What is CAGR?
CAGR, or Compound Annual Growth Rate, is the constant annual rate that would turn your starting capital into your ending value.
CAGR (%) = [(ending value ÷ starting value)1/years − 1] × 100
Without deposits or withdrawals, KRW 1 million growing to KRW 1.21 million in two years has a 10% CAGR. It matches a steady path of 1 million → 1.1 million → 1.21 million. You need not have earned 10% in each year.
Cumulative return is the total increase: 21% here. The arithmetic average return adds the annual returns and divides by the number of years.
Why does +50% followed by -50% lose money?
KRW 1 million rises to KRW 1.5 million, then falls to KRW 750,000. The returns add up to zero, yet a quarter of your original capital is gone.
| Measure | 0%, 0% | +50%, -50% |
|---|---|---|
| Assets · KRW million | 1 → 1 → 1 | 1 → 1.5 → 0.75 |
| Arithmetic average | 0.00% | 0.00% |
| Cumulative return | 0.00% | -25.00% |
| CAGR | 0.00% | -13.40% |
You earned KRW 500,000 in year one but lost KRW 750,000 in year two. The same percentage applies to a different amount of money. After a 50% loss, the remaining assets need a 100% gain to recover.
Try two annual returns
First try 50% and -50%, then change both returns to 0%. How do final assets differ when the arithmetic average stays at zero?
| Measure | Result |
|---|---|
| Arithmetic average | 0.00% |
| Cumulative return | -25.00% |
| CAGR | -13.40% |
| Final assets · KRW | 750,000.00 |
| Time | Assets · KRW |
|---|---|
| Start | 1,000,000.00 |
| Year 1 | 1,500,000.00 |
| Year 2 | 750,000.00 |
Calculation assumptions and rounding
The starting capital is KRW 1,000,000 in both languages. Each period is one full year. The entered returns apply in sequence, without external cash flows, taxes, fees or FX conversion. Dividends are not added separately; they must already be included in an entered return if you intend a total-return example.
Amounts are not rounded between years. Displayed returns round to two decimal places, and amounts to KRW 0.01, using HALF_UP rounding. Chart bars share a scale starting at zero and show only the start and year-end values, not the path within each year.
A -100% year leaves zero assets. Without new deposits, later percentage gains cannot restore capital. If year one loses everything, the realized return for year two and the arithmetic average are undefined.
How do you calculate CAGR?
KRW 10 million becomes KRW 20 million in five years. Doubling over five years gives a CAGR of 14.87%.
Substitute those values: [(20 ÷ 10)1/5 − 1] × 100 ≈ 14.87%. Compounding at about 14.87% each year would double your money in five years.
Dividing the 100% cumulative return by five gives 20%, which misses compounding. From the second year onward, earlier gains also earn returns.
How does the +50% / -50% example fit the formula?
Use starting capital of KRW 1 million, ending assets of KRW 750,000 and two years: [(0.75 ÷ 1)1/2 − 1] × 100 ≈ -13.40%. The arithmetic average instead gives (+50% − 50%) ÷ 2 = 0%.
Can the same CAGR hide different investment paths?
| Measure | Investment A | Investment B |
|---|---|---|
| Asset path | 1 → 1.1 → 1.21 | 1 → 0.6 → 1.21 |
| Year 1 return | 10.00% | -40.00% |
| Year 2 return | 10.00% | About 101.67% |
| CAGR | 10.00% | 10.00% |
| Observed MDD | 0.00% | -40.00% |
Both end at KRW 1.21 million, but B falls to KRW 600,000 after the first year. If you needed the money and sold then, you would miss the later recovery. The same CAGR can hide very different holding experiences.
MDD here uses only the start and two year-end observations. A larger decline within a year would change the actual daily MDD.
In the investment backtest, look at declines along with final returns. Use the MDD calculator to measure the fall from a prior peak.
MDD and the gain needed to recover
When does CAGR differ from an average annual return?
Compare +20% followed by 0% with a steady +10% in both years. Both average 10%, but KRW 1 million becomes KRW 1.2 million and KRW 1.21 million, respectively.
In the first investment, the KRW 200,000 earned in year one grows no further in year two. In the second, the first year's gains also earn 10%. The two CAGRs are about 9.54% and 10%.
The arithmetic average adds returns and divides by the number of periods. The geometric average reflects their compounded result. With annual periods and no cash flows, that geometric return equals CAGR. If a source says only “average annual return,” check which method it uses.
How does volatility affect compound growth?
Each year's growth factor is 1 + return. For two years, multiply the factors, take the square root and subtract 1. Do not multiply the percentage returns themselves.
For positive growth factors, the geometric average cannot exceed the arithmetic average. Equality requires identical annual returns. Uneven returns can lower compound growth at a given arithmetic average, often called volatility drag. This does not mean every volatile asset has lower returns: average returns and periods also matter.
Use the compound interest calculator to apply a fixed annual return assumption.
What should you check before using CAGR?
Were dividends reinvested?
Price-only CAGR differs from total-return CAGR with reinvestment. Even for the same asset, dividend treatment changes the result. Check dividend yield versus total return and compare matching assumptions.
Are you treating one month's gain as a year's return?
A 10% gain in one month annualizes to about 213.84%. That repeats the same gain for 12 months; it is not an observed one-year return. Starting near a low or ending near a high can also make performance look better.
Have you counted deposits as investment gains?
Invest KRW 1 million and add KRW 500,000 with no investment gain: the balance becomes KRW 1.5 million. That extra money is not a return. For recurring contributions, use a measure such as XIRR that accounts for deposit amounts and dates.
Calculation limits for cash flows, zero assets and negative values
Money-weighted measures such as XIRR account for cash-flow amounts and dates. Time-weighted returns instead separate external cash flows when comparing management performance. Some cash-flow patterns have no IRR solution or multiple solutions.
Conventional investment CAGR needs positive starting capital and a period greater than zero. A zero starting value makes division undefined. Negative starting or ending values, such as leveraged debt accounts, may not have a meaningful conventional CAGR and are unsupported by this calculator.
This site treats zero ending assets as total loss and displays -100% CAGR. If assets reach zero and later become positive, check for new deposits or other changes. This simulator assumes no external cash flows.
Past CAGR does not guarantee future returns. Taxes, fees, currency changes and inflation can also change the result you retain.
Calculate CAGR for your investment
Enter starting capital, ending value and duration to find compound annual growth.
Open the CAGR calculatorFrequently asked questions
Can two investments that both double have different CAGRs?
Yes. Reaching the same doubled value in less time gives a higher CAGR. Equal cumulative returns do not imply equal annual growth rates.
Can I add cash dividends to the ending value?
If you kept them in the account with no external cash flows, combine the remaining investments and cash to calculate account CAGR. This differs from reinvesting the dividends. If you withdrew them, use a return measure that accounts for those cash flows.
Is early 2021 to early 2026 five years or six?
Five years. Use elapsed time, not the number of year labels. If the starting and ending months differ, account for that difference too.
Sources and calculation basis
Sources checked October 22, 2026. All numerical paths are hypothetical, not product performance.
- CFA Institute · Exponential Wealth (2026), pp.45–46 — CAGR, arithmetic and geometric averages.
- FINRA · Evaluating Performance — annualized compound returns.
- CFA Institute · GIPS Standards Handbook — short-period annualization, money-weighted and time-weighted returns.
- SEC Investor.gov · Fund Distributions — distributions and reinvestment.
- SEC Investor.gov · Past Performance.