Compound Annual Growth Rate (CAGR) Calculator

Calculate CAGR for Investment Growth Over Time

Compound Annual Growth Rate (CAGR) Formula

Formula

\[ \text{CAGR} = \left(\frac{V_f}{V_i}\right)^{\frac{1}{n}} - 1 \]

Where:

$V_f$ — final value of the investment at the end of the period
$V_i$ — initial value of the investment at the start of the period
$n$ — number of years in the period

The formula gives the constant annual growth rate that would take the investment from $V_i$ to $V_f$ over $n$ years, assuming all gains are reinvested and compound each year. Multiply the result by 100 to express it as a percentage.

Compound Annual Growth Rate – Calculation Example

Example: an investment grows from $1,000 to $2,000 over 5 years.

\[ \text{CAGR} = \left(\frac{2000}{1000}\right)^{\frac{1}{5}} - 1 = 2^{0.2} - 1 \approx 0.1487 \]

Result: the Compound Annual Growth Rate is approximately 14.87% per year. In other words, $1,000 compounding at 14.87% annually would double to $2,000 in 5 years.

How to use the calculator

Enter the Initial Value — the amount the investment was worth at the start of the period (default: $1,000).
Enter the Final Value — the amount it was worth at the end of the period (default: $2,000).
Enter the Number of Years the investment lasted (default: 5). The value must be at least 1.
Read the Compound Annual Growth Rate in percent, rounded to three decimal places.

What is CAGR and why it matters

The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a period longer than one year, assuming profits are reinvested at the end of each year. It answers the question: "At what steady yearly rate would this investment have grown from its starting value to its ending value?"

CAGR is more informative than a simple average of yearly returns. Investment values rarely grow at a constant pace — a portfolio might gain 30% one year and lose 10% the next. Averaging those annual numbers can seriously overstate or understate real performance. CAGR smooths out this volatility and gives a single, comparable figure that reflects the actual compounding path between the first and last value.

This makes CAGR a standard tool for comparing investments of different lengths and sizes: two stocks over different periods, revenue growth of two companies, or the performance of a fund against a benchmark index. It is also useful for projecting future values, since you can apply the CAGR as an assumed growth rate in compound growth models. Note that intermediate fluctuations are invisible to CAGR — it only uses the starting and ending values, so two investments with the same CAGR can have very different risk profiles along the way.

Assumptions, limitations and practical tips

Only endpoints matter: CAGR ignores everything between the first and last year. A smooth grower and a roller-coaster investment can share the same CAGR, so consider volatility and drawdowns separately when comparing options.
Full years: the formula assumes the period is measured in whole years. For fractional periods (e.g. 4.5 years), the result is an approximation of the annualized rate.
No cash flows: CAGR assumes a single lump sum at the start with no deposits or withdrawals during the period. If you added or removed money, use a money-weighted measure such as the internal rate of return instead.
Reinvestment assumption: gains are assumed to be reinvested and compounded annually. If returns were withdrawn, the actual growth of your wealth would differ.
Extrapolate with caution: a high historical CAGR is not a guarantee of future growth. Long-run averages tend to be more reliable than rates computed from short, volatile windows.
Past performance: CAGR is descriptive, not predictive — always pair it with risk measures before making decisions.

To sanity-check how long a growth rate needs to double your money, try our Rule of 72 calculator or the Rule of 70 calculator. If you want to compare CAGR with an effective annual rate that accounts for more frequent compounding, see the Annual Percentage Yield calculator, or work out the compounding effect of regular savings with the Reinvestment Plan Deposits calculator.

Frequently Asked Questions

How do I calculate CAGR by hand with a regular calculator?

Divide the final value by the initial value, take the n-th root (using the power key with exponent 1/n), then subtract 1. For example, $10,000 growing to $16,000 in 4 years: $16000/10000 = 1.6$, then $1.6^{0.25} \approx 1.1247$, so $1.1247 - 1 = 0.1247$ or about 12.47% per year. The currency or unit does not matter — only the ratio between the two values does.

What is a good or normal CAGR?

There is no universal benchmark. For context, the long-run CAGR of the broad US stock market has been roughly 7% per year after inflation and about 10% before inflation. Savings accounts and bonds have historically been lower. A CAGR far above these levels usually signals high risk, a short measurement window, or a bull-market lucky streak. Always compare like with like and consider volatility, not just the headline rate. Past performance does not guarantee future results.

What does a negative CAGR mean?

A negative CAGR simply means the investment lost value over the period: the final value is smaller than the initial value. For example, dropping from $10,000 to $8,100 over 3 years gives $(8100/10000)^{1/3} - 1 \approx -10\%$ per year. Note that a negative CAGR is not symmetric with a positive one: a 50% loss one year needs a 100% gain the next year just to break even.

How do I convert months into years for the CAGR formula?

Divide the number of months by 12 and use that as n. For example, 30 months is 2.5 years. The formula then estimates an annualized rate even though the period is not a whole number of years. Alternatively, some analysts first compute the total growth over the months and then annualize it — both approaches give the same mathematical answer when the fraction is used consistently.

Why is CAGR different from the average of yearly returns?

Yearly returns compound geometrically, not additively. If an investment gains 40% one year and loses 20% the next, the simple average is +10%, but the actual result is $1.4 \times 0.8 = 1.12$, or only 6% total — a CAGR of about 2.97% per year. Arithmetic averages overstate performance whenever returns fluctuate, which is why CAGR is the standard measure for multi-year growth.

Can I use CAGR if I made deposits or withdrawals during the period?

No. CAGR only works for a single lump sum left untouched from start to finish. Any cash inflows or outflows change the growth path, and the formula cannot tell how much growth came from the market versus from your added money. In that case, use the internal rate of return (IRR) or a time-weighted return, which accounts for the timing and size of each cash flow.

What are common mistakes when calculating CAGR?

The most frequent errors are: using the wrong n (counting the first year as year zero, or mixing months with years), subtracting 1 before taking the root, averaging yearly percentages instead of using the endpoint formula, and using CAGR for periods shorter than a year, where annualizing exaggerates the rate. Also remember the calculator requires positive values — a zero or negative initial value makes the growth rate mathematically undefined.

Compound Annual Growth Rate Estimator