The CAGR Formula (with a Worked Example)
CAGR = (end value / start value)^(1 / years) - 1
End value = start value x (1 + CAGR)^years
Years = ln(end value / start value) / ln(1 + CAGR)
Worked example: $10,000 grows to $18,000 in 3 years. CAGR = (18,000 / 10,000)^(1 / 3) - 1 = 1.8^(1/3) - 1 = 0.2164, or 21.64% per year. That single rate, compounded three times, reproduces the ending balance.
CAGR for Common Growth Multiples
| Growth | Years | CAGR |
|---|---|---|
| 2x (double) | 5 years | 14.87% |
| 3x (triple) | 5 years | 24.57% |
| 2x (double) | 10 years | 7.18% |
CAGR vs Average Return: Why They Differ
CAGR is a geometric average, and it is almost always lower than the simple arithmetic average of the yearly returns. The reason is volatility drag: a year of plus 50% followed by a year of minus 50% averages to zero on paper, but the account is actually down 25%, because the loss works on a bigger base. The bumpier the path, the wider the gap between the smooth CAGR line and the straight simple-average line in the chart above.
This is why CAGR is the fairer number for comparing investments or trading records. An average return can be flattered by one huge year, while CAGR reflects the compounding reality of the whole period. When someone quotes an average annual return, ask whether it is the arithmetic average or the compound rate, because the difference can be large.
Using CAGR on a Trading Account
CAGR is a clean way to state a trading record, but it hides everything about the ride. Two accounts can share the same CAGR while one drifted up smoothly and the other doubled, halved, and clawed back. So a growth rate on its own is only half the story: always pair it with the maximum drawdown to see what the smooth number cost in stress and risk.
Be careful annualizing short windows, too. Turning a strong three month run into a CAGR implies it will repeat all year, which it rarely does. Use full years where you can, treat sub-year figures as rough, and read the caution the calculator shows when the span is under a year.
