Plug the original cost basis and the current value into the financial calculator and solve for I/Y. That's your CAGR. Then compare it to the headline index return for the same period — you might be surprised. Fees, timing, and a few bad picks can quietly drag CAGR down by a couple points per year, which compounds into a massive difference over a decade.

This article is for general education and is not investment advice. See our Terms.