Investment
How To Calculate CAGR
CAGR compresses a messy multi-year history into one smooth annual rate. Because it reports the same kind of number for a seven-year stock hold and a five-year revenue line, it is the standard way to put two very different histories on one scale.
Quick Answer
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
- EV
- Ending value at the close of the period
- BV
- Beginning value at the start of the period
- n
- Number of years between them
- CAGR
- Smoothed annual growth rate; negative if EV < BV
Divide the ending value by the beginning value, raise the result to the power of one divided by the number of years, then subtract 1 and express it as a percentage. The answer is the constant annual growth rate that connects the two endpoints.
What Is CAGR?
Compound annual growth rate answers a deceptively narrow question: if this value had grown by exactly the same percentage every single year, what percentage would have taken it from the starting figure to the ending figure? Nothing about the real path is assumed to be smooth — CAGR deliberately discards it and reports only the constant rate that would have produced the same endpoints.
That smoothing is simultaneously its value and its weakness. A fund that returned 40%, then −20%, then 15% and a fund that returned 9% every year can finish at nearly the same place, so their CAGRs may look similar even though the risk profiles are nothing alike. Whenever volatility matters to the decision — which for most investments it does — CAGR must be read next to standard deviation, drawdown, and the year-by-year sequence.
The calculation is the geometric mean wearing practical clothing. Averaging the yearly returns arithmetically always overstates growth when returns vary, sometimes dramatically: +50% followed by −50% has an arithmetic average of 0%, but actually loses 25% of the money. CAGR cannot make this mistake, because it operates on the ratio of endpoints rather than on the average of the intermediate rates.
CAGR also handles declines correctly without any special handling. When the ending value is below the beginning value the ratio falls below 1, the exponent keeps it below 1, and the result is a negative rate. A portfolio that fell from $50,000 to $42,000 over three years reports a CAGR of about −5.65%, which is the honest per-year answer rather than an error state.
One variable deserves more care than the others: n. It is the elapsed time in years, not the count of calendar years touched. A position opened in December 2019 and closed in December 2024 covers exactly five years, even though six calendar years appear on the statements. Dividing by the wrong n inflates or deflates the rate in the exponent, where errors are hard to spot by eye.
Finally, CAGR is retrospective by construction. It describes what already happened between two known points and cannot forecast anything on its own. Projecting it forward assumes the past path repeats, which is precisely the assumption its smoothing was designed to hide.
Formula
CAGR = (EV / BV)^(1/n) - 1
Take the total growth factor, raise it to 1/n to spread it evenly across every year, and subtract 1 to convert the factor back into a rate.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| BV | Beginning value | currency | Value at the very start of the measurement window. |
| EV | Ending value | currency | Value at the end of the window. Include reinvested income so both endpoints are measured the same way. |
| n | Elapsed time in years | years | Fractions are allowed: 18 months is 1.5. Count elapsed time, not the number of calendar years touched. |
EV = BV x (1 + CAGR)^n
The same relationship solved for the endpoint. Useful for checking your work and for projecting what a given constant rate produces over n years.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| CAGR | Annual growth rate | decimal | Expressed as a decimal when used inside this formula. |
How To Calculate CAGR
- 1
Establish the two endpoint values
Beginning value is what the position was worth at the start; ending value is what it is worth at the end. Measure both the same way — if the ending value includes reinvested dividends, the beginning value should reflect a likewise reinvested basis.
- 2
Divide ending by beginning to get total growth
$25,000 / $10,000 = 2.5, meaning the money grew by a factor of two and a half. This single ratio carries all the growth information; everything after this step only re-expresses it.
- 3
Count elapsed years precisely
Use fractions rather than whole calendar years whenever the window does not land on an anniversary. eighteen months is 1.5, forty-two months is 3.5. Getting n wrong is the most common hidden error because its effect is diluted inside the exponent.
- 4
Raise the growth factor to the power 1/n
2.5^(1/7) = 1.1399. This spreads the total growth evenly over every year, which is exactly what makes the result comparable across windows of different length.
- 5
Subtract 1 and convert to a percentage
1.1399 - 1 = 0.1399, so CAGR = 13.99%. Sanity-check by compounding it back: $10,000 x 1.1399^7 should reproduce $25,000.
Examples
Example 1: Portfolio growth — $10,000 to $25,000 over 7 years
- BV
- $10,000
- EV
- $25,000
- n
- 7 years
| Step | Calculation | Result |
|---|---|---|
| Growth factor | $25,000 ÷ $10,000 | 2.5 |
| Exponent | 1 ÷ 7 | 0.142857 |
| Annual factor | 2.5^0.142857 | 1.139852 |
| Subtract one | 1.139852 - 1 | 0.139852 |
| As a percentage | 0.139852 x 100% | 13.99% |
Result: CAGR = 13.99% per year
Example 2: Portfolio decline — $50,000 to $42,000 over 3 years
- BV
- $50,000
- EV
- $42,000
- n
- 3 years
| Step | Calculation | Result |
|---|---|---|
| Growth factor | $42,000 ÷ $50,000 | 0.84 |
| Exponent | 1 ÷ 3 | 0.333333 |
| Annual factor | 0.84^0.333333 | 0.943538 |
| Subtract one | 0.943538 - 1 | -0.056462 |
| As a percentage | -0.056462 x 100% | -5.65% |
Result: CAGR = -5.65% per year
Calculator
Compound annual growth rate
13.99%
- Total growth
- 150.00%
- Growth multiple
- 2.5
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the CAGR calculator page.
Common Mistakes
Using the arithmetic average of yearly returns instead
Averaging annual percentages always overstates growth when returns vary. Gains of +50% and -50% average to 0% but actually lose 25% of the capital. Only the geometric treatment, which CAGR performs, gives the true per-year result.
Counting calendar years rather than elapsed years
A window from December 2019 to December 2024 touches six calendar years but spans exactly five. Using the wrong n puts the error inside the exponent, where it is invisible and can shift the answer by more than a percentage point.
Ignoring cash flows during the period
CAGR assumes nothing was added or withdrawn. Contributions make it overstate performance, withdrawals make it understate. With meaningful cash flows, use a time-weighted return or internal rate of return instead.
Treating the smoothed rate as the actual path
Two portfolios can share a 10% CAGR while one rose steadily and the other swung violently between extremes. CAGR says nothing about volatility, sequence of returns, or the worst single year.
Projecting the historical CAGR forward
CAGR describes the past with certainty and the future not at all. Extrapolating it assumes conditions repeat, which is exactly the variability the metric was built to smooth away. Use scenarios rather than a single projected rate.
FAQ
What is the difference between CAGR and average annual return?
Average annual return takes the arithmetic mean of each years return, which overstates growth whenever returns vary. CAGR is geometric, so it reflects actual compounding. The gap between them widens with volatility, and can be several percentage points on a volatile portfolio.
Can CAGR be used when a value decreased?
Yes. When the ending value is lower than the beginning value the ratio is below one and CAGR comes out negative. A negative result is a legitimate measurement of the average yearly decline, not an error.
Is CAGR the same as the internal rate of return?
No. CAGR uses only the two endpoint values and ignores everything between them. IRR accounts for the timing and size of every cash flow in between. They coincide only when there are no interim contributions or withdrawals.
What period length should I use?
Use the elapsed time in years, including fractions. Three and a half years is 3.5. Longer windows give a more stable picture, while very short ones let a single unusual month dominate the result, so three to ten years suits most comparisons.
Why does CAGR look lower than the return I remember?
Usually because the remembered figure is the total cumulative gain rather than the annualized one. A 150% total gain over seven years annualizes to about 13.99%, not to 21% — dividing the total by the number of years always produces too large a number.
References
- [1]Corporate Finance Institute, Compound Annual Growth Rate (CAGR) — https://corporatefinanceinstitute.com/resources/accounting/cagr/
- [2]U.S. Securities and Exchange Commission, Investor.gov, Investment Performance Charts and Standardized Performance — https://www.investor.gov/introduction-investing/general-resources/news-alerts
- [3]CFA Institute, Global Investment Performance Standards (GIPS) — https://www.cfainstitute.org/en/ethics-standards/gips